A new approach for marginal modelling of the clustered data with informative cluster size

The most important feature of clustered data is that the observations are correlated within clusters. Clustered data analysis allows the analysis of the effects of both individual-level and cluster-level factors on the outcome variable and generalized estimation equation (GEE) is used in the marginal modeling of these effects. The informative cluster size (the non-ignorable cluster size), a concept that expresses the dependence between the outcome variable and the size of the cluster, is a special case in the clustered data structures. In this case, the marginal model is essentially fitted and predictions are performed with two different approaches: within-cluster resampling (WCR) and cluster weighted generalized estimating equations (CWGEE). Weighted GEE (WGEE) and doubly robust GEE (DR-GEE) approaches are used in marginal modeling of clustered data with missing values. CWGEE is defined as a special form of the WGEE approach, in which the inverse probability weighting, a step of the WGEE approach, is stated in terms of cluster size. This study, starting out with the fact that DR-GEE approach is an alternative to the WGEE approach, considers that some form of the DR-GEE approach can be an alternative approach for CWGEE. Two different methods(named DRGEE(1) and DRGEE(2)) are proposed for weighting the DR-GEEapproach with regards to the cluster size. The aim is to compare the newly proposed DR-GEE(1) and DR-GEE(2) methods with the current approaches. Real data from a study including 206 individuals were used to determine the factors that cause periodontal disease. The presence of periodontal disease is modeled by 6 explanatory variables. The simulation study was designed to include a single explanatory variable and parameter estimates were obtained with simulated data of different sample sizes (50, 100, 200 and 500) and different cluster sizes (10, 20 and 50) with 100 replications. Parameter estimations were initially obtained by GEE, WCR and CWGEE approaches, and then, analysis using the proposed inference methods (DR-GEE (1) and DR-GEE(2)) and the results obtained by four methods were compared. As a result of comparing the three existing and two proposed inference approaches; GEE is the worst performing approach in terms of bias. While the CWGEE approach suggested in the informative cluster size literature has the best performance, the WCR approach is performing between the GEE and CWGEE. It was revealed that the DR-GEE(2) approach, the second proposed method within the scope of the thesis, has the best performance in terms of bias in high cluster size and cluster number scenarios and can be used as an alternative to CWGEE and WCR approaches.