On outcome-dependent sampling designs for longitudinal binary response data with time-varying covariates

Abstract

A typical longitudinal study prospectively collects both repeated measures of a health status outcome as well as covariates that are used either as the primary predictor of interest or as important adjustment factors. In many situations, all covariates are measured on the entire study cohort. However, in some scenarios the primary covariates are time dependent yet may be ascertained retrospectively after completion of the study. One common example would be covariate measurements based on stored biological specimens such as blood plasma. While authors have previously proposed generalizations of the standard case-control design in which the clustered outcome measurements are used to selectively ascertain covariates (Neuhaus and Jewell, 1990) and therefore provide resource efficient collection of information, these designs do not appear to be commonly used. One potential barrier to the use of longitudinal outcome-dependent sampling designs would be the lack of a flexible class of likelihood-based analysis methods. With the relatively recent development of flexible and practical methods such as generalized linear mixed models (Breslow and Clayton, 1993) and marginalized models for categorical longitudinal data (see Heagerty and Zeger, 2000, for an overview), the class of likelihood-based methods is now sufficiently well developed to capture the major forms of longitudinal correlation found in biomedical repeated measures data. Therefore, the goal of this manuscript is to promote the consideration of outcome-dependent longitudinal sampling designs and to both outline and evaluate the basic conditional likelihood analysis allowing for valid statistical inference.

Fig. 1.

Profile log-likelihood surface plots: A grid search was used for combinations of β₀ and β₁ values, and log-likelihoods were maximized with respect to the marginalized transition model dependence parameter γ. Panels on the left and center denote the original cohort log-likelihood surfaces and the outcome-dependent sample conditional log-likelihood surfaces, respectively. Both sets of plots have been centered at their maxima. The panels on the right represent the summary likelihood or the difference between the maximum likelihood and the conditional maximum likelihood surfaces. The top, middle, and bottom rows depict surfaces for which ρ_x values are equal to 0, 0.5, and 1, respectively. Each contour represents a log-likelihood value difference of 1, and the range (width and height) for all plots in the same row is 5 conditional maximum likelihood standard error estimates wide. 1