The Cytel blog keeps you up to speed with the latest developments in biostatistics and clinical biometrics.
By Ashwini Joshi
For small sample data or rare events data, exact non-parametric tests perform better than asymptotic tests. But they come with the disadvantage of conservativeness. Many corrections have been suggested to reduce this conservativeness but none of them solve the problems entirely. StatXact provides various methods of computing exact p-values. Depending upon the problem at hand, the user can decide which one to use.
Let’s consider a hypothetical example of stratified count data. The example shows two sample data with two strata. Events in Treatment1 are rare as compared to the ones in Treatment0. But the event rates are comparable.
When conducting Maximum Likelihood Estimation, it is assumed that the maximum likelihood estimate follows a normal distribution. However, this may not be true in the case of small sample or sparse data.
Since the standard errors of the general linear model are based on asymptotic variance, they may not be a good estimator of standard error for small samples. In particular, Wald Confidence Intervals may not perform very well. One should only use the Wald Confidence Interval if the likelihood function is symmetric about the MLE.