A nonparametric Bayesian model for inference in related longitudinal studies

Summary.  We discuss a method for combining different but related longitudinal studies to improve predictive precision. The motivation is to borrow strength across clinical studies in which the same measurements are collected at different frequencies. Key features of the data are heterogeneous populations and an unbalanced design across three studies of interest. The first two studies are phase I studies with very detailed observations on a relatively small number of patients. The third study is a large phase III study with over 1500 enrolled patients, but with relatively few measurements on each patient. Patients receive different doses of several drugs in the studies, with the phase III study containing significantly less toxic treatments. Thus, the main challenges for the analysis are to accommodate heterogeneous population distributions and to formalize borrowing strength across the studies and across the various treatment levels. We describe a hierarchical extension over suitable semiparametric longitudinal data models to achieve the inferential goal. A nonparametric random-effects model accommodates the heterogeneity of the population of patients. A hierarchical extension allows borrowing strength across different studies and different levels of treatment by introducing dependence across these nonparametric random-effects distributions. Dependence is introduced by building an analysis of variance (ANOVA) like structure over the random-effects distributions for different studies and treatment combinations. Model structure and parameter interpretation are similar to standard ANOVA models. Instead of the unknown normal means as in standard ANOVA models, however, the basic objects of inference are random distributions, namely the unknown population distributions under each study. The analysis is based on a mixture of Dirichlet processes model as the underlying semiparametric model.     

Measurement error correction for the cumulative average model in the survival analysis of nutritional data: application to Nurses’ Health Study

The use of the cumulative average model to investigate the association between disease incidence and repeated measurements of exposures in medical follow-up studies can be dated back to the 1960s (Kahn and Dawber, J Chron Dis 19:611–620, 1966). This model takes advantage of all prior data and thus should provide a statistically more powerful test of disease-exposure associations. Measurement error in covariates is common for medical follow-up studies. Many methods have been proposed to correct for measurement error. To the best of our knowledge, no methods have been proposed yet to correct for measurement error in the cumulative average model. In this article, we propose a regression calibration approach to correct relative risk estimates for measurement error. The approach is illustrated with data from the Nurses’ Health Study relating incident breast cancer between 1980 and 2002 to time-dependent measures of calorie-adjusted saturated fat intake, controlling for total caloric intake, alcohol intake, and baseline age.     

The average area under correlated receiver operating characteristic curves: a nonparametric approach based on generalized two-sample Wilcoxon statistics

It is well known that, when sample observations are independent, the area under the receiver operating characteristic (ROC) curve corresponds to the Wilcoxon statistics if the area is calculated by the trapezoidal rule. Correlated ROC curves arise often in medical research and have been studied by various parametric methods. On the basis of the Mann–Whitney U-statistics for clustered data proposed by Rosner and Grove, we construct an average ROC curve and derive nonparametric methods to estimate the area under the average curve for correlated ROC curves obtained from multiple readers. For the more complicated case where, in addition to multiple readers examining results on the same set of individuals, two or more diagnostic tests are involved, we derive analytic methods to compare the areas under correlated average ROC curves for these diagnostic tests. We demonstrate our methods in an example and compare our results with those obtained by other methods. The nonparametric average ROC curve and the analytic methods that we propose are easy to explain and simple to implement.