---
title: "GEE cluster standard errors and predictions for glm objects" 
author: Klaus Holst & Thomas Scheike
date: "2026-05-24"
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Utility functions for GLM objects
=================================

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


``` r
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:


``` r
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)
```

<img src="figure/glm-utility-unnamed-chunk-3-1.png" alt="GLM predicted probabilities with confidence region."  />

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

SessionInfo
============



``` r
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             future.apply_1.20.2   
#>  [7] listenv_0.10.1         lava_1.9.1             stats4_4.6.0          
#> [10] grid_4.6.0             evaluate_1.0.5         yaml_2.3.12           
#> [13] mvtnorm_1.3-7          numDeriv_2016.8-1.1    compiler_4.6.0        
#> [16] codetools_0.2-20       Rcpp_1.1.1-1.1         ucminf_1.2.3          
#> [19] future_1.70.0          lattice_0.22-9         digest_0.6.39         
#> [22] parallelly_1.47.0      parallel_4.6.0         splines_4.6.0         
#> [25] Matrix_1.7-5           tools_4.6.0            RcppArmadillo_15.2.6-1
#> [28] globals_0.19.1
```