Manuscript 2 from Fernanda Hansen P. de Moraes Thesis - Cortical folding alterations in humans due to aging and diseases

Description of the procedures and analysis present in Manuscript 2, Establishing a baseline for human cortical folding morphological variables: a multicenter study, at the Doctorate Thesis presented to the Programa de Pós-Graduação em Ciências Médicas at the Instituto D’Or de Pesquisa e Ensino as a partial requirement to obtain the Doctorate Degree.

Part of the data used here cannot be shared due to restrictions of the Ethic Committee. Data can be shared upon reasonable request to the corresponding author. To fulfill these limitation, we will generate random data to simulate the results.

Get in touch with us (fernandahmoraes@gmail.com) in case any help is needed, our aim is to improve the code as needed!

1 RMARKDOWN AND R SETUP

setwd("D:/GitHub/Typical-values")

## define functions

# test angular coeficinet versus theoretical value
test_coef <- function(reg, coefnum, val){
  co <- coef(summary(reg))
  tstat <- (co[coefnum,1] - val)/co[coefnum,2]
  2 * pt(abs(tstat), reg$df.residual, lower.tail = FALSE)
}

# wrap text
wrapper <- function(x, ...) paste(strwrap(x, ...), collapse = "\n")

library(readr)
library(tidyverse)
library(lubridate)
library(ggpubr)
library(kableExtra)
library(broom)
library(lme4)
library(lsmeans)
library(MuMIn)
library(arm)
library(effects)

# COLOR BLIND PALETTE WITH BLACK
cbbPalette <- c("#000000", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbbPalette2 <- c("#56B4E9", "#E69F00", "#CC79A7", "#56B4E9", "#D55E00", "#0072B2", "#009E73", "#F0E442")

2 set seed for random process

set.seed(1)

# dados_datasetscomp <- read_csv("dados_datasetscomp2.csv")
dados_datasetscomp <- read_csv("data_typical_values.csv")

dados_datasetscomp <- dados_datasetscomp %>%
  filter(Sample != "HCP500r", Diagnostic != "MCI")

3 DATA PREPARATION

# estimate cortical folding variables
dados_datasetscomp <- dados_datasetscomp %>%
  mutate(
    # create new variables
    GMvolume = ifelse(!is.na(GMvolume),GMvolume,AvgThickness*TotalArea),
    logAvgThickness = log10(AvgThickness),
    logTotalArea = log10(TotalArea),
    logExposedArea = log10(ExposedArea),
    localGI = TotalArea / ExposedArea,
    k = sqrt(AvgThickness) * TotalArea / (ExposedArea ^ 1.25),
    K = 1 / 4 * log10(AvgThickness ^ 2)  + log10(TotalArea) - 5 / 4 * log10(ExposedArea),
    S = 3 / 2 * log10(TotalArea) + 3 / 4 * log10(ExposedArea) - 9 /  4 * log10(AvgThickness ^
                                                                                 2) ,
    I = log10(TotalArea) + log10(ExposedArea) + log10(AvgThickness ^ 2),
    # c = as.double(ifelse(
    #   ROI == "hemisphere", NA, 4 * pi / GaussianCurvature
    # )),
    TotalArea_corrected = ifelse(ROI == "hemisphere", TotalArea, TotalArea * c),
    ExposedArea_corrected = ifelse(ROI == "hemisphere", ExposedArea, ExposedArea * c),
    logTotalArea_corrected = log10(TotalArea_corrected),
    logExposedArea_corrected = log10(ExposedArea_corrected),
    localGI_corrected = ifelse(
      ROI == "hemisphere",
      TotalArea / ExposedArea,
      TotalArea_corrected / ExposedArea_corrected
    ),
    k_corrected = ifelse(
      ROI == "hemisphere",
      sqrt(AvgThickness) * log10(TotalArea) / (log10(ExposedArea) ^ 1.25),
      sqrt(AvgThickness) * log10(TotalArea_corrected) / (log10(ExposedArea_corrected ^
                                                                 1.25))
    ),
    K_corrected =  ifelse(
      ROI == "hemisphere",
      1 / 4 * log10(AvgThickness ^ 2) + log10(TotalArea) - 5 / 4 * log10(ExposedArea),
      1 / 4 * log10(AvgThickness ^ 2) + log10(TotalArea_corrected) - 5 / 4 * log10(ExposedArea_corrected)
    ),
    I_corrected = ifelse(
      ROI == "hemisphere",
      log10(TotalArea) + log10(ExposedArea) + log10(AvgThickness ^ 2) ,
      log10(TotalArea_corrected) + log10(ExposedArea_corrected) + log10(AvgThickness ^ 2)
    ),
    S_corrected = ifelse(
      ROI == "hemisphere",
      3 / 2 * log10(TotalArea) + 3 / 4 * log10(ExposedArea) - 9 /  4 * log10(AvgThickness ^ 2) ,
      3 / 2 * log10(TotalArea_corrected) + 3 / 4 * log10(ExposedArea_corrected) - 9 /  4 * log10(AvgThickness ^ 2)
    ),
    Knorm = K_corrected / sqrt(1 + (1 / 4) ^ 2 + (5 / 4) ^ 2),
    Snorm = S_corrected / sqrt((3 / 2) ^ 2 + (3 / 4) ^ 2 + (9 / 4) ^ 2),
    Inorm = I_corrected / sqrt(1 ^ 2 + 1 ^ 2 + 1 ^ 1)
  )

# create age intervals
dados_datasetscomp$Age_interval <- cut(dados_datasetscomp$Age,
                                       breaks = c(0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100),
                                       right = FALSE,
                                       include.lowest = TRUE)

dados_datasetscomp$Age_interval10 <- cut(dados_datasetscomp$Age,
                                         breaks = c(0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100),
                                         right = FALSE,
                                         include.lowest = TRUE)

dados_all <- dados_datasetscomp %>% filter(!is.na(logAvgThickness), ExposedArea != 0 | !is.na(localGI), !is.infinite(logExposedArea)) %>% 
  droplevels()

dados_datasetscomp <- dados_all

dados_datasetscomp$Diagnostic <- as.factor(dados_datasetscomp$Diagnostic)
dados_datasetscomp$Diagnostic <- relevel(dados_datasetscomp$Diagnostic, ref = "CTL")

4 Deaging

# define age for deaging
Age.cor = 25

# DEAGING + HARMONIZATION FULL DATA ----

dados_datasetscomp_rate <-
  filter(dados_datasetscomp, Diagnostic == "CTL")

dados_datasetscomp_rate$Sample <-
  as.factor(dados_datasetscomp_rate$Sample)

dados_datasetscomp_rate$ROI <-
  factor(dados_datasetscomp_rate$ROI,
         levels = c("hemisphere", "F", "O", "P", "T"))

4.1 GM volume

m.1 <-
  lme4::lmer(GMvolume ~ Age * ROI + (1|Sample:ROI), data = dados_datasetscomp_rate)

re <- as_tibble(ranef(m.1)) %>%
  filter(grpvar == "Sample:ROI") %>%
  mutate(
    GM_shift = condval,
    sd_GM_shift = condsd,
    Sample = str_split(grp, pattern = ":", simplify = TRUE)[, 1],
    ROI = str_split(grp, pattern = ":", simplify = TRUE)[, 2]
  ) %>%
  dplyr::select(-c(condval, grpvar, term, condsd, grp))

Age.trend <- as_tibble(lstrends(m.1, ~ ROI, var = "Age")) %>%
  mutate(Age.trend_GM = Age.trend) %>%
  dplyr::select(c(ROI, Age.trend_GM))

dados_datasetscomp <- full_join(dados_datasetscomp, Age.trend) %>%
  full_join(re) %>%
  mutate(
    GMvolume_shiftc = GMvolume - GM_shift,
    GMvolume_age_decay = GMvolume - Age.trend_GM * (Age - Age.cor),
    GMvolume_age_decay_shiftc = GMvolume - GM_shift - Age.trend_GM *
      (Age - Age.cor)
  )

4.2 AvgThickness

m.1 <-
  lme4::lmer(AvgThickness ~ Age * ROI + (1|Sample:ROI), data = dados_datasetscomp_rate)

re <- as_tibble(ranef(m.1)) %>%
  filter(grpvar == "Sample:ROI") %>%
  mutate(
    T_shift = condval,
    sd_T_shift = condsd,
    Sample = str_split(grp, pattern = ":", simplify = TRUE)[, 1],
    ROI = str_split(grp, pattern = ":", simplify = TRUE)[, 2]
  ) %>%
  dplyr::select(-c(condval, grpvar, term, condsd, grp))

Age.trend <- as_tibble(lstrends(m.1, ~ ROI, var = "Age")) %>%
  mutate(Age.trend_T = Age.trend) %>%
  dplyr::select(c(ROI, Age.trend_T))

dados_datasetscomp <- full_join(dados_datasetscomp, Age.trend) %>%
  full_join(re) %>%
  mutate(
    AvgThickness_shiftc = AvgThickness - T_shift,
    AvgThickness_age_decay = AvgThickness - Age.trend_T * (Age - Age.cor),
    AvgThickness_age_decay_shiftc = AvgThickness - T_shift - Age.trend_T *
      (Age - Age.cor),
    logAvgThickness_shiftc = log10(AvgThickness_shiftc),
    logAvgThickness_age_decay = log10(AvgThickness_age_decay),
    logAvgThickness_age_decay_shiftc = log10(AvgThickness_age_decay_shiftc)
  )

