Bayesian estimation of false-negative rate in a clinical trial of sentinel node biopsy

Estimating the false-negative rate is a major issue in evaluating sentinel node biopsy (SNB) for staging cancer. In a large multicentre trial of SNB for intra-operative staging of clinically node-negative breast cancer, two sources of information on the false-negative rate are available.Direct information is available from a preliminary validation phase: all patients underwent SNB followed by axillary nodal clearance or sampling. Of 803 patients with successful sentinel node localization, 19 (2.4 per cent) were classed as false negatives. Indirect information is also available from the randomized phase. Ninety-seven (25.4 per cent) of 382 control patients undergoing axillary clearance had positive axillae. In the experimental group, 94/366 (25.7 per cent) were apparently node positive. Taking a simple difference of these proportions gives a point estimate of -0.3 per cent for the proportion of patients who had positive axillae but were missed by SNB. This estimate is clearly inadmissible. In this situation, a Bayesian analysis yields interpretable point and interval estimates. We consider the single proportion estimate from the validation phase; the difference between independent proportions from the randomized phase, both unconstrained and constrained to non-negativity; and combined information from the two parts of the study. As well as tail-based and highest posterior density interval estimates, we examine three obvious point estimates, the posterior mean, median and mode. Posterior means and medians are similar for the validation and randomized phases separately and combined, all between 2 and 3 per cent, indicating similarity rather than conflict between the two data sources.