Computation of CIs for Binomial proportions in SAS and its practical difficulties
نویسنده
چکیده
In clinical trial data analysis, one of the most commonly used method for the analysis of categorical data is the Binomial proportion and their confidence intervals. If the variable of interest is a dichotomous categorical one, i.e. a variable with two levels (e.g. Subjects with serious AEs/Subjects without any serious AEs) then Binomial proportions (or percentages) and their CIs (or %CIs) can be used in the analysis. SAS procedure which is usually used to obtain these proportions and CIs is the PROC FREQ. This paper describes the computation of Clopper Pearson CIs for binomial proportions using the PROC FREQ in SAS, practical difficulties in obtaining the correct CI values in situations like computing the CIs for responders when there are no responses available in the data, and also provides some programming tips to avoid erroneous CI computations. INTRODUCTION In the field of statistics, the Binomial distribution is commonly used in a variety of applications, especially in situations in which the outcomes of interest can be categorized into two, i.e. either a success or a failure. Binomial proportions and their confidence intervals are widely used in oncology trials to evaluate the response rate and are sometimes used in the other trials to assess the overall incidence of adverse events. Confidence intervals for a binomial proportion can be estimated using various methods like Wald’s (Normal Approximation) method or the Clopper-Pearson (exact) method. NORMAL APPROXIMATION METHOD The ‘Normal approximation’ method got its name because of the use of the z-value from the Normal Distribution. Normal approximation method is easy to compute and use of normal approximation method is supported by the central limit theorem and with sufficiently large sample size ‘n’, the Normal distribution is a good estimate of the Binomial distribution. Equation to compute the Binomial CI using the Normal approximation method is given below confidence of level desired for value” “Z ) confidence (desired ce significan of Level size sample n interest of proportion p where, ) 1 (
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