4.3 TotalArea

m.1 <-
  lme4::lmer(TotalArea_corrected ~ Age * ROI + (1 | Sample:ROI), data = dados_datasetscomp_rate)

re <- as_tibble(ranef(m.1)) %>%
  filter(grpvar == "Sample:ROI") %>%
  mutate(
    AT_shift = condval,
    sd_AT_shift = condsd,
    Sample = str_split(grp, pattern = ":", simplify = TRUE)[, 1],
    ROI = str_split(grp, pattern = ":", simplify = TRUE)[, 2]
  ) %>%
  dplyr::select(-c(condval, grpvar, term, condsd, grp))

Age.trend <-
  as_tibble(lstrends(m.1, ~ ROI, var = "Age")) %>%
  mutate(Age.trend_AT = Age.trend) %>%
  dplyr::select(c(ROI, Age.trend_AT))

dados_datasetscomp <- full_join(dados_datasetscomp, re) %>%
  full_join(Age.trend) %>%
  mutate(
    TotalArea_shiftc = TotalArea_corrected - AT_shift,
    TotalArea_age_decay = TotalArea_corrected - Age.trend_AT * (Age - Age.cor),
    TotalArea_age_decay_shiftc = TotalArea_corrected - AT_shift - Age.trend_AT *
      (Age - Age.cor),
    logTotalArea_shiftc = log10(TotalArea_shiftc),
    logTotalArea_age_decay = log10(TotalArea_age_decay),
    logTotalArea_age_decay_shiftc = log10(TotalArea_age_decay_shiftc)
  )

4.4 ExposedArea

m.1 <-
  lme4::lmer(
    ExposedArea_corrected  ~ Age * ROI + (1 | Sample:ROI), data = dados_datasetscomp_rate)

re <- as_tibble(ranef(m.1)) %>%
  filter(grpvar == "Sample:ROI") %>%
  mutate(
    AE_shift = condval,
    sd_AE_shift = condsd,
    Sample = str_split(grp, pattern = ":", simplify = TRUE)[, 1],
    ROI = str_split(grp, pattern = ":", simplify = TRUE)[, 2]
  ) %>%
  dplyr::select(-c(condval, grpvar, term, condsd, grp))

Age.trend <-
  as_tibble(lstrends(m.1, ~ ROI, var = "Age")) %>%
  mutate(Age.trend_AE = Age.trend) %>%
  dplyr::select(c(ROI, Age.trend_AE))

dados_datasetscomp <- full_join(dados_datasetscomp, re) %>%
  full_join(Age.trend) %>%
  mutate(
    ExposedArea_shiftc = ExposedArea_corrected - AE_shift,
    ExposedArea_age_decay = ExposedArea_corrected - Age.trend_AE * (Age - Age.cor),
    ExposedArea_age_decay_shiftc = ExposedArea_corrected - AE_shift - Age.trend_AE * (Age - Age.cor),
    logExposedArea_shiftc = log10(ExposedArea_shiftc),
    logExposedArea_age_decay = log10(ExposedArea_age_decay),
    logExposedArea_age_decay_shiftc = log10(ExposedArea_age_decay_shiftc)
  )

4.5 Lobes correction factor

m.1 <-
  lme4::lmer(c ~ Age * ROI + (1|Sample:ROI), data = dados_datasetscomp_rate)

re <- as_tibble(ranef(m.1)) %>%
  filter(grpvar == "Sample:ROI") %>%
  mutate(
    c_shift = condval,
    sd_c_shift = condsd,
    Sample = str_split(grp, pattern = ":", simplify = TRUE)[, 1],
    ROI = str_split(grp, pattern = ":", simplify = TRUE)[, 2]
  ) %>%
  dplyr::select(-c(condval, grpvar, term, condsd, grp))

Age.trend <- as_tibble(lstrends(m.1, ~ ROI, var = "Age")) %>%
  mutate(Age.trend_c = Age.trend) %>%
  dplyr::select(c(ROI, Age.trend_c))

dados_datasetscomp <- full_join(dados_datasetscomp, Age.trend) %>%
  full_join(re) %>%
  mutate(
    c_shiftc = c - c_shift,
    c_age_decay = c - Age.trend_c * (Age - Age.cor),
    c_age_decay_shiftc = c - c_shift - Age.trend_c *
      (Age - Age.cor)
  )

# ----
dados_datasetscomp <- dados_datasetscomp %>%
  mutate(
    localGI_age_decay = TotalArea_age_decay/ExposedArea_age_decay,
    localGI_shiftc = TotalArea_shiftc/ExposedArea_shiftc,
    localGI_age_decay_shiftc = TotalArea_age_decay_shiftc/ExposedArea_age_decay_shiftc,
    K_age_decay = log10(TotalArea_age_decay) + 1/4*log10(AvgThickness_age_decay^2) - 5/4*log10(ExposedArea_age_decay),
    K_shiftc = log10(TotalArea_shiftc) + 1/4*log10(AvgThickness_shiftc^2) - 5/4*log10(ExposedArea_shiftc),
    K_age_decay_shiftc = log10(TotalArea_age_decay_shiftc) + 1/4*log10(AvgThickness_age_decay_shiftc^2) - 5/4*log10(ExposedArea_age_decay_shiftc),
    I_age_decay = log10(TotalArea_age_decay) + log10(ExposedArea_age_decay) + log10(AvgThickness_age_decay^2),
    I_shiftc = log10(TotalArea_shiftc) + log10(ExposedArea_shiftc) + log10(AvgThickness_shiftc^2),
    I_age_decay_shiftc = log10(TotalArea_age_decay_shiftc) + log10(ExposedArea_age_decay_shiftc) + log10(AvgThickness_age_decay_shiftc^2),
    S_age_decay = 3/2*log10(TotalArea_age_decay) + 3/4*log10(ExposedArea_age_decay) - 9/4*log10(AvgThickness_age_decay^2),
    S_shiftc = 3/2*log10(TotalArea_shiftc) + 3/4*log10(ExposedArea_shiftc) - 9/4*log10(AvgThickness_shiftc^2),
    S_age_decay_shiftc = 3/2*log10(TotalArea_age_decay_shiftc) + 3/4*log10(ExposedArea_age_decay_shiftc) - 9/4*log10(AvgThickness_age_decay_shiftc^2),
    Knorm_shiftc = K_shiftc / sqrt(1 + (1 / 4) ^ 2 + (5 / 2) ^ 2),
    Snorm_shiftc = S_shiftc / sqrt((3 / 2) ^ 2 + (3 / 4) ^ 2 + (9 / 4) ^ 2),
    Inorm_shiftc = I_shiftc / sqrt(1 ^ 2 + 1 ^ 2 + 1 ^ 2),
    Knorm_age_decay = K_age_decay / sqrt(1 + (1 / 4) ^ 2 + (5 / 2) ^ 2),
    Snorm_age_decay = S_age_decay / sqrt((3 / 2) ^ 2 + (3 / 4) ^ 2 + (9 / 4) ^ 2),
    Inorm_age_decay = I_age_decay / sqrt(1 ^ 2 + 1 ^ 2 + 1 ^ 2),
    Knorm_age_decay_shiftc = K_age_decay_shiftc / sqrt(1 + (1 / 4) ^ 2 + (5 / 2) ^ 2),
    Snorm_age_decay_shiftc = S_age_decay_shiftc / sqrt((3 / 2) ^ 2 +  (3 / 4) ^ 2 + (9 / 4) ^ 2),
    Inorm_age_decay_shiftc = I_age_decay_shiftc / sqrt(1 ^ 2 + 1 ^ 2 + 1 ^ 2)
  )

5 RESULTS

5.1 Data description

Table 1

Sample	Diagnostic	N	age	age_range
ADNI	CTL	868	75 ± 6.5	56 ; 96
ADNI	AD	542	75 ± 8	56 ; 92
AHEAD	CTL	100	42 ± 19	24 ; 76
AOMICPIOP1	CTL	208	22 ± 1.8	18 ; 26
AOMICPIOP2	CTL	224	22 ± 1.8	18 ; 26
HCPr900	CTL	881	29 ± 3.6	24 ; 37
IDOR	CTL	77	66 ± 8.4	43 ; 80
IDOR	AD	13	77 ± 6.1	63 ; 86
IXI-Guys	CTL	314	51 ± 16	20 ; 86
IXI-HH	CTL	181	47 ± 17	20 ; 82
IXI-IOP	CTL	68	42 ± 17	20 ; 86
NKI	CTL	168	34 ± 19	4 ; 85
OASIS	CTL	312	45 ± 24	18 ; 94

Diagnostic	N	age	age_range
CTL	3095	46 ± 23	4 ; 96
AD	555	75 ± 8	56 ; 92

5.2 Correlation between K, S, and I with Age for the Healthy Control group

5.2.1 K

figS6a <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"),
       aes(x = Age , y = K)) +
  geom_point(aes(color = Sample, fill = Sample, alpha = 0.4)) +
  geom_smooth(color = "black", method = "lm") +
  # stat_cor() +
  theme_pubr() +
  guides(alpha = "none")+ 
  labs(x = "Age [years]") +
  scale_x_continuous(limits = c(0,100))

cor.test(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$K, filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$K and filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age
## t = -100.83, df = 6800, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7834543 -0.7643992
## sample estimates:
##        cor 
## -0.7741021

