Fit MMRM using R

We will generate longitudinal continuous data, then fit the MMRM using several different functions.

• Note that the glmmTMB package vignettes specifies how to fit the MMRM: https://cran.r-project.org/web/packages/glmmTMB/vignettes/covstruct.html

• The good folks at Roche pharma are making great progress on moving the entire analysis of clinical trial data away from SAS and into R. Here are links for fitting the MMRM using the lme4 package.

  • link 1: https://bit.ly/2ZSxBRG
  • link 2: https://drive.google.com/file/d/1sOZUAFOc004H4jO8vuUc_4HyYHEgu45b/view?usp=sharing&usp=embed_facebook

Generate MMRM Data

library(SPR)
library(MASS)
library(glmmTMB) # https://cran.r-project.org/web/packages/glmmTMB/vignettes/covstruct.html
library(emmeans)
library(nlme)
library(lme4)

  set.seed(03212021)
  
  out <- sim_dat(N = 100, 
                 number.groups = 2 , 
                 number.timepoints = 4, 
                 reg.formula = formula( ~ Time + Group + Time*Group),
                 Beta = 0,
                 corr = 'ar1', 
                 cor.value = 0.8, 
                 var.values = 2)
                
  
  dat <- out$dat
  dat <- dropout(dat = dat, 
                 type_dropout  = c('mar'), 
                 prop.miss = 0.3)
  

SAS Users

Note that the following line seems through testing to be the best approach to writing out R data for reading back into SAS:

  write.table(dat, na = '.', quote = F, sep = ', ', row.names = F, file = 'filename.txt')

Estimate: Fit MMRM to the Data

#  OLS Regression Model 
  mod.ols1 <- lm(Y_comp ~ Time + Group + Time*Group, 
                 data = dat)

  mod.ols2 <- lm(Y_mar ~ Group + Time + Group*Time, 
                            data = dat)


#   MMRM 
  mod.gls1 <- nlme::gls(Y_comp ~ Group + Time + Group*Time,
                  data = dat,
                  correlation = corSymm(form = ~ 1 | USUBJID),    #  unstructured correlation
                  weights = varIdent(form = ~ 1 | Time),          #  freely estimate variance at subsequent timepoints
                  na.action = na.exclude)


  mod.gls2 <- nlme::gls(Y_mar ~ Group + Time + Group*Time,
                  data = dat,
                  correlation = corSymm(form = ~ 1 | USUBJID),    #  unstructured correlation
                  weights = varIdent(form = ~ 1 | Time),          #  freely estimate variance at subsequent timepoints
                  na.action = na.exclude)
  
  
# MMRM - 
  mod.us1 <- glmmTMB::glmmTMB(Y_comp ~ Group + Time + Group*Time + us(Time + 0 | USUBJID), 
                  data=dat, 
                  REML = T,
                  dispformula=~0)
  
  mod.us2 <- glmmTMB::glmmTMB(Y_mar ~ Group + Time + Group*Time + us(Time + 0 | USUBJID),
                  data=dat,
                  REML = T,
                  dispformula=~0)
  
  
  # MMRM - 
  #  https://bit.ly/2ZSxBRG
  #  https://drive.google.com/file/d/1sOZUAFOc004H4jO8vuUc_4HyYHEgu45b/view?usp=sharing&usp=embed_facebook
  mod.lmer1 <- lme4::lmer(Y_comp ~ Group + Time + Group*Time + ( -1 + Time | USUBJID), 
                    data = dat, 
                    control = lmerControl(check.nobs.vs.nRE = 'ignore')) 
  
  
  mod.lmer2 <- lme4::lmer(Y_mar ~ Group + Time + Group*Time + (0 + Time | USUBJID), 
                    data = dat, 
                    control = lmerControl(check.nobs.vs.nRE = 'ignore')) 
  

Estimate Marginal Means

  # Compute marginal means
  library(emmeans)
  mod.emms.ols1 <- emmeans(mod.ols1, pairwise ~ Group | Time, adjust = 'none',  mode = 'df.error')
  mod.emms.ols2 <- emmeans(mod.ols2, pairwise ~ Group | Time, adjust = 'none',  mode = 'df.error')

  mod.emms.gls1 <- emmeans(mod.gls1, pairwise ~ Group | Time, adjust = 'none',  mode = 'satterthwaite')
  mod.emms.gls2 <- emmeans(mod.gls2, pairwise ~ Group | Time, adjust = 'none',  mode = 'satterthwaite')

  mod.emms.us1 <- emmeans(mod.us1, pairwise ~ Group | Time, adjust = 'none',  mode = 'df.error')
  mod.emms.us2 <- emmeans(mod.us2, pairwise ~ Group | Time, adjust = 'none',  mode = 'df.error')


  # Kenward Rogers Degrees of Freedom
  mod.emms.lmer1.kr <- emmeans(mod.lmer1, pairwise ~ Group | Time, adjust = 'none', mode = "kenward" )
  mod.emms.lmer2.kr <- emmeans(mod.lmer2, pairwise ~ Group | Time, adjust = 'none', mode = "kenward" )
# Does not align with SAS output
  
  # Satterthwaite Degrees of Freedom:
  mod.emms.lmer1.sat <- emmeans(mod.lmer1, pairwise ~ Group | Time, adjust = 'none', mode = 'satterthwaite' )
  mod.emms.lmer2.sat <- emmeans(mod.lmer2, pairwise ~ Group | Time, adjust = 'none', mode = 'satterthwaite' )

Evaluate Model output

  out$Beta
  mod.emms.ols1$contrasts
  mod.emms.gls1$contrasts
  mod.emms.us1$contrasts
  mod.emms.lmer1.kr$contrasts
  mod.emms.lmer1.sat$contrasts
 
  # Compare the variance-covariance matrices:
  out$sigma # Generating
  SPR::VarCov_gls(mod.gls1) # gls()
  summary(mod.ols1)$sigma
  glmmTMB::VarCorr(mod.us1)$cond
  
  # The lmer() hack yields an unidentified variance-covariance matrix:
  VarCorr(mod.lmer1)
  glmmTMB::VarCorr(mod.us1)
  # https://stat.ethz.ch/pipermail/r-sig-mixed-models/2015q2/023520.html
  

Examine Output

Print all output to console:

# Print to console the different model estimates:
  
for(nn in c('ols1', 'ols2', 'gls1', 'gls2', 'us1', 'us2', 'lmer1.kr', 'lmer2.kr', 'lmer1.sat', 'lmer2.sat')){
    
    mod.out <- get(paste0('mod.emms.', nn))
    mod.out <- as.data.frame(mod.out$contrasts)
    cat(paste0('Model: ', nn, '\n'))
    print(mod.out)
    
  }