A model for repeated clustered data with informative cluster sizes

Marginal analysis of multiple outcomes with informative cluster size

In surveillance studies of periodontal disease, the relationship between disease and other health and socioeconomic conditions is of key interest. To determine whether a patient has periodontal disease, multiple clinical measurements (eg, clinical attachment loss, alveolar bone loss, and tooth mobility) are taken at the tooth-level. Researchers often create a composite outcome from these measurements or analyze each outcome separately. Moreover, patients have varying number of teeth, with those who are more prone to the disease having fewer teeth compared to those with good oral health. Such dependence between the outcome of interest and cluster size (number of teeth) is called informative cluster size and results obtained from fitting conventional marginal models can be biased. We propose a novel method to jointly analyze multiple correlated binary outcomes for clustered data with informative cluster size using the class of generalized estimating equations (GEE) with cluster-specific weights. We compare our proposed multivariate outcome cluster-weighted GEE results to those from the convectional GEE using the baseline data from Veterans Affairs Dental Longitudinal Study. In an extensive simulation study, we show that our proposed method yields estimates with minimal relative biases and excellent coverage probabilities.

Informatively empty clusters with application to multigenerational studies

Exposures with multigenerational effects have profound implications for public health, affecting increasingly more people as the exposed population reproduces. Multigenerational studies, however, are susceptible to informative cluster size, occurring when the number of children to a mother (the cluster size) is related to their outcomes, given covariates. A natural question then arises: what if some women bear no children at all? The impact of these potentially informative empty clusters is currently unknown. This article first evaluates the performance of standard methods for informative cluster size when cluster size is permitted to be zero. We find that if the informative cluster size mechanism induces empty clusters, standard methods lead to biased estimates of target parameters. Joint models of outcome and size are capable of valid conditional inference as long as empty clusters are explicitly included in the analysis, but in practice empty clusters regularly go unacknowledged. In contrast, estimating equation approaches necessarily omit empty clusters and therefore yield biased estimates of marginal effects. To resolve this, we propose a joint marginalized approach that readily incorporates empty clusters and even in their absence permits more intuitive interpretations of population-averaged effects than do current methods. Competing methods are compared via simulation and in a study of the impact of in-utero exposure to diethylstilbestrol on the risk of attention-deficit/hyperactivity disorder (ADHD) among 106 198 children to 47 540 nurses from the Nurses Health Study.

Marginal analysis of ordinal clustered longitudinal data with informative cluster size

The issue of informative cluster size (ICS) often arises in the analysis of dental data. ICS describes a situation where the outcome of interest is related to cluster size. Much of the work on modeling marginal inference in longitudinal studies with potential ICS has focused on continuous outcomes. However, periodontal disease outcomes, including clinical attachment loss, are often assessed using ordinal scoring systems. In addition, participants may lose teeth over the course of the study due to advancing disease status. Here we develop longitudinal cluster-weighted generalized estimating equations (CWGEE) to model the association of ordinal clustered longitudinal outcomes with participant-level health-related covariates, including metabolic syndrome and smoking status, and potentially decreasing cluster size due to tooth-loss, by fitting a proportional odds logistic regression model. The within-teeth correlation coefficient over time is estimated using the two-stage quasi-least squares method. The motivation for our work stems from the Department of Veterans Affairs Dental Longitudinal Study in which participants regularly received general and oral health examinations. In an extensive simulation study, we compare results obtained from CWGEE with various working correlation structures to those obtained from conventional GEE which does not account for ICS. Our proposed method yields results with very low bias and excellent coverage probability in contrast to a conventional generalized estimating equations approach.