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A prospective cohort study of men with newly diagnosed early prostate cancer was undertaken Talcott et al. (1998) in order to evaluate both the patient-level and the physician-level determinants of physician recommendations for radical prostatectomy (surgery) versus radiation therapy. Each patient sought recommendations from as many as six physicians, and each physician provided recommendations for as many as 113 patients. Thus, the recommendations are clustered within physician and within patient. While methods have been developed for binary data with multiple-nested sources of clustering, they have not been fully explored for binary data with non-nested sources of clustering, such as the treatment recommendations. Here we propose reclustering the data to form binary data with one source of clustering. Because the reclustered data result in one very large cluster and several clusters of size one and two, marginal logistic regression models for the probability of a recommendation of surgery fit using a generalized estimating equation approach would produce unreliable estimates of uncertainty for the parameters. Thus, in addition to the mean model, we attempt to model the associations in as much detail as possible. We compare this model to a mixed-effects model that implicitly adjusts for both sources of clustering and to models based on the assumption of conditional independence with regard to one source of clustering.

Binary data with two, non-nested sources of clustering: an analysis of physician recommendations for early prostate cancer treatment