New Zealand Statistical Association 2024 Conference

Bradley Drayton

University of Auckland | Waipapa Taumata Rau

Variance estimators for mixed-effects proportional hazards models fitted to complex samples

The mixed-effects proportional hazards model for complex samples is designed to analyse correlated time-to-event data collected through complex sampling methods. A significant challenge in this context is variance estimation, which becomes complicated due to model misspecification from sampling weights and cluster correlation from data generation or sampling processes. The current variance estimator, which relies on the information matrix, tends to underestimate variance.

To address this challenge, I developed a robust sandwich estimator and utilised resampling-based variance estimators from the R survey package to create five new variance estimators for the fixed effects in these models. These new estimators are included in the svycoxme package.

I evaluated these new variance estimators against the information-based estimator using two sampling schemes: simple random cluster sampling and stratified, multi-stage sampling. The cluster-level jackknife method performed the best, while the multistage rescaled bootstrap, sandwich estimator, and information-based estimator also showed acceptable performance in many scenarios.

Interestingly, the bootstrap method showed unexpected results, with undercoverage for cluster-level effects. We explore the reasons behind this and suggest directions for future research in this area.