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Estimating tumor response rates using shrinkage estimates
Author(s) -
Kathman S. J.,
Hale M. D.
Publication year - 2004
Publication title -
clinical pharmacology and therapeutics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.941
H-Index - 188
eISSN - 1532-6535
pISSN - 0009-9236
DOI - 10.1016/j.clpt.2003.11.161
Subject(s) - statistics , bayes' theorem , estimator , shrinkage estimator , variance (accounting) , econometrics , estimation , mathematics , mean squared error , shrinkage , computer science , bayesian probability , minimum variance unbiased estimator , bias of an estimator , accounting , management , economics , business
The development of anti‐cancer therapies usually involve small to moderate size studies to provide initial estimates of response rates before initiating larger studies to better quantify response. These early trials often each contain a single tumor type, possibly using other stratification factors. Response rate for a given tumor type is routinely reported as the percentage of patients meeting a pre‐specified criteria for tumor shrinkage, without any regard to response in the other studies. These estimates have variances that are usually large, especially for small to moderate size studies, so that the estimates may be far from the true values. The approach presented here is offered as a way to improve overall estimation of response rates when several small trials are considered. Shrinkage estimates (James‐Stein/Empirical Bayes and Hierarchical Bayes) are alternative estimates that use information from all studies to provide potentially better estimates for each study. While these estimates introduce a small bias, they have a considerably smaller variance, and thus tend to be better in terms of total mean squared error. These procedures provide a better view of drug performance in that group of tumor types as a whole, as opposed to estimating each response rate individually without consideration of the others. In technical terms, the vector of estimates is nearer the true values, on average, than the vector of the usual unbiased estimators applied to such trials. This presentation considers the practical use and performance of these estimates for estimating tumor response rates from multiple studies, with each study having different tumor types. In particular, it will be illustrated (mainly through simulations) that these estimates are better in terms of mean squared error; on average these estimates are nearer to the true response rates. Practical advice will be given on how to calculate these estimates. The methods will be applied to data from a group of real trials, as well as simulated data. Clinical Pharmacology & Therapeutics (2004) 75 , P43–P43; doi: 10.1016/j.clpt.2003.11.161