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.

Quasi-least squares regression method with dentistry data.

BACKGROUND: In dentistry, single-jaw surgery or double-jaw surgery is performed depending on the patient's need to correct severe skeletal malocclusions. The effect of these surgical methods used in treatment is to be investigated with quasi-least squares regression (QLS), which is a new data analysis method for correlated data obtained by extending generalized estimating equations (GEE). AIM: The aim of this study is to investigate whether jaw surgery methods (single jaw and double jaw) and time are effective on some outcome variables (C point menton distance, cervical plane angle, distance from point C to pogonion perpendicular, angle between cervical plane and facial plane) using QLS method. METHODS: In application, 114 measurements were performed on the lateral cephalometric radiographs of 34 patients aged 18 years and older who received orthodontic treatment and underwent surgery in the period of 2000-2018. The effects of time and group variables on four dependent variables were investigated and evaluated using QLS and GEE methods. RESULTS: Single-jaw surgery and double-jaw surgery as a group variable on all outcome variables were not significant. Among the working correlation structures used in QLS, the highest correlation value was obtained by "Markov" working correlation structure. CONCLUSION: Single-jaw surgery and double-jaw surgery were found to be statistically insignificant for outcome variables examined. QLS is superior to GEE in cases where repeated measurements are performed at unequal time intervals and there are missing observations.

Design and analysis considerations for cohort stepped wedge cluster randomized trials with a decay correlation structure.

A stepped wedge cluster randomized trial is a type of longitudinal cluster design that sequentially switches clusters to intervention over time until all clusters are treated. While the traditional posttest-only parallel design requires adjustment for a single intraclass correlation coefficient, the stepped wedge design allows multiple outcome measurements from the same cluster and so additional correlation parameters are necessary to characterize the within-cluster correlation structure. Although a number of studies have differentiated between the concepts of within-period and between-period correlations, only a few studies have allowed the between-period correlation to decay over time. In this article, we consider the proportional decay correlation structure for a cohort stepped wedge design, and provide a matrix-adjusted quasi-least squares approach to accurately estimate the correlation parameters along with the marginal intervention effect. We further develop the sample size and power procedures accounting for the correlation decay, and investigate the accuracy of the power procedure with continuous outcomes in a simulation study. We show that the empirical power agrees well with the prediction even with as few as nine clusters, when data are analyzed with matrix-adjusted quasi-least squares concurrently with a suitable bias-corrected sandwich variance. Two trial examples are provided to illustrate the new sample size procedure.

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.

A note on implementation of decaying product correlation structures for quasi-least squares.

This note implements an unstructured decaying product matrix via the quasi-least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations. The structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix. It is straightforward to show that the quasi-least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure. Furthermore, subject to conditions that are easily checked, the quasi-least squares estimators are valid for longitudinal Bernoulli data. We demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable.