Loss weighting and the human cost of experimentation

This paper analyzes the dilemma faced by clinicians who must determine a proper sample size for a clinical trial. A large sample size may be used to ensure significant results. In so doing, many patients may be randomized to the wrong arm of a clinical trial. Alternatively, fewer patients may be used in a clinical trial, however, the resulting conclusions will be less certain, and future patients may be harmed by false conclusions. This study introduces a ratio of relative human cost or loss associated with a single present patient receiving incorrect therapy during the clinical trial to a single future patient given incorrect therapy after the trial is over. This "loss weighting" ratio can be estimated, the trade-off between present and future loss can be evaluated and the total loss from a clinical trial can be minimized. The resulting method, based on the loss weighting ratio, suggests an inverse relationship between the number of future patients potentially affected by a clinical trial and the size of desired type I and type II error. The conclusions derived from this paper can be incorporated easily into the current process of sample size determination. This is illustrated with examples from two well-known clinical trials.