5.2.2 S

figS6b <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"),
       aes(x = Age, y = S)) +
  geom_point(aes(color = Sample, fill = Sample, alpha = 0.4)) +
  geom_smooth(color = "black", method = "lm") +
  # stat_cor() +
  theme_pubr() +
  guides(alpha = "none", color = FALSE,fill = FALSE)+ 
  labs(x = "Age [years]") +
  theme(legend.position= "none") +
  scale_x_continuous(limits = c(0,100))

cor.test(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$S, filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$S and filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age
## t = 37.406, df = 6800, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3931982 0.4326213
## sample estimates:
##       cor 
## 0.4131033

5.2.3 I

figS6c <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"),
       aes(x = Age, y = I)) +
  geom_point(aes(color = Sample, fill = Sample, alpha = 0.4)) + 
  geom_smooth(color = "black", method = "lm") +
  # stat_cor() +
  theme_pubr() +
  guides(alpha = "none", color = FALSE,fill = FALSE)+ 
  labs(x = "Age [years]") +
  theme(legend.position= "none") +
  scale_x_continuous(limits = c(0,100))

cor.test(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$I, filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$I and filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age
## t = -70.698, df = 6800, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6643648 -0.6369635
## sample estimates:
##        cor 
## -0.6508761

figS6 <- ggarrange(figS6a, ggarrange(figS6b, figS6c,labels = c("B","C"), nrow = 1, ncol = 2, font.label = list(size = 11)),labels = c("A"), nrow = 2, ncol = 1, font.label = list(size = 11), common.legend = TRUE, legend = "top")

ggsave("figS6.pdf", plot = figS6, width = 18, height = 22, units = "cm", device = "pdf")

FIGURE 1

figS6

Through age, every Healthy Control subject for the independent morphological component, K, S, and I. For HCPr900 and AHEAD, ages are determined by an interval of years, thereby considering the mean age. The solid line represents a linear regression with a 95% confidence interval.

5.3 Slope

summary(lm(
  1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
  data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere",
       Diagnostic == "CTL"),
  na.action = na.omit
))

## 
## Call:
## lm(formula = 1/2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea), 
##     data = filter(dados_datasetscomp, Sample != "Mota&Houzel2015", 
##         ROI == "hemisphere", Diagnostic == "CTL"), na.action = na.omit)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.154606 -0.025469  0.000308  0.026792  0.098626 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        -1.11930    0.05546  -20.18   <2e-16 ***
## log10(ExposedArea)  1.37800    0.01208  114.07   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03218 on 6800 degrees of freedom
## Multiple R-squared:  0.6568, Adjusted R-squared:  0.6567 
## F-statistic: 1.301e+04 on 1 and 6800 DF,  p-value: < 2.2e-16

summary(lm(
  1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
  data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere", Age > 18 & Age < 40,
       Diagnostic == "CTL"),
  na.action = na.omit
))

## 
## Call:
## lm(formula = 1/2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea), 
##     data = filter(dados_datasetscomp, Sample != "Mota&Houzel2015", 
##         ROI == "hemisphere", Age > 18 & Age < 40, Diagnostic == 
##             "CTL"), na.action = na.omit)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.075674 -0.012016  0.002633  0.013807  0.065150 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        -0.55119    0.05033  -10.95   <2e-16 ***
## log10(ExposedArea)  1.25912    0.01095  115.02   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02063 on 3534 degrees of freedom
## Multiple R-squared:  0.7892, Adjusted R-squared:  0.7891 
## F-statistic: 1.323e+04 on 1 and 3534 DF,  p-value: < 2.2e-16

## Displays confidence interval
# tidy(lm(
#   1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
#   data = dados_hemi_v1,
#   na.action = na.omit
# ), conf.int = TRUE)

paste(
  "Student's t test comapring slope with theoretical value 1.25. t = ",
  signif(abs(coef(summary(
    lm(
      1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
      data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere",
       Diagnostic == "CTL"),
      na.action = na.omit
    )
  ))[2, 1] - 1.25) / coef(summary(
    lm(
      1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
      data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere",
       Diagnostic == "CTL"),
      na.action = na.omit
    )
  ))[2, 2], 3) 
)

## [1] "Student's t test comapring slope with theoretical value 1.25. t =  10.6"

paste(
  "Student's t test comapring slope with theoretical value 1.25. p value = ",
  signif(test_coef(
    lm(
      1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
      data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere",
       Diagnostic == "CTL"),
      na.action = na.omit
    ),
    2,
    1.25
  ),3)
)

## [1] "Student's t test comapring slope with theoretical value 1.25. p value =  4.98e-26"

5.3.1 Correlation

lm_Age <-
  filter(
    dados_datasetscomp,
    Sample != "Mota&Houzel2015",
    ROI == "hemisphere",
    Diagnostic == "CTL",
    Age_interval != "[0,5)",
    Age_interval != "[5,10)",
    Age_interval != "[10,15)"
  ) %>%
  group_by(Age_interval10) %>%
  do(fit_Age = tidy(
    lm(
      1 / 2 * log10(AvgThickness) +  log10(TotalArea) ~  log10(ExposedArea),
      data = .,
      na.action = na.omit
    ),
    conf.int = TRUE
  )) %>%
  unnest(cols = c(fit_Age))

lm_Age <- lm_Age %>% mutate(Age_interval10 = as.double((str_sub(Age_interval10,2,3))))

cor.test(filter(lm_Age, term == "log10(ExposedArea)")$estimate, filter(lm_Age, term == "log10(ExposedArea)")$Age_interval10)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(lm_Age, term == "log10(ExposedArea)")$estimate and filter(lm_Age, term == "log10(ExposedArea)")$Age_interval10
## t = -3.2156, df = 7, p-value = 0.01474
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.9494277 -0.2218865
## sample estimates:
##        cor 
## -0.7722149

5.4 Uncertainties estimation for baseline

Part of Table 2 - Natural fluctuation and Type B errors

5.4.1 GM volume ~ Age

m.1 <- lme4::lmer(GMvolume ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: GMvolume ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: 183968.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8395 -0.6727 -0.0320  0.6298  4.5351 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev.
##  Sample:Diagnostic (Intercept)  27722513  5265   
##  Sample            (Intercept) 366049150 19132   
##  Residual                      733577651 27085   
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                   Estimate Std. Error t value
## (Intercept)      303365.74    6119.08  49.577
## Age               -1061.86      27.79 -38.216
## DiagnosticAD     -67730.51    9855.71  -6.872
## Age:DiagnosticAD    725.19     105.75   6.858
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.196              
## DiagnostcAD -0.083  0.195       
## Ag:DgnstcAD  0.052 -0.263 -0.809

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.3957362 0.6067994

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##    lsmean
##     <dbl>
## 1 250218.

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 27000

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##       19000

5.4.2 AvgThickness ~ Age

m.1 <- lme4::lmer(AvgThickness ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## AvgThickness ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -13111.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -7.8038 -0.6167  0.0104  0.6495  3.4140 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev.
##  Sample:Diagnostic (Intercept) 0.0006026 0.02455 
##  Sample            (Intercept) 0.0071880 0.08478 
##  Residual                      0.0110146 0.10495 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)       2.7038037  0.0270734  99.869
## Age              -0.0044384  0.0001077 -41.194
## DiagnosticAD     -0.3421007  0.0405587  -8.435
## Age:DiagnosticAD  0.0029937  0.0004098   7.305
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.172              
## DiagnostcAD -0.084  0.183       
## Ag:DgnstcAD  0.045 -0.263 -0.762

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.4615061 0.6845916

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   2.48

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.1

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##       0.085

5.4.3 TotalArea ~ Age

m.1 <- lme4::lmer(TotalArea ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: TotalArea ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: 167642
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9066 -0.7162 -0.0476  0.6633  4.2777 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept)        0    0    
##  Sample            (Intercept) 23918246 4891    
##  Residual                      93180143 9653    
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)      113025.061   1543.436  73.229
## Age                -244.189      9.866 -24.750
## DiagnosticAD     -13184.422   2852.379  -4.622
## Age:DiagnosticAD    152.485     37.675   4.047
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.277              
## DiagnostcAD -0.073  0.259       
## Ag:DgnstcAD  0.072 -0.263 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.2353489 0.3915348

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##    lsmean
##     <dbl>
## 1 100803.

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 9700

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##        4900

5.4.4 ExposedArea ~ Age

m.1 <- lme4::lmer(ExposedArea ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## ExposedArea ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: 148576.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8868 -0.7093 -0.0618  0.6706  3.8432 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept)       0     0.0  
##  Sample            (Intercept)  279141   528.3  
##  Residual                      8382585  2895.3  
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                   Estimate Std. Error t value
## (Intercept)      40714.770    207.022 196.669
## Age                -40.602      2.859 -14.204
## DiagnosticAD      -262.931    853.269  -0.308
## Age:DiagnosticAD     1.535     11.275   0.136
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.597              
## DiagnostcAD -0.151  0.249       
## Ag:DgnstcAD  0.152 -0.255 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

r.squaredGLMM(m.1)

##             R2m       R2c
## [1,] 0.09982676 0.1288366

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1 38683.

