Marginal analysis of ordinal clustered longitudinal data with informative cluster size

Abstract

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.

Keywords: clustered data; generalized estimating equations; informative cluster size; longitudinal data; ordinal outcome; quasi-least squares.

Figure 1.

Coverage probability and absolute relative bias of all parameters by sample size and correlation for three models, MULTGEE Ind, ORDGEE Ind, CWGEE AR1 (proposed method) from simulation study. Correlation (τ is the correlation parameter between teeth and α is the correlation parameter over time within a tooth): none (τ = 0, α = 0); low (τ = 0.25, α = 0.4); med (τ = 0.5, α = 0.6); high (τ = 0.75, α = 0.8). Parameters: η₁ − η₃, β₁ − β₃.

Figure 2.

Left Panel: Relationship between number of teeth and mean clinical attachment loss (CAL) score (0: <2mm, 1: 2–2.9mm, 2: 3–4.9mm, 3: ≥5mm) at baseline per participant from the Dapartment of Veterans Affairs Longitudinal Dental Study (N = 456). Right Panel: Relationship between number of teeth at baseline and maximum number of temporal observation made on each participant’s tooth.