GEECORR: A SAS macro for regression models of correlated binary responses and within-cluster correlation using generalized estimating equations

Multiple Imputation for Partial Recording Periodontal Examination Protocols

AIM

Partial-mouth recording protocols often result in underestimation of population prevalence and extent of periodontitis. We posit that multiple imputation of measures such as clinical attachment loss for nonselected tooth sites in partial-mouth samples can reduce bias in periodontitis estimates.

METHODS

Multiple imputation for correlated site-level dichotomous outcomes in a generalized estimating equations framework is used to impute site-level binary indicators for clinical attachment loss exceeding a fixed threshold in partial-mouth samples. Periodontitis case definitions are applied to the imputed "complete" dentitions, enabling estimation of prevalence and other summaries of periodontitis for partial-mouth samples as if for full-mouth examinations. A multiple imputation-bootstrap procedure is described and applied for point and variance estimation of these periodontitis measures. The procedure is evaluated with pseudo-partial-mouth samples based on random site selection protocols of 28 to 84 periodontal sites repeatedly generated from full-mouth periodontal examinations of 3,621 participants in the 2013 to 2014 National Health and Nutrition Examination Survey (NHANES) survey.

RESULTS

Multiple imputation applied to partial-mouth samples overestimated periodontitis mean extent, defined as the number of sites with clinical attachment loss 3 mm or greater, by 9.5% in random site selection protocols with 84 sites and overestimated prevalence by 5% to 10% in all the evaluated protocols.

CONCLUSIONS

In the 2013 to 2014 NHANES data, multiple imputation of site-level periodontal indicators provides less biased estimates of periodontitis prevalence and extent than has been reported from estimates based on the direct application of full-mouth case definitions to partial-mouth samples. Multiple imputation provides a promising solution to the longstanding, vexing problem of estimation bias in partial-mouth recording, with potential application to a wide array of case definitions, periodontitis measures, and partial recording protocols.

KNOWLEDGE TRANSFER STATEMENT

Partial-mouth sampling, while a resource-efficient strategy for obtaining oral disease estimates, often results in underestimation of periodontitis metrics. Multiple imputation for nonselected periodontal sites produces pseudo-full-mouth data sets that may be analyzed and combined to produce estimates with small bias.

Patterns of site-level periodontal disease and within-mouth correlation among older adults in the Hispanic Community Health Study/Study of Latinos

OBJECTIVES

Clinical measures of periodontal disease such as attachment loss (CAL) and probing depth (PD) vary considerably between and within individuals with periodontitis and are known to be influenced by person-level factors (e.g. age and race/ethnicity) as well as intraoral characteristics (e.g. tooth type and location). This study sought to characterize site-level disease patterns and correlations using both person-level and intraoral factors through a model-based approach.

METHODS

This study used full-mouth, six sites per tooth, periodontal examination data collected from 2301 Hispanic/Latino adults aged 60-74 years in the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). The presence of site-level CAL ≥3 mm and PD ≥4 mm was estimated using generalized estimating equations (GEE), explicitly modelling pairwise periodontal site correlations, while adjusting for number of teeth, sex and Hispanic/Latino background. Subsequently tooth- and tooth-site patterns of intraoral CAL ≥3 mm and PD ≥4 mm were estimated and visualized in the HCHS/SOL population.

RESULTS

The findings showed that posterior sites had the highest odds of CAL ≥3 mm and PD ≥4 mm. Sites located in the interproximal space had higher odds of PD ≥4 mm but lower odds of CAL ≥3 mm than non-interproximal sites. Mexicans had the lowest odds of CAL ≥3 mm among all Hispanic/Latino backgrounds. While Mexicans had lower odds of PD ≥4 mm than Central Americans and Cubans, they had higher odds than Dominicans and Puerto Ricans. Site-level proportions and pairwise correlations of PD ≥4 mm were generally smaller than those of CAL ≥3 mm.

CONCLUSIONS

The patterns of site-level probabilities of clinical measures of periodontal disease can be defined based on tooth, site and individual-level characteristics. Intraoral correlation patterns, while complex, are quantifiable. The risk factors for site-level CAL ≥3 mm may differ from those of PD ≥4 mm. Likewise, participant risk factors for site-level clinical measures of periodontal disease are distinct from those that affect individual-level periodontitis prevalence. Future epidemiological investigations should consider model-based approaches when examining site-level disease probabilities to identify intra-oral patterns of periodontal disease and make inferences about the larger population.

GEEMAEE: A SAS macro for the analysis of correlated outcomes based on GEE and finite-sample adjustments with application to cluster randomized trials

BACKGROUND AND OBJECTIVES

Generalized estimating equations (GEE) are used to analyze correlated outcomes in marginal regression models with population-averaged interpretations of exposure effects. Limitations of popular software for GEE include: (i) user choice is restricted to a small set of within-cluster pairwise correlation (intra-class correlation; ICC) structures; and (ii) inference on ICC parameters is usually not possible because the precision of their estimates is not quantified. This is important because ICC values inform the design of cluster randomized trials. Beyond the standard GEE implementation, use of paired estimating equations (Prentice 1988) provides: (i) flexible specification of models for pairwise correlations and (ii) standard errors for ICC estimates. However, most GEEs give biased estimates of standard errors and correlations when the number of clusters is small (roughly, ≤40). Consequently, there is a need for software to provide GEE analysis with finite-sample bias-corrections.

METHODS

The SAS macro GEEMAEE implements paired estimating equations to simultaneously estimate parameters in marginal mean and ICC models. It provides bias-corrected standard errors and uses matrix-adjusted estimating equations (MAEE) for bias-corrected estimation of correlations. Several built-in correlation matrix options, rarely found in software, are offered for multi-period, cluster randomized trials and similarly structured longitudinal observational data structures. Additional options include user-specified correlation structures and deletion diagnostics, namely Cooks' Distance and DBETA statistics that estimate the influence of observations, cluster-periods (when applicable) and clusters.

RESULTS

GEEMAEE is illustrated for a binary and a count outcome in two stepped wedge cluster randomized trials and a binary outcome in a longitudinal study of disease surveillance. Use of MAEE resulted in larger values of correlation estimates compared to uncorrected estimating equations. Use of bias-corrected variance estimators resulted in (appropriately) larger values of standard errors compared to the usual sandwich estimators. Deletion diagnostics identified the clusters and cluster-periods having the most influence.

CONCLUSIONS

The SAS macro GEEMAEE provides regression analysis for clustered or longitudinal responses, and is particularly useful when the number of clusters is small. Flexible specification and bias-corrected estimation of pairwise correlation parameters and standard errors are key features of the software to provide valid inference in real-world settings.