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 2900

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##         530

5.4.5 GI ~ Age

m.1 <- lme4::lmer(localGI ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: localGI ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -14689.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7049 -0.6845 -0.0074  0.6784  6.4692 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept) 0.000000 0.00000 
##  Sample            (Intercept) 0.012446 0.11156 
##  Residual                      0.009017 0.09496 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)       2.7763677  0.0339367   81.81
## Age              -0.0034689  0.0000975  -35.58
## DiagnosticAD     -0.3178661  0.0280689  -11.32
## Age:DiagnosticAD  0.0037476  0.0003707   10.11
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.124              
## DiagnostcAD -0.033  0.260       
## Ag:DgnstcAD  0.033 -0.264 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.2623413 0.6900971

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   2.60

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.095

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##        0.11

5.4.6 K ~ Age

m.1 <- lme4::lmer(K ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: K ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -42555
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -6.9733 -0.6065  0.0381  0.6446  5.2725 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev.
##  Sample:Diagnostic (Intercept) 4.607e-06 0.002146
##  Sample            (Intercept) 4.410e-04 0.021001
##  Residual                      2.658e-04 0.016304
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)      -4.920e-01  6.412e-03  -76.73
## Age              -8.612e-04  1.675e-05  -51.40
## DiagnosticAD     -8.439e-02  5.444e-03  -15.50
## Age:DiagnosticAD  8.855e-04  6.366e-05   13.91
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.113              
## DiagnostcAD -0.039  0.221       
## Ag:DgnstcAD  0.030 -0.264 -0.882

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.4372324 0.7897408

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1 -0.535

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.016

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##       0.021

5.4.7 S ~ Age

m.1 <- lme4::lmer(S ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: S ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -10789.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5837 -0.6903 -0.0315  0.6406  5.5519 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev.
##  Sample:Diagnostic (Intercept) 0.0003168 0.01780 
##  Sample            (Intercept) 0.0057953 0.07613 
##  Residual                      0.0147855 0.12160 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)       9.0840260  0.0242645 374.375
## Age               0.0017030  0.0001246  13.664
## DiagnosticAD      0.1969053  0.0413152   4.766
## Age:DiagnosticAD -0.0013879  0.0004747  -2.924
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.222              
## DiagnostcAD -0.079  0.212       
## Ag:DgnstcAD  0.058 -0.263 -0.866

r.squaredGLMM(m.1)

##            R2m      R2c
## [1,] 0.1515722 0.399721

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   9.17

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.12

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##       0.076

5.4.8 I ~ Age

m.1 <- lme4::lmer(I ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

Model summary and R squared:

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: I ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -17050
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.9306 -0.6593 -0.0005  0.6762  3.2113 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev.
##  Sample:Diagnostic (Intercept) 0.0001859 0.01364 
##  Sample            (Intercept) 0.0013945 0.03734 
##  Residual                      0.0067038 0.08188 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)       1.053e+01  1.259e-02 836.069
## Age              -3.118e-03  8.371e-05 -37.254
## DiagnosticAD     -1.829e-01  2.848e-02  -6.421
## Age:DiagnosticAD  1.747e-03  3.196e-04   5.467
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.287              
## DiagnostcAD -0.109  0.200       
## Ag:DgnstcAD  0.075 -0.262 -0.844

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.4505911 0.5554086

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   10.4

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.082

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##       0.037

5.5 Multisite harmonization

S_lifespan_b <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"), aes(x = Age, y = S_shiftc, alpha = 0.4))+
    geom_point(aes(color = Sample, fill = Sample, alpha = 0.1)) +
    geom_smooth(method = "lm", color = "black") + geom_smooth(aes(color = Sample, fill = Sample), method = "lm") +
    guides(alpha = "none") + 
  theme_pubr() +
  labs(y = "S (harmonized)") +
  scale_x_continuous(limits = c(0,100))

I_lifespan_b <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"), aes(x = Age, y = I_shiftc, alpha = 0.4))+
    geom_point(aes(color = Sample, fill = Sample, alpha = 0.1)) +
    geom_smooth(method = "lm", color = "black") + geom_smooth(aes(color = Sample, fill = Sample), method = "lm") +
    guides(alpha = "none") + 
  theme_pubr() +
  labs(y = "I (harmonized)") +
  scale_x_continuous(limits = c(0,100))

lifespan_shift <- ggarrange(K_lifespan_b, S_lifespan_b, I_lifespan_b,labels = c("A","B", "C"), nrow = 3, ncol = 1, font.label = list(size = 11), common.legend = TRUE, legend = "right", vjust = 1.2)

ggsave("lifespan_shift.pdf", plot = lifespan_shift, width = 18, height = 16, units = "cm", device = "pdf")

lifespan_shift

FIGURE 2

K_lifespan

K through age for Healthy Controls (A) raw data, (B) after harmonizing (removing the estimated residual from the Linear Mixed Model) from T, AT, and AE resulting in the harmonized values of K.

5.6 Baseline and rate estimates and Diagnostic discrimination based on changing rates

# dados_datasetscomp$Diagnostic <- as.factor(dados_datasetscomp$Diagnostic)
# dados_datasetscomp$Diagnostic <- relevel(dados_datasetscomp$Diagnostic, ref = "CTL")

5.6.1 Slope

summary(lm(
  1 / 2 * log10(AvgThickness_shiftc) + log10(TotalArea_shiftc) ~ log10(ExposedArea_shiftc),
  data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere",
       Diagnostic == "CTL"),
  na.action = na.omit
))

## 
## Call:
## lm(formula = 1/2 * log10(AvgThickness_shiftc) + log10(TotalArea_shiftc) ~ 
##     log10(ExposedArea_shiftc), data = filter(dados_datasetscomp, 
##     Sample != "Mota&Houzel2015", ROI == "hemisphere", Diagnostic == 
##         "CTL"), na.action = na.omit)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.126471 -0.016037  0.002491  0.017389  0.093314 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               -1.195278   0.040456  -29.55   <2e-16 ***
## log10(ExposedArea_shiftc)  1.394751   0.008818  158.18   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02417 on 6800 degrees of freedom
## Multiple R-squared:  0.7863, Adjusted R-squared:  0.7863 
## F-statistic: 2.502e+04 on 1 and 6800 DF,  p-value: < 2.2e-16

## Displays confidence interval
# tidy(lm(
#   1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
#   data = dados_hemi_v1,
#   na.action = na.omit
# ), conf.int = TRUE)

lm_Age <-
  filter(
    dados_datasetscomp,
    Sample != "Mota&Houzel2015",
    ROI == "hemisphere",
    Diagnostic == "CTL",
    Age_interval != "[0,5)",
    Age_interval != "[5,10)",
    Age_interval != "[10,15)"
  ) %>%
  group_by(Age_interval10) %>%
  do(fit_Age = tidy(
    lm(
      1 / 2 * log10(AvgThickness_shiftc) +  log10(TotalArea_shiftc) ~  log10(ExposedArea_shiftc),
      data = .,
      na.action = na.omit
    ),
    conf.int = TRUE
  )) %>%
  unnest(cols = c(fit_Age))

lm_Age %>%
  kable(digits = 2) %>%
  kable_styling()

Age_interval10	term	estimate	std.error	statistic	p.value	conf.low	conf.high
[10,20)	(Intercept)	-0.89	0.19	-4.76	0.00	-1.26	-0.52
[10,20)	log10(ExposedArea_shiftc)	1.33	0.04	32.78	0.00	1.25	1.41
[20,30)	(Intercept)	-0.56	0.04	-13.85	0.00	-0.64	-0.48
[20,30)	log10(ExposedArea_shiftc)	1.26	0.01	144.01	0.00	1.24	1.28
[30,40)	(Intercept)	-0.53	0.06	-8.81	0.00	-0.65	-0.41
[30,40)	log10(ExposedArea_shiftc)	1.25	0.01	95.40	0.00	1.23	1.28
[40,50)	(Intercept)	-0.18	0.11	-1.74	0.08	-0.39	0.02
[40,50)	log10(ExposedArea_shiftc)	1.17	0.02	51.29	0.00	1.13	1.22
[50,60)	(Intercept)	-0.37	0.10	-3.72	0.00	-0.56	-0.17
[50,60)	log10(ExposedArea_shiftc)	1.21	0.02	55.97	0.00	1.17	1.26
[60,70)	(Intercept)	0.21	0.09	2.46	0.01	0.04	0.38
[60,70)	log10(ExposedArea_shiftc)	1.08	0.02	57.57	0.00	1.05	1.12
[70,80)	(Intercept)	-0.05	0.07	-0.69	0.49	-0.19	0.09
[70,80)	log10(ExposedArea_shiftc)	1.14	0.02	72.06	0.00	1.11	1.17
[80,90)	(Intercept)	-0.16	0.12	-1.34	0.18	-0.40	0.08
[80,90)	log10(ExposedArea_shiftc)	1.16	0.03	43.60	0.00	1.11	1.22
[90,100]	(Intercept)	0.16	0.39	0.40	0.69	-0.64	0.95
[90,100]	log10(ExposedArea_shiftc)	1.09	0.08	12.84	0.00	0.92	1.26

lm_Age <- lm_Age %>% mutate(Age_interval10 = as.double((str_sub(Age_interval10,2,3))))

