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Monte Carlo modified profile likelihood in models for clustered data. (English) Zbl 1462.62381

Summary: 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.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62N01 Censored data models
62D10 Missing data
62G20 Asymptotic properties of nonparametric inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C05 Monte Carlo methods

Software:

bootlib; panelMPL; gee; survival; R
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Full Text: DOI arXiv Euclid

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