Likelihood-based analysis of longitudinal data from outcome-related sampling designs.

Investigators commonly gather longitudinal data to assess changes in responses over time and to relate these changes to within-subject changes in predictors. With rare or expensive outcomes such as uncommon diseases and costly radiologic measurements, outcome-dependent, and more generally outcome-related, sampling plans can improve estimation efficiency and reduce cost. Longitudinal follow up of subjects gathered in an initial outcome-related sample can then be used to study the trajectories of responses over time and to assess the association of changes in predictors within subjects with change in response. In this article, we develop two likelihood-based approaches for fitting generalized linear mixed models (GLMMs) to longitudinal data from a wide variety of outcome-related sampling designs. The first is an extension of the semi-parametric maximum likelihood approach developed in Neuhaus, Scott and Wild (2002, Biometrika 89, 23-37) and Neuhaus, Scott and Wild (2006, Biometrics 62, 488-494) and applies quite generally. The second approach is an adaptation of standard conditional likelihood methods and is limited to random intercept models with a canonical link. Data from a study of attention deficit hyperactivity disorder in children motivates the work and illustrates the findings.

A Hardy-Weinberg equilibrium test for analyzing population genetic surveys with complex sample designs.

Testing for deviations from Hardy-Weinberg equilibrium is a widely recommended practice for population-based genetic association studies. However, current methods for this test assume a simple random sample and may not be appropriate for sample surveys with complex survey designs. In this paper, the authors present a test for Hardy-Weinberg equilibrium that adjusts for the sample weights and correlation of data collected in complex surveys. The authors perform this test by using a simple adjustment to procedures developed to analyze data from complex survey designs available within the SAS statistical software package (SAS Institute, Inc., Cary, North Carolina). Using 90 genetic markers from the Third National Health and Nutrition Examination Survey, the authors found that survey-adjusted and -unadjusted estimates of the disequilibrium coefficient were generally similar within self-reported races/ethnicities. However, estimates of the variance of the disequilibrium coefficient were significantly different between the 2 methods. Because the results of the survey-adjusted tests account for correlation among participants sampled within the same cluster, and the possibility of having related individuals sampled from the same household, the authors recommend use of this test when analyzing genetic data originating from sample surveys with complex survey designs to assess deviations from Hardy-Weinberg equilibrium.

Secondary analysis of case-control data.

We extend the discussion of Lee et al. and others on methods for performing secondary analyses of case-control sampled data and carry out an extensive investigation of efficiency and robustness. We find that, with the exception of the 'analyse-the-controls-only' strategy for populations in which cases are rare, ad hoc methods in common usage often lead to extremely misleading conclusions and that it is not possible to tell in advance when this will happen. Weighted likelihood and semi-parametric maximum likelihood methods are justified theoretically. We find that semi-parametric maximum likelihood can be as much as twice as efficient as the weighted method, but is subject to bias in estimating parameters of interest when the nuisance models this method requires have been mis-specified. The weighted method needs no nuisance models and thus is robust in this regard, but we cannot tell when it is going to be very inefficient without sophisticated modelling as through the SPML method. Practitioners should routinely use both methods and will often have to weigh up the practical consequences of severe inefficiency and lack of robustness in the context of their enquiries.