cor.test(filter(lm_Age, term == "log10(ExposedArea_shiftc)")$estimate, filter(lm_Age, term == "log10(ExposedArea_shiftc)")$Age_interval10)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(lm_Age, term == "log10(ExposedArea_shiftc)")$estimate and filter(lm_Age, term == "log10(ExposedArea_shiftc)")$Age_interval10
## t = -4.7078, df = 7, p-value = 0.002189
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.9727213 -0.4931597
## sample estimates:
##        cor 
## -0.8717632

amostra_Coef <- filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL", Age_interval != "[0,5)", Age_interval != "[95,100]") %>%
    group_by(Age_interval10) %>%
    do(fit_amostra = tidy(lm(1/2 * log10(AvgThickness_shiftc) + log10(TotalArea_shiftc) ~ log10(ExposedArea_shiftc), data = ., na.action = na.omit), conf.int = TRUE, conf.level = 0.95)) %>% 
    unnest(fit_amostra)

amostras_Coef_age <- filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL", Age_interval != "[0,5)", Age_interval != "[95,100]") %>%
    group_by(Age_interval10) %>%
    summarise(
        N = n_distinct(SUBJ),
        min_age = min(Age),
        max_age = max(Age))

amostra_Coef <- full_join(amostra_Coef, amostras_Coef_age) %>% filter(term == "log10(ExposedArea_shiftc)")

fig_slope_ageinterval <- ggplot(amostra_Coef, aes(y = estimate, x = Age_interval10)) +
    geom_errorbar(aes(ymin = conf.low, ymax = conf.high), width = 0.2) +
    geom_point() +
  geom_line(group = 1) + 
  geom_hline(yintercept = 1.25, linetype = "dashed") +
    theme_pubr() + 
    theme(axis.text.x = element_text(angle = 45, hjust = 1, size=9)
    ) + labs(y ="Slope (after harmonization)", x = "Age interval") +  geom_text(aes(label = N), nudge_y = 0.2)

ggsave("fig_slope_ageinterval.pdf", plot = fig_slope_ageinterval, width = 18, height = 14, units = "cm", device = "pdf")

FIGURE 3

fig_slope_ageinterval

Slope alpha derived from the Cortical Folding model from Mota & Houzel through age for Healthy Controls. Data points from (0, 5] and [95, 100] years old were omitted due to the reduced data. The numbers on top of each point indicates the number of subjects at each interval. Mean value for all ages were 1.38+-0.012 and correlation of alpha and Age is Pearson’s r₌-0.69, p₌0.0031 from [15,20) years old.

summary(lm(
  1 / 2 * log10(AvgThickness_shiftc) + log10(TotalArea_shiftc) ~ log10(ExposedArea_shiftc),
  data = filter(dados_datasetscomp,
       Sample != "Mota&Houzel2015",
       ROI == "hemisphere",
       Diagnostic == "AD"),
  na.action = na.omit
))

## 
## Call:
## lm(formula = 1/2 * log10(AvgThickness_shiftc) + log10(TotalArea_shiftc) ~ 
##     log10(ExposedArea_shiftc), data = filter(dados_datasetscomp, 
##     Sample != "Mota&Houzel2015", ROI == "hemisphere", Diagnostic == 
##         "AD"), na.action = na.omit)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.105523 -0.015849  0.001627  0.017815  0.052604 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               -0.49777    0.08615  -5.778 9.81e-09 ***
## log10(ExposedArea_shiftc)  1.23286    0.01884  65.434  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02369 on 1108 degrees of freedom
## Multiple R-squared:  0.7944, Adjusted R-squared:  0.7942 
## F-statistic:  4282 on 1 and 1108 DF,  p-value: < 2.2e-16

## Displays confidence interval
# tidy(lm(
#   1 / 2 * log10(AvgThickness) + log10(TotalArea) ~ log10(ExposedArea),
#   data = dados_hemi_v1,
#   na.action = na.omit
# ), conf.int = TRUE)

amostra_Coef <- filter(dados_datasetscomp, ROI == "hemisphere", Age_interval != "[0,5)", Age_interval != "[95,100]") %>%
    group_by(Diagnostic, Age_interval10) %>%
    do(fit_amostra = tidy(lm(1/2 * log10(AvgThickness_shiftc) + log10(TotalArea_shiftc) ~ log10(ExposedArea_shiftc), data = ., na.action = na.omit), conf.int = TRUE, conf.level = 0.95)) %>% 
    unnest(fit_amostra)

amostras_Coef_age <- filter(dados_datasetscomp, ROI == "hemisphere", Age_interval != "[0,5)", Age_interval != "[95,100]") %>%
    group_by(Diagnostic, Age_interval10) %>%
    summarise(
        N = n_distinct(SUBJ),
        min_age = min(Age),
        max_age = max(Age))

amostra_Coef <- full_join(amostra_Coef, amostras_Coef_age) %>% filter(term == "log10(ExposedArea_shiftc)")

fig_slope_ageinterval_AD <- ggplot(amostra_Coef, aes(y = estimate, x = Age_interval10, color = Diagnostic)) +
    geom_errorbar(aes(ymin = conf.low, ymax = conf.high), width = 0.2) +
    geom_point() +
  geom_line(aes(group=Diagnostic)) + 
  geom_hline(yintercept = 1.25, linetype = "dashed") +
    theme_pubr() + 
    theme(axis.text.x = element_text(angle = 45, hjust = 1, size=9)
    ) + labs(y ="Slope (after harmonization)", x = "Age interval") +  geom_text(aes(label = N), nudge_y = 0.2) +
  scale_fill_manual(values=cbbPalette2) +
  scale_colour_manual(values=cbbPalette2)

fig_slope_ageinterval_AD

ggsave("fig_slope_ageinterval_AD.pdf", plot = fig_slope_ageinterval_AD, width = 18, height = 14, units = "cm", device = "pdf")

5.6.2 GM volume ~ Age

m.1 <- lme4::lmer(GMvolume_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## GMvolume_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: 183907.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8431 -0.6738 -0.0306  0.6297  4.5365 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept) 0.00e+00     0   
##  Sample            (Intercept) 0.00e+00     0   
##  Residual                      7.33e+08 27074   
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                   Estimate Std. Error t value
## (Intercept)      303346.92     740.16 409.837
## Age               -1062.07      14.43 -73.583
## DiagnosticAD     -72189.07    7734.48  -9.333
## Age:DiagnosticAD    732.24     102.94   7.113
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")
pairs <- pairs(m.lstk) 

mean <- as_tibble(mean)
m.lstk <- as_tibble(m.lstk)


lst <- m.lstk %>%
  mutate(TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableGM <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "GM_shiftc")
 
coefs <- data.frame(coef(summary(m.1)))
coefs$p.z <- 2 * (1 - pnorm(abs(coefs$t.value)))
coefs

##                     Estimate Std..Error    t.value          p.z
## (Intercept)      303346.9208  740.16472 409.837041 0.000000e+00
## Age               -1062.0694   14.43361 -73.583075 0.000000e+00
## DiagnosticAD     -72189.0707 7734.47570  -9.333415 0.000000e+00
## Age:DiagnosticAD    732.2418  102.94214   7.113140 1.134426e-12

pairs %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	-732.2418	102.9421	Inf	-7.11314	0

ggplot(data = as_tibble(pairs), aes(
    x = contrast,
    y = estimate,
    ymin = estimate - SE,
    ymax = estimate + SE)) +
    geom_hline(yintercept = 0,
               linetype = "11",
               colour = "grey60") +
    geom_pointrange( position = position_dodge(width = 0.2)) +
   geom_text(aes(label = str_c("p adj ", signif(p.value, digits = 2))), nudge_x = 0.3, nudge_y = 0.0003) +
    coord_flip() + 
    labs(y =  expression('Differences in slopes ('*Delta*'GM/'*Delta*'Age)'), x = "Contrast") +
  theme_pubr() + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10), text = element_text(size = 10))

e <- effect("Age:Diagnostic", m.1)
e <- as.data.frame(e)

ggplot(e, aes(x = Age, y = fit,ymin=lower, ymax=upper, shape = Diagnostic)) + geom_pointrange() + geom_line() + theme_pubr() + labs(x = "Age [years]", y = "K", shape = "Diagnostic") + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10), text = element_text(size = 10))

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##    lsmean
##     <dbl>
## 1 250189.

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 27000

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.3 AvgThickness ~ Age

m.1 <- lme4::lmer(AvgThickness_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: AvgThickness_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 |  
##     Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -13173.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -7.8059 -0.6167  0.0103  0.6500  3.4058 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept) 0.00000  0.0000  
##  Sample            (Intercept) 0.00000  0.0000  
##  Residual                      0.01101  0.1049  
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)       2.704e+00  2.869e-03 942.562
## Age              -4.440e-03  5.594e-05 -79.376
## DiagnosticAD     -3.695e-01  2.998e-02 -12.325
## Age:DiagnosticAD  3.029e-03  3.990e-04   7.592
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")

mean <- as_tibble(mean)
m.lstk <- as_tibble(m.lstk)

lst <- m.lstk %>%
  mutate(TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableT <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "T_shiftc")

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   2.48

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.1

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.4 TotalArea ~ Age

m.1 <- lme4::lmer(TotalArea_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## TotalArea_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: 167586.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9088 -0.7169 -0.0470  0.6641  4.2805 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept)        0    0    
##  Sample            (Intercept)        0    0    
##  Residual                      93066204 9647    
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)      113025.783    263.740 428.550
## Age                -244.375      5.143 -47.515
## DiagnosticAD     -13212.654   2755.994  -4.794
## Age:DiagnosticAD    152.779     36.681   4.165
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

sigma.hat(m.1)

## $sigma
## $sigma$data
## [1] 9647.083
## 
## $sigma$`Sample:Diagnostic`
## (Intercept) 
##           0 
## 
## $sigma$Sample
## (Intercept) 
##           0 
## 
## 
## $cors
## $cors$data
## [1] NA
## 
## $cors$`Sample:Diagnostic`
## [1] NA
## 
## $cors$Sample
## [1] NA

r.squaredGLMM(m.1)

##            R2m       R2c
## [1,] 0.2795186 0.2795186

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")

mean <- as_tibble(mean)
m.lstk <- as_tibble(m.lstk)

 lst <- m.lstk %>%
   mutate(
     TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableAT <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "AT_shiftc")

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##    lsmean
##     <dbl>
## 1 100795.

