Author: Klaus Holst & Thomas Scheike
Date: 2026-05-23

# GEE cluster standard errors and predictions for glm objects

#### Klaus Holst & Thomas Scheike

#### 2026-05-23

# Utility functions for GLM objects

Computing odds ratios with confidence intervals using GEE (sandwich) standard errors:

    set.seed(100)

    library(mets)
    data(bmt);
    bmt$id <- sample(1:100,408,replace=TRUE)

    glm1 <- glm(tcell~platelet+age,bmt,family=binomial)
    summaryGLM(glm1)
    #> $coef
    #>             Estimate Std.Err    2.5%   97.5%   P-value
    #> (Intercept)  -2.4371  0.2225 -2.8732 -2.0009 6.481e-28
    #> platelet      1.1368  0.3076  0.5340  1.7397 2.189e-04
    #> age           0.5927  0.1551  0.2888  0.8966 1.319e-04
    #>
    #> $or
    #>               Estimate       2.5%     97.5%
    #> (Intercept) 0.08741654 0.05651794 0.1352076
    #> platelet    3.11688928 1.70573194 5.6955015
    #> age         1.80895115 1.33489115 2.4513641
    #>
    #> $fout
    #> NULL

    ## GEE robust standard errors
    summaryGLM(glm1,id=bmt$id)
    #> $coef
    #>             Estimate Std.Err    2.5%   97.5%   P-value
    #> (Intercept)  -2.4371  0.2157 -2.8599 -2.0142 1.361e-29
    #> platelet      1.1368  0.2830  0.5822  1.6914 5.877e-05
    #> age           0.5927  0.1434  0.3117  0.8738 3.568e-05
    #>
    #> $or
    #>               Estimate       2.5%     97.5%
    #> (Intercept) 0.08741654 0.05727471 0.1334211
    #> platelet    3.11688928 1.79006045 5.4271903
    #> age         1.80895115 1.36575550 2.3959664
    #>
    #> $fout
    #> NULL

Predictions are equally straightforward:

    age <- seq(-2,2,by=0.1)
    nd <- data.frame(platelet=0,age=seq(-2,2,by=0.1))
    pnd <- predictGLM(glm1,nd)
    head(pnd$pred)
    #>      Estimate       2.5%      97.5%
    #> p1 0.02601899 0.01115243 0.05951051
    #> p2 0.02756409 0.01214068 0.06136414
    #> p3 0.02919819 0.01321187 0.06328733
    #> p4 0.03092608 0.01437206 0.06528441
    #> p5 0.03275278 0.01562757 0.06736019
    #> p6 0.03468351 0.01698493 0.06952008
    plot(age,pnd$pred[,1],type="l",ylab="predictions",xlab="age",ylim=c(0,0.3))
    plotConfRegion(age,pnd$pred[,2:3],col=2)

    ###matlines(age,pnd$pred[,-1],col=2,lty=1)

# SessionInfo

    sessionInfo()
    #> R version 4.6.0 (2026-04-24)
    #> Platform: x86_64-pc-linux-gnu
    #> Running under: Ubuntu 24.04.4 LTS
    #>
    #> Matrix products: default
    #> BLAS:   /home/kkzh/.asdf/installs/r/4.6.0/lib/R/lib/libRblas.so
    #> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0  LAPACK version 3.12.0
    #>
    #> locale:
    #>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
    #>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
    #>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
    #>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
    #>  [9] LC_ADDRESS=C               LC_TELEPHONE=C
    #> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
    #>
    #> time zone: Europe/Copenhagen
    #> tzcode source: system (glibc)
    #>
    #> attached base packages:
    #> [1] stats     graphics  grDevices utils     datasets  methods   base
    #>
    #> other attached packages:
    #> [1] timereg_2.0.7  survival_3.8-6 mets_1.3.10
    #>
    #> loaded via a namespace (and not attached):
    #>  [1] cli_3.6.6              knitr_1.51             rlang_1.2.0
    #>  [4] xfun_0.57              otel_0.2.0             jsonlite_2.0.0
    #>  [7] listenv_0.10.1         future.apply_1.20.2    lava_1.9.1
    #> [10] htmltools_0.5.9        stats4_4.6.0           sass_0.4.10
    #> [13] rmarkdown_2.31         grid_4.6.0             evaluate_1.0.5
    #> [16] jquerylib_0.1.4        fastmap_1.2.0          numDeriv_2016.8-1.1
    #> [19] yaml_2.3.12            mvtnorm_1.3-7          lifecycle_1.0.5
    #> [22] compiler_4.6.0         codetools_0.2-20       ucminf_1.2.3
    #> [25] Rcpp_1.1.1-1.1         future_1.70.0          lattice_0.22-9
    #> [28] digest_0.6.39          R6_2.6.1               parallelly_1.47.0
    #> [31] parallel_4.6.0         splines_4.6.0          Matrix_1.7-5
    #> [34] bslib_0.11.0           tools_4.6.0            RcppArmadillo_15.2.6-1
    #> [37] globals_0.19.1         cachem_1.1.0