Monte Carlo modified profile likelihood in models for clustered data

TL;DR

This paper introduces a Monte Carlo simulation method to approximate modified profile likelihoods in complex clustered data models, improving inference accuracy in challenging scenarios like missing data and survival analysis.

Contribution

It presents a widely applicable Monte Carlo approach for modified profile likelihood estimation in nonstandard clustered data models, addressing limitations of classical methods.

Findings

Method performs well in simulations

Effective in missing-data models

Improves inference in survival models

Abstract

The main focus of the analysts who deal with clustered data is usually not on the clustering variables, and hence the group-specific parameters are treated as nuisance. If a fixed effects formulation is preferred and the total number of clusters is large relative to the single-group sizes, classical frequentist techniques relying on the profile likelihood are often misleading. The use of alternative tools, such as modifications to the profile likelihood or integrated likelihoods, for making accurate inference on a parameter of interest can be complicated by the presence of nonstandard modelling and/or sampling assumptions. We show here how to employ Monte Carlo simulation in order to approximate the modified profile likelihood in some of these unconventional frameworks. The proposed solution is widely applicable and is shown to retain the usual properties of the modified profile likelihood. The approach is examined in two instances particularly relevant in applications, i.e. missing-data models and survival models with unspecified censoring distribution. The effectiveness of the proposed solution is validated via simulation studies and two clinical trial applications.