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 9600

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.5 ExposedArea ~ Age

m.1 <- lme4::lmer(ExposedArea_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## ExposedArea_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: 148540.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8881 -0.7093 -0.0605  0.6726  3.8448 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev. 
##  Sample:Diagnostic (Intercept) 1.753e-13 4.187e-07
##  Sample            (Intercept) 3.654e-13 6.045e-07
##  Residual                      8.372e+06 2.893e+03
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                   Estimate Std. Error t value
## (Intercept)      40729.774     79.104 514.890
## Age                -41.214      1.543 -26.718
## DiagnosticAD      -321.787    826.609  -0.389
## Age:DiagnosticAD     2.208     11.002   0.201
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")

mean <- as_tibble(mean)
m.lstk <- as_tibble(m.lstk)

 lst <- m.lstk %>% mutate(
     TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableAE <- full_join(mean, lst, by = c("Diagnostic")) %>% mutate(percent = Age.trend*100/abs(lsmean), Variable = "AE_shiftc")

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1 38667.

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 2900

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##       6e-07

5.6.6 GI ~ Age

m.1 <- lme4::lmer(localGI_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## localGI_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -14560.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7703 -0.6798 -0.0048  0.6759  6.4327 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept) 0.000000 0.00000 
##  Sample            (Intercept) 0.000000 0.00000 
##  Residual                      0.009238 0.09611 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)       2.778e+00  2.628e-03 1057.14
## Age              -3.509e-03  5.124e-05  -68.49
## DiagnosticAD     -3.243e-01  2.746e-02  -11.81
## Age:DiagnosticAD  3.811e-03  3.655e-04   10.43
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")

mean <- as_tibble(mean)
m.lstk <- as_tibble(m.lstk)

lst <- m.lstk %>%
  mutate(
    TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableGI <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "localGI_shiftc")

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   2.60

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.096

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.7 K ~ Age

m.1 <- lme4::lmer(K_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: K_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -42446
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -6.5322 -0.6041  0.0391  0.6431  5.2736 
## 
## Random effects:
##  Groups            Name        Variance  Std.Dev.
##  Sample:Diagnostic (Intercept) 0.0000000 0.00000 
##  Sample            (Intercept) 0.0000000 0.00000 
##  Residual                      0.0002717 0.01648 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error  t value
## (Intercept)      -4.916e-01  4.507e-04 -1090.92
## Age              -8.600e-04  8.788e-06   -97.86
## DiagnosticAD     -8.706e-02  4.709e-03   -18.49
## Age:DiagnosticAD  8.940e-04  6.268e-05    14.26
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

coefs <- data.frame(coef(summary(m.1)))
coefs$p.z <- 2 * (1 - pnorm(abs(coefs$t.value)))
coefs

##                       Estimate   Std..Error     t.value p.z
## (Intercept)      -0.4916413892 4.506654e-04 -1090.92322   0
## Age              -0.0008599766 8.788218e-06   -97.85563   0
## DiagnosticAD     -0.0870584281 4.709304e-03   -18.48647   0
## Age:DiagnosticAD  0.0008939612 6.267857e-05    14.26263   0

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1 -0.535

Mean values:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
pairs_means <- pairs(mean) 
mean <- as_tibble(mean)

pairs_means %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	0.0423146	0.0016447	Inf	25.72712	0

paste("Difference in pct ", as_tibble(pairs_means)[2]*100/mean$lsmean[1])

## [1] "Difference in pct  -7.91394490809058"

Trends:

m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")
pairs_trends <- pairs(m.lstk) 
m.lstk <- as_tibble(m.lstk)

pairs_trends %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	-0.000894	6.27e-05	Inf	-14.26263	0

lst <- m.lstk %>%
  mutate(
    TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableK <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "K_shiftc")

Figures:

fig_TX_K_age_c <- ggplot(data = as_tibble(pairs), aes(
    x = contrast,
    y = estimate,
    ymin = estimate - SE,
    ymax = estimate + SE)) +
    geom_hline(yintercept = 0,
               linetype = "11",
               colour = "grey60") +
    geom_pointrange( position = position_dodge(width = 0.2)) +
   geom_text(aes(label = str_c("p adj ", signif(p.value, digits = 2))), nudge_x = 0.3, nudge_y = 0.0003) +
    coord_flip() + 
    labs(y =  expression('Differences in slopes ('*Delta*'K/'*Delta*'Age)'), x = "Contrast") +
  theme_pubr() + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10), text = element_text(size = 10))

e <- effect("Age:Diagnostic", m.1)
e <- as.data.frame(e)

fig_K_age_c <- ggplot(e, aes(x = Age, y = fit,ymin=lower, ymax=upper, shape = Diagnostic)) + geom_pointrange() + geom_line() + theme_pubr() + labs(x = "Age [years]", y = "K", shape = "Diagnostic") + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10), text = element_text(size = 10))

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.016

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.8 S ~ Age

m.1 <- lme4::lmer(S_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: S_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -10771.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4726 -0.6906 -0.0334  0.6362  5.8254 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept) 0.00000  0.0000  
##  Sample            (Intercept) 0.00000  0.0000  
##  Residual                      0.01492  0.1221  
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error  t value
## (Intercept)       9.088e+00  3.339e-03 2721.724
## Age               1.606e-03  6.511e-05   24.671
## DiagnosticAD      2.073e-01  3.489e-02    5.943
## Age:DiagnosticAD -1.339e-03  4.644e-04   -2.884
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

coefs <- data.frame(coef(summary(m.1)))
coefs$p.z <- 2 * (1 - pnorm(abs(coefs$t.value)))
coefs

##                      Estimate   Std..Error     t.value          p.z
## (Intercept)       9.087638690 3.338928e-03 2721.723676 0.000000e+00
## Age               0.001606360 6.511088e-05   24.671142 0.000000e+00
## DiagnosticAD      0.207341356 3.489069e-02    5.942599 2.805383e-09
## Age:DiagnosticAD -0.001339213 4.643782e-04   -2.883885 3.928021e-03

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   9.17

Mean values:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
pairs_means <- pairs(mean) 
mean <- as_tibble(mean)

pairs_means %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	-0.1403122	0.0121857	Inf	-11.51445	0

paste("Difference in pct ", as_tibble(pairs_means)[2]*100/mean$lsmean[1])

## [1] "Difference in pct  -1.53044891669301"

Trends:

m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")
pairs_trends <- pairs(m.lstk) 
m.lstk <- as_tibble(m.lstk)

pairs_trends %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	0.0013392	0.0004644	Inf	2.883885	0.003928

lst <- m.lstk %>% mutate(
    TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableS <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "S_shiftc")

Figures:

fig_TX_S_age_c <- ggplot(data = as_tibble(pairs), aes(
    x = contrast,
    y = estimate,
    ymin = estimate - SE,
    ymax = estimate + SE)) +
    geom_hline(yintercept = 0,
               linetype = "11",
               colour = "grey60") +
    geom_pointrange( position = position_dodge(width = 0.2)) +
   geom_text(aes(label = str_c("p adj ", signif(p.value, digits = 2))), nudge_x = 0.3, nudge_y = 0.0003) +
    coord_flip() + 
    labs(y =  expression('Differences in slopes ('*Delta*'S/'*Delta*'Age)'), x = "Contrast") +
  theme_pubr() + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10), text = element_text(size = 10))

e <- effect("Age:Diagnostic", m.1)
e <- as.data.frame(e)

fig_S_age_c <- ggplot(e, aes(x = Age, y = fit,ymin=lower, ymax=upper, shape = Diagnostic)) + geom_pointrange() + geom_line() + theme_pubr() + labs(x = "Age [years]", y = "S", shape = "Diagnostic") + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10),
    text = element_text(size = 10), legend.position = "none")

