Dataset Information

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

SUBMITTER: Pavlou M

PROVIDER: S-EPMC8254921 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundRecent work has shown that cluster-randomised trials can estimate two distinct estimands: the participant-average and cluster-average treatment effects. These can differ when participant outcomes or the treatment effect depends on the cluster size (termed informative cluster size). In this case, estimators that target one estimand (such as the analysis of unweighted cluster-level summaries, which targets the cluster-average effect) may be biased for the other. Furthermore, commonly used estimators such as mixed-effects models or generalised estimating equations with an exchangeable correlation structure can be biased for both estimands. However, there has been little empirical research into whether informative cluster size is likely to occur in practice.MethodWe re-analysed a cluster-randomised trial comparing two different thresholds for red blood cell transfusion in patients with acute upper gastrointestinal bleeding to explore whether estimates for the participant- and cluster-average effects differed, to provide empirical evidence for whether informative cluster size may be present. For each outcome, we first estimated a participant-average effect using independence estimating equations, which are unbiased under informative cluster size. We then compared this to two further methods: (1) a cluster-average effect estimated using either weighted independence estimating equations or unweighted cluster-level summaries, and (2) estimates from a mixed-effects model or generalised estimating equations with an exchangeable correlation structure. We then performed a small simulation study to evaluate whether observed differences between cluster- and participant-average estimates were likely to occur even if no informative cluster size was present.ResultsFor most outcomes, treatment effect estimates from different methods were similar. However, differences of >10% occurred between participant- and cluster-average estimates for 5 of 17 outcomes (29%). We also observed several notable differences between estimates from mixed-effects models or generalised estimating equations with an exchangeable correlation structure and those based on independence estimating equations. For example, for the EQ-5D VAS score, the independence estimating equation estimate of the participant-average difference was 4.15 (95% confidence interval: -3.37 to 11.66), compared with 2.84 (95% confidence interval: -7.37 to 13.04) for the cluster-average independence estimating equation estimate, and 3.23 (95% confidence interval: -6.70 to 13.16) from a mixed-effects model. Similarly, for thromboembolic/ischaemic events, the independence estimating equation estimate for the participant-average odds ratio was 0.43 (95% confidence interval: 0.07 to 2.48), compared with 0.33 (95% confidence interval: 0.06 to 1.77) from the cluster-average estimator.ConclusionIn this re-analysis, we found that estimates from the various approaches could differ, which may be due to the presence of informative cluster size. Careful consideration of the estimand and the plausibility of assumptions underpinning each estimator can help ensure an appropriate analysis methods are used. Independence estimating equations and the analysis of cluster-level summaries (with appropriate weighting for each to correspond to either the participant-average or cluster-average treatment effect) are a desirable choice when informative cluster size is deemed possible, due to their unbiasedness in this setting.