Model selection for semiparametric marginal mean regression accounting for within-cluster subsampling variability and informative cluster size

To retrieve aerosol properties from satellite measurements, micro-physical aerosol models have to be assumed. Due to the spatial and temporal inhomogeneity of aerosols, choosing an appropriate aerosol model is an important task. In this paper, we use a Bayesian algorithm that takes into account model uncertainties to retrieve the aerosol optical depth and layer height from synthetic and real TROPOMI O2A band measurements. The results show that in case of insufficient information for an appropriate micro-physical model selection, the Bayesian algorithm improves the accuracy of the solution.

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Risk prediction in multicentre studies when there is confounding by cluster or informative cluster size

BMC Medical Research Methodology ◽

10.1186/s12874-021-01321-x ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Menelaos Pavlou ◽

Gareth Ambler ◽

Rumana Z. Omar

Keyword(s):

Risk Prediction ◽

Cluster Size ◽

Linear Models ◽

Prediction Models ◽

Predictive Accuracy ◽

Clustered Data ◽

Predictor Variable ◽

Simulated Data ◽

Predictive Ability ◽

Informative Cluster Size

Abstract Background Clustered data arise in research when patients are clustered within larger units. Generalised Estimating Equations (GEE) and Generalised Linear Models (GLMM) can be used to provide marginal and cluster-specific inference and predictions, respectively. Methods Confounding by Cluster (CBC) and Informative cluster size (ICS) are two complications that may arise when modelling clustered data. CBC can arise when the distribution of a predictor variable (termed ‘exposure’), varies between clusters causing confounding of the exposure-outcome relationship. ICS means that the cluster size conditional on covariates is not independent of the outcome. In both situations, standard GEE and GLMM may provide biased or misleading inference, and modifications have been proposed. However, both CBC and ICS are routinely overlooked in the context of risk prediction, and their impact on the predictive ability of the models has been little explored. We study the effect of CBC and ICS on the predictive ability of risk models for binary outcomes when GEE and GLMM are used. We examine whether two simple approaches to handle CBC and ICS, which involve adjusting for the cluster mean of the exposure and the cluster size, respectively, can improve the accuracy of predictions. Results Both CBC and ICS can be viewed as violations of the assumptions in the standard GLMM; the random effects are correlated with exposure for CBC and cluster size for ICS. Based on these principles, we simulated data subject to CBC/ICS. The simulation studies suggested that the predictive ability of models derived from using standard GLMM and GEE ignoring CBC/ICS was affected. Marginal predictions were found to be mis-calibrated. Adjusting for the cluster-mean of the exposure or the cluster size improved calibration, discrimination and the overall predictive accuracy of marginal predictions, by explaining part of the between cluster variability. The presence of CBC/ICS did not affect the accuracy of conditional predictions. We illustrate these concepts using real data from a multicentre study with potential CBC. Conclusion Ignoring CBC and ICS when developing prediction models for clustered data can affect the accuracy of marginal predictions. Adjusting for the cluster mean of the exposure or the cluster size can improve the predictive accuracy of marginal predictions.

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