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.12

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.9 I ~ Age

m.1 <- lme4::lmer(I_shiftc ~ Age * Diagnostic +(1|Sample) + (1|Sample:Diagnostic) , data = filter(dados_datasetscomp, ROI == "hemisphere"))

summary(m.1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: I_shiftc ~ Age * Diagnostic + (1 | Sample) + (1 | Sample:Diagnostic)
##    Data: filter(dados_datasetscomp, ROI == "hemisphere")
## 
## REML criterion at convergence: -16982.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.7921 -0.6605  0.0035  0.6753  3.2170 
## 
## Random effects:
##  Groups            Name        Variance Std.Dev.
##  Sample:Diagnostic (Intercept) 0.000000 0.00000 
##  Sample            (Intercept) 0.000000 0.00000 
##  Residual                      0.006801 0.08247 
## Number of obs: 7912, groups:  Sample:Diagnostic, 13; Sample, 11
## 
## Fixed effects:
##                    Estimate Std. Error  t value
## (Intercept)       1.053e+01  2.255e-03 4669.930
## Age              -3.074e-03  4.397e-05  -69.929
## DiagnosticAD     -1.938e-01  2.356e-02   -8.226
## Age:DiagnosticAD  1.702e-03  3.136e-04    5.426
## 
## Correlation of Fixed Effects:
##             (Intr) Age    DgnsAD
## Age         -0.896              
## DiagnostcAD -0.096  0.086       
## Ag:DgnstcAD  0.126 -0.140 -0.992
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

coefs <- data.frame(coef(summary(m.1)))
coefs$p.z <- 2 * (1 - pnorm(abs(coefs$t.value)))
coefs

##                      Estimate   Std..Error     t.value          p.z
## (Intercept)      10.528806334 2.254596e-03 4669.930202 0.000000e+00
## Age              -0.003074501 4.396583e-05  -69.929319 0.000000e+00
## DiagnosticAD     -0.193800114 2.355978e-02   -8.225888 2.220446e-16
## Age:DiagnosticAD  0.001701526 3.135693e-04    5.426315 5.752943e-08

Mean value:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
as_tibble(mean)[1,2]

## # A tibble: 1 x 1
##   lsmean
##    <dbl>
## 1   10.4

Mean values:

mean <- lsmeans(m.1, ~ Diagnostic, var="Age")
pairs_means <- pairs(mean) 
mean <- as_tibble(mean)

pairs_means %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	0.1086367	0.0082284	Inf	13.20271	0

paste("Difference in pct ", as_tibble(pairs_means)[2]*100/mean$lsmean[1])

## [1] "Difference in pct  1.04710882243449"

Trends:

m.lstk <- lstrends(m.1, ~ Diagnostic, var="Age")
pairs_trends <- pairs(m.lstk) 
m.lstk <- as_tibble(m.lstk)

pairs_trends %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value
CTL - AD	-0.0017015	0.0003136	Inf	-5.426315	1e-07

lst <- m.lstk %>% mutate(
    TX = paste(signif(Age.trend, 2), "±", signif(SE, 2)))

tableI <- full_join(mean, lst, by = c("Diagnostic")) %>%
  mutate(percent = Age.trend*100/abs(lsmean), Variable = "I_shiftc")

Figures:

fig_TX_I_age_c <- ggplot(data = as_tibble(pairs), aes(
    x = contrast,
    y = estimate,
    ymin = estimate - SE,
    ymax = estimate + SE)) +
    geom_hline(yintercept = 0,
               linetype = "11",
               colour = "grey60") +
    geom_pointrange( position = position_dodge(width = 0.2)) +
   geom_text(aes(label = str_c("p adj ", signif(p.value, digits = 2))), nudge_x = 0.3, nudge_y = 0.0003) +
    coord_flip() + 
    labs(y =  expression('Differences in slopes ('*Delta*'I/'*Delta*'Age)'), x = "Contrast") +
  theme_pubr() + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10), text = element_text(size = 10))

e <- effect("Age:Diagnostic", m.1)
e <- as.data.frame(e)

fig_I_age_c <- ggplot(e, aes(x = Age, y = fit,ymin=lower, ymax=upper, shape = Diagnostic)) + geom_pointrange() + geom_line() + theme_pubr() + labs(x = "Age [years]", y = "I", shape = "Diagnostic") + 
  theme(axis.title = element_text(size = 11),
    axis.text = element_text(size = 10),
    text = element_text(size = 10), legend.position = "none")

Natural fluctuation error:

signif(sigma.hat(m.1)$sigma$data,2)

## [1] 0.082

Type B error:

signif(sigma.hat(m.1)$sigma$Sample,2)

## (Intercept) 
##           0

5.6.10 rates

TABLE 3

rate %>%
  kable(digits = 2) %>%
  kable_styling()

Variable	CTL	AD
T_shiftc	-0.0044 ± 5.6e-05 ( -0.18 )	-0.0014 ± 4e-04 ( -0.062 )
AT_shiftc	-240 ± 5.1 ( -0.24 )	-92 ± 36 ( -0.096 )
AE_shiftc	-41 ± 1.5 ( -0.11 )	-39 ± 11 ( -0.1 )
K_shiftc	-0.00086 ± 8.8e-06 ( -0.16 )	3.4e-05 ± 6.2e-05 ( 0.0059 )
S_shiftc	0.0016 ± 6.5e-05 ( 0.018 )	0.00027 ± 0.00046 ( 0.0029 )
I_shiftc	-0.0031 ± 4.4e-05 ( -0.03 )	-0.0014 ± 0.00031 ( -0.013 )
localGI_shiftc	-0.0035 ± 5.1e-05 ( -0.13 )	3e-04 ± 0.00036 ( 0.012 )
GM_shiftc	-1100 ± 14 ( -0.42 )	-330 ± 100 ( -0.15 )

5.7 Correlation between K, S, and I with Age for the Healthy Control group

5.7.1 K

figS6a_alt <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"),
       aes(x = Age , y = K_shiftc)) +
  geom_point(aes(color = Sample, fill = Sample, alpha = 0.4)) +
  geom_smooth(color = "black", method = "lm") +
  # stat_cor() +
  theme_pubr() +
  guides(alpha = "none")+ 
  labs(x = "Age [years]", y ="K (after harmonization)") +
  scale_x_continuous(limits = c(0,100))

cor.test(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$K_shiftc, filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$K_shiftc and filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age
## t = -107.66, df = 6800, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8024991 -0.7849177
## sample estimates:
##        cor 
## -0.7938742

5.7.2 S

figS6b_alt <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"),
       aes(x = Age, y = S_shiftc)) +
  geom_point(aes(color = Sample, fill = Sample, alpha = 0.4)) +
  geom_smooth(color = "black", method = "lm") +
  # stat_cor() +
  theme_pubr() +
  guides(alpha = "none", color = FALSE,fill = FALSE)+ 
  labs(x = "Age [years]", y ="S (after harmonization)") +
  theme(legend.position= "none") +
  scale_x_continuous(limits = c(0,100))

cor.test(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$S_shiftc, filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$S_shiftc and filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age
## t = 25.606, df = 6800, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2747209 0.3180738
## sample estimates:
##       cor 
## 0.2965501

5.7.3 I

figS6c_alt <- ggplot(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL"),
       aes(x = Age, y = I_shiftc)) +
  geom_point(aes(color = Sample, fill = Sample, alpha = 0.4)) + 
  geom_smooth(color = "black", method = "lm") +
  # stat_cor() +
  theme_pubr() +
  guides(alpha = "none", color = FALSE,fill = FALSE)+ 
  labs(x = "Age [years]", y ="I (after harmonization)") +
  theme(legend.position= "none") +
  scale_x_continuous(limits = c(0,100))

cor.test(filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$I_shiftc, filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$I_shiftc and filter(dados_datasetscomp, ROI == "hemisphere", Diagnostic == "CTL")$Age
## t = -73.86, df = 6800, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6801680 -0.6537884
## sample estimates:
##        cor 
## -0.6671873

figS6_alt <- ggarrange(figS6a_alt, ggarrange(figS6b_alt, figS6c_alt,labels = c("B","C"), nrow = 1, ncol = 2, font.label = list(size = 11)),labels = c("A"), nrow = 2, ncol = 1, font.label = list(size = 11), common.legend = TRUE, legend = "top")

ggsave("figS6_alt.pdf", plot = figS6_alt, width = 18, height = 22, units = "cm", device = "pdf")

FIGURE 1_alternativa

figS6_alt

5.7.4 Figures

fig_age_c <- ggarrange(fig_K_age_c, ggarrange(fig_S_age_c, fig_I_age_c,labels = c("B","C"), nrow = 1, ncol = 2, font.label = list(size = 11)),labels = c("A"), nrow = 2, ncol = 1, font.label = list(size = 11), common.legend = TRUE, legend = "top")

ggsave("fig_age_c.pdf", plot = fig_age_c, width = 18, height = 18, units = "cm", device = "pdf")

FIGURE4

fig_age_c

Fitted values extracted from the linear regression model after data harmonization. Bars represent the 95 confidence interval. Complete summary of linear models in Supplementary Material. (A) Concerning K, Alzheimer’s Disease (AD) has a shallow slope, meaning small changes with Age. Compared to healthy controls, AD values of K are almost constant and similar to older subjects (AD slope p-value<0.0001 and CTL slope p-value<0.0001; pairwise comparison estimate -0.000903, p<0.0001). (B) For S, the AD and CTL patterns have similar intercepts, but statistically different slopes (AD slope p-value=0.004 and CTL slope p-value<0.0001; pairwise comparison estimate 0.0013, p=0.004). (C) For I, that reflects brain volume, CTL has a decreasing volume with aging, while AD has a smaller slope (AD slope p-value<0.0001 and CTL slope p-value<0.0001; pairwise comparison estimate -0.00168, p<0.0001).

