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Abstract:
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In a clinical trial, many times a treatment effect is expressed as ratio of two random variables, such as treatment difference relative to placebo. This presents a problem of computing the confidence interval (CI) where there is no closed form expression for a ratio of two random variables. Bootstrap is a well accepted method to obtain such confidence interval since the method is non-parametric and it is well defined for implementation. But it takes time for bootstrap. In this presentation, we present an alternative method that notably shortens the time of computation under few reasonable assumptions. This method is based on the concept of Fieller’s theorem and assume that two estimated treatment effects follow a bivariate normal distribution and use numerical method directly obtain the frequency distribution using histogram of the ratio and then calculate the confidence interval from the histogram. The proposed method extends Fieller’s method and can be utilized to calculate a confidence interval of any function of two random variables in addition to ratio, e.g., relative treatment effect in terms of two medians with normal assumption on the ranks of sample median. This results from the real trial data are the very similar to as bootstrap method, but confidence interval can always be obtained with relatively much shorter duration.
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