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# Generalizability/Reproducibility Probability

DOI link for Generalizability/Reproducibility Probability

Generalizability/Reproducibility Probability book

# Generalizability/Reproducibility Probability

DOI link for Generalizability/Reproducibility Probability

Generalizability/Reproducibility Probability book

## ABSTRACT

For marketing approval of a new drug product, the United States Food and Drug Administration (FDA) requires that at least two adequate and well-controlled clinical trials be conducted to provide substantial evidence regarding the effectiveness of the drug product under investigation (FDA, 1988). The purpose of conducting the second trial is to study whether the observed clinical result from the Œrst trial is reproducible on the same target patient population. Let H0 be the null hypothesis that the mean response of the drug product is the same as the mean response of a control (e.g., placebo) and Ha be the alternative hypothesis. An observed result from a clinical trial is said to be signiŒcant if it leads to the rejection of H0. It is often of interest to determine whether clinical trials that produced signiŒcant clinical results provide substantial evidence to assure that the results will be reproducible in a future clinical trial with the same study protocol. Under certain circumstance, the FDA Modernization Act (FDAMA) of 1997 includes a provision (Section 115 of FDAMA) to allow data from one adequate and well-controlled clinical trial investigation and conŒrmatory evidence to establish the effectiveness for the risk-beneŒt assessment of drug and biological candidates for approval. Suppose that the null hypothesis H0 is rejected if and only if |T| > c, where c is a positive known constant and T is a test statistic. This is usually related to a two-sided alternative hypothesis. The discussion for one-sided alternative hypotheses is similar. In statistical theory, the probability of observing a signiŒcant clinical result when Ha is indeed true is referred to as the power of the test procedure. If the statistical model under Ha is a parametric model, then the power is

P T c H P T ca( | ) ( | ),> = > θ (25.1)

where θ is an unknown parameter or vector of parameters. Suppose now that one clinical trial has been conducted and the result is signiŒcant. What is the probability that the second trial will produce a signiŒcant result, that is, the signiŒcant result from the Œrst trial is reproducible? Mathematically, if the two

trials are independent, the probability of observing a signiŒcant result from the second trial when Ha is true is still given by (25.1), regardless of whether the result from the Œrst trial is signiŒcant or not. However, information from the Œrst clinical trial should be useful in the evaluation of the probability of observing a signiŒcant result in the second trial. This leads to the concept of reproducibility probability, which is different from the power deŒned by (25.1).