5.8 Lobes

dados_datasetscomp_lobes <- filter(dados_datasetscomp, ROI != "hemisphere", Diagnostic == "CTL" | Diagnostic == "AD", Sample != "IDOR-CCD-Control")
dados_datasetscomp_lobes$Diagnostic <- factor(dados_datasetscomp_lobes$Diagnostic, levels = c("CTL", "MCI","AD"))
dados_datasetscomp_lobes$Sample <- as.factor(dados_datasetscomp_lobes$Sample)

Sample	Diagnostic	N	age	age_range
ADNI	CTL	868	75 ± 6.5	56 ; 96
ADNI	AD	542	75 ± 8	56 ; 92
AHEAD	CTL	100	42 ± 19	24 ; 76
AOMICPIOP1	CTL	208	22 ± 1.8	18 ; 26
AOMICPIOP2	CTL	224	22 ± 1.8	18 ; 26
HCPr900	CTL	881	29 ± 3.6	24 ; 37
IDOR	CTL	77	66 ± 8.4	43 ; 80
IDOR	AD	13	77 ± 6.1	63 ; 86
IXI-Guys	CTL	314	51 ± 16	20 ; 86
IXI-HH	CTL	181	47 ± 17	20 ; 82
IXI-IOP	CTL	68	42 ± 17	20 ; 86
NKI	CTL	168	34 ± 19	4 ; 85
OASIS	CTL	312	45 ± 24	18 ; 94

Diagnostic	N	age	age_range
CTL	3095	46 ± 23	4 ; 96
AD	555	75 ± 8	56 ; 92

5.8.1 K ~ Age

## Linear mixed model fit by REML ['lmerMod']
## Formula: K_shiftc ~ Age * Diagnostic * ROI + (1 | Sample:Diagnostic:ROI)
##    Data: dados_datasetscomp_lobes
## 
## REML criterion at convergence: -139166.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -6.3529 -0.6169  0.0203  0.6414  5.3896 
## 
## Random effects:
##  Groups                Name        Variance  Std.Dev.
##  Sample:Diagnostic:ROI (Intercept) 0.0000000 0.00000 
##  Residual                          0.0004934 0.02221 
## Number of obs: 29188, groups:  Sample:Diagnostic:ROI, 48
## 
## Fixed effects:
##                         Estimate Std. Error  t value
## (Intercept)           -5.062e-01  6.403e-04 -790.494
## Age                   -9.198e-04  1.247e-05  -73.752
## DiagnosticAD          -9.008e-02  6.343e-03  -14.201
## ROIO                   4.222e-02  9.055e-04   46.621
## ROIP                   4.204e-02  9.055e-04   46.429
## ROIT                   2.639e-02  9.055e-04   29.142
## Age:DiagnosticAD       9.744e-04  8.447e-05   11.536
## Age:ROIO               2.355e-04  1.764e-05   13.352
## Age:ROIP              -2.060e-04  1.764e-05  -11.680
## Age:ROIT              -3.828e-05  1.764e-05   -2.170
## DiagnosticAD:ROIO      3.362e-02  8.970e-03    3.748
## DiagnosticAD:ROIP     -4.009e-02  8.970e-03   -4.469
## DiagnosticAD:ROIT      6.636e-03  8.970e-03    0.740
## Age:DiagnosticAD:ROIO -4.070e-04  1.195e-04   -3.407
## Age:DiagnosticAD:ROIP  4.587e-04  1.195e-04    3.840
## Age:DiagnosticAD:ROIT -2.046e-04  1.195e-04   -1.713
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

Trends:

pairs %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value	Contrast.1	Contrast.2	Diagnostic.1	ROI.1	Diagnostic.2	ROI.2	contrast_ROI
CTL-AD	-0.0009744	8.45e-05	Inf	-11.535618	0	CTL F	AD F	CTL	F	AD	F	F-F
CTL-AD	-0.0005674	8.45e-05	Inf	-6.716977	0	CTL O	AD O	CTL	O	AD	O	O-O
CTL-AD	-0.0014331	8.45e-05	Inf	-16.966067	0	CTL P	AD P	CTL	P	AD	P	P-P
CTL-AD	-0.0007698	8.45e-05	Inf	-9.113069	0	CTL T	AD T	CTL	T	AD	T	T-T

5.8.2 S ~ Age

## Linear mixed model fit by REML ['lmerMod']
## Formula: S_shiftc ~ Age * Diagnostic * ROI + (1 | Sample:Diagnostic:ROI)
##    Data: dados_datasetscomp_lobes
## 
## REML criterion at convergence: -29380.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.2192 -0.6718 -0.0240  0.6368  5.8473 
## 
## Random effects:
##  Groups                Name        Variance Std.Dev.
##  Sample:Diagnostic:ROI (Intercept) 0.00000  0.0000  
##  Residual                          0.02126  0.1458  
## Number of obs: 29188, groups:  Sample:Diagnostic:ROI, 48
## 
## Fixed effects:
##                         Estimate Std. Error  t value
## (Intercept)            8.731e+00  4.203e-03 2076.999
## Age                    2.681e-03  8.187e-05   32.752
## DiagnosticAD           2.785e-01  4.164e-02    6.689
## ROIO                  -2.149e-01  5.945e-03  -36.156
## ROIP                   6.513e-01  5.945e-03  109.566
## ROIT                  -4.981e-02  5.945e-03   -8.379
## Age:DiagnosticAD      -2.415e-03  5.545e-04   -4.355
## Age:ROIO              -1.212e-03  1.158e-04  -10.464
## Age:ROIP              -1.198e-04  1.158e-04   -1.035
## Age:ROIT              -5.236e-04  1.158e-04   -4.522
## DiagnosticAD:ROIO     -1.154e-01  5.889e-02   -1.960
## DiagnosticAD:ROIP      2.092e-01  5.889e-02    3.552
## DiagnosticAD:ROIT     -2.767e-02  5.889e-02   -0.470
## Age:DiagnosticAD:ROIO  9.338e-04  7.842e-04    1.191
## Age:DiagnosticAD:ROIP -2.442e-03  7.842e-04   -3.114
## Age:DiagnosticAD:ROIT  9.578e-04  7.842e-04    1.221
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

Trends:

pairs %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value	Contrast.1	Contrast.2	Diagnostic.1	ROI.1	Diagnostic.2	ROI.2	contrast_ROI
CTL-AD	0.0024148	0.0005545	Inf	4.354852	0.0003550	CTL F	AD F	CTL	F	AD	F	F-F
CTL-AD	0.0014810	0.0005545	Inf	2.670780	0.1315406	CTL O	AD O	CTL	O	AD	O	O-O
CTL-AD	0.0048567	0.0005545	Inf	8.758395	0.0000000	CTL P	AD P	CTL	P	AD	P	P-P
CTL-AD	0.0014570	0.0005545	Inf	2.627543	0.1459513	CTL T	AD T	CTL	T	AD	T	T-T

5.8.3 I ~ Age

## Linear mixed model fit by REML ['lmerMod']
## Formula: I_shiftc ~ Age * Diagnostic * ROI + (1 | Sample:Diagnostic:ROI)
##    Data: dados_datasetscomp_lobes
## 
## REML criterion at convergence: -47911.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.5924 -0.6391  0.0025  0.6538  4.0292 
## 
## Random effects:
##  Groups                Name        Variance Std.Dev.
##  Sample:Diagnostic:ROI (Intercept) 0.00000  0.0000  
##  Residual                          0.01127  0.1061  
## Number of obs: 29188, groups:  Sample:Diagnostic:ROI, 48
## 
## Fixed effects:
##                         Estimate Std. Error  t value
## (Intercept)            1.029e+01  3.060e-03 3363.538
## Age                   -3.634e-03  5.959e-05  -60.975
## DiagnosticAD          -2.590e-01  3.031e-02   -8.546
## ROIO                  -7.612e-01  4.327e-03 -175.911
## ROIP                   3.175e-01  4.327e-03   73.373
## ROIT                   7.542e-02  4.327e-03   17.429
## Age:DiagnosticAD       2.767e-03  4.036e-04    6.855
## Age:ROIO               7.472e-04  8.428e-05    8.866
## Age:ROIP               5.915e-04  8.428e-05    7.018
## Age:ROIT               6.682e-04  8.428e-05    7.928
## DiagnosticAD:ROIO      1.045e-01  4.286e-02    2.437
## DiagnosticAD:ROIP     -2.042e-03  4.286e-02   -0.048
## DiagnosticAD:ROIT      8.302e-03  4.286e-02    0.194
## Age:DiagnosticAD:ROIO -1.215e-03  5.708e-04   -2.129
## Age:DiagnosticAD:ROIP  5.997e-05  5.708e-04    0.105
## Age:DiagnosticAD:ROIT -7.663e-04  5.708e-04   -1.342
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

Trends:

pairs %>%
  kable() %>%
  kable_styling()

contrast	estimate	SE	df	z.ratio	p.value	Contrast.1	Contrast.2	Diagnostic.1	ROI.1	Diagnostic.2	ROI.2	contrast_ROI
CTL-AD	-0.0027668	0.0004036	Inf	-6.854835	0.0000000	CTL F	AD F	CTL	F	AD	F	F-F
CTL-AD	-0.0015513	0.0004036	Inf	-3.843424	0.0030554	CTL O	AD O	CTL	O	AD	O	O-O
CTL-AD	-0.0028267	0.0004036	Inf	-7.003407	0.0000000	CTL P	AD P	CTL	P	AD	P	P-P
CTL-AD	-0.0020005	0.0004036	Inf	-4.956275	0.0000198	CTL T	AD T	CTL	T	AD	T	T-T