Model Selection for Semiparametric Marginal Mean Regression Accounting for Within-Cluster Subsampling Variability and Informative Cluster Size

Abstract

We propose a model selection criterion for semiparametric marginal mean regression based on generalized estimating equations. The work is motivated by a longitudinal study on the physical frailty outcome in the elderly, where the cluster size, that is, the number of the observed outcomes in each subject, is "informative" in the sense that it is related to the frailty outcome itself. The new proposal, called Resampling Cluster Information Criterion (RCIC), is based on the resampling idea utilized in the within-cluster resampling method (Hoffman, Sen, and Weinberg, 2001, Biometrika 88, 1121-1134) and accommodates informative cluster size. The implementation of RCIC, however, is free of performing actual resampling of the data and hence is computationally convenient. Compared with the existing model selection methods for marginal mean regression, the RCIC method incorporates an additional component accounting for variability of the model over within-cluster subsampling, and leads to remarkable improvements in selecting the correct model, regardless of whether the cluster size is informative or not. Applying the RCIC method to the longitudinal frailty study, we identify being female, old age, low income and life satisfaction, and chronic health conditions as significant risk factors for physical frailty in the elderly.

A model selection criterion for clustered survival analysis with informative cluster size

“…The RCSIC is then equivalent to the RCIC. Under the situations with constant cluster size () considered, the second and third terms of the RCSIC perspicuously reduces to a model dimension multiplied by a cluster size penalty term () for the model selection criterion 32 . Since the RCSIC puts a larger penalty on model dimension than the traditional Akaike information criterion, 37 the RCSIC can reduce risks for choosing an overfitted model, in comparison with the traditional Akaike information criterion that is known to easily prefer selecting a larger model 38 .…”

“…Under the situations with constant cluster size (n) considered, the second and third terms of the RCSIC perspicuously reduces to a model dimension p multiplied by a cluster size penalty term (n þ 1) for the model selection criterion. 32 Since the RCSIC puts a larger penalty on model dimension p than the traditional Akaike information criterion, 37 the RCSIC can reduce risks for choosing an overfitted model, in comparison with the traditional Akaike information criterion that is known to easily prefer selecting a larger model. 38 Our simulations below show comparison results where, in terms of the clustered survival data, it seems that the proposed RCSIC can also reduce risks for selecting an overfitted model by the existing model selection method based on the Akaike information criterion in survival analysis, AIC, 39 regardless of whether cluster size is informative or not.…”

“…On the other hand, to our knowledge about the model selection criterion with informative cluster size, Shen and Chen 32 proposed a model selection criterion, called Resampling Cluster Information Criterion (RCIC), for selection of semiparametric marginal mean model under GEE. The RCIC accounts for the possible informativeness of cluster size on the clustered data with quantitative and qualitative outcomes.…”

Clinical risk prediction models and informative cluster size: Assessing the performance of a suicide risk prediction algorithm

“…The influence of clustering and informative cluster size on inference is well documented, and methods exist for valid inference on marginal parameters in a variety of settings (Benhin et al., 2005; Hoffman et al., 2001; Huang & Leroux, 2011; Pavlou et al., 2013; Seaman et al., 2014; Shen & Chen, 2018; Williamson et al., 2003, 2008). By contrast, the impact of clustering and informative cluster size in prediction modeling has not been closely examined.…”