Saddlepoint Approximations for Permutation Tests and Confidence Intervals

P-values and confidence intervals for weighted log-rank tests under truncated binomial design based on clustered medical data

The randomization design employed to gather the data is the basis for the exact distributions of the permutation tests. One of the designs that is frequently used in clinical trials to force balance and remove experimental bias is the truncated binomial design. The exact distribution of the weighted log-rank class of tests for censored cluster medical data under the truncated binomial design is examined in this paper. For p-values in this class, a double saddlepoint approximation is developed using the truncated binomial design. With the right censored cluster data, the saddlepoint approximation's speed and accuracy over the normal asymptotic make it easier to invert the weighted log-rank tests and find nominal 95 % confidence intervals for the treatment effect.

P-values and confidence intervals of linear rank tests for left-truncated data under truncated binomial design

The paper provides computations comparing the accuracy of the saddlepoint approximation approach and the normal approximation method in approximating the mid-p-value of Wilcoxon and log-rank tests for the left-truncated data using a truncated binomial design. The paper uses real data examples to apply the comparison, along with some simulated studies. Confidence intervals are provided by the inversion of the tests under consideration.

The weighted log-rank tests based on stratified clustered survival data: saddle-point p-values and confidence intervals

Clinical studies sometimes provide clustered data with censored failure times. A crucial factor of the randomized design that lessens selection bias is the random allocation rule. Given this, the weighted rank tests' p-values for stratified survival clustered sampling based on the random allocation rule are approximated using the double saddle-point approximation technique. For tests of significance and confidence intervals for the treatment effect, this approximation can be utilized. Through simulation experiments, the accuracy of the saddle-point approximation is examined by comparing saddle-point and normal approximations to the exact underlying permutation distribution.

Saddlepoint approximation for weighted log-rank tests based on block truncated binomial design

Clustered data frequently occur in biomedical research fields and clinical trials. The log-rank tests are widely used for two-independent samples of clustered data tests. The randomized block design and truncated binomial design are used for forcing balance in clinical trials and reducing selection bias. In this paper, survival clustered data are randomized by generalized randomized block, and subsequently clustered data in each block are randomized by truncated binomial design. Consequently, the p-values of the null permutation distribution of log-rank tests for clustered data are approximated via the double saddlepoint approximation method. Comprehensive numerical studies are carried out to assess the accuracy of the saddlepoint approximation. This approximation has a great accuracy over the asymptotic normal approximation.

Statistical Inference of the Class of Nonparametric Tests for the Panel Count and Current Status Data from the Perspective of the Saddlepoint Approximation

Many statisticians resort to using the asymptotic normal approximation method to carry out statistical inference for many statistical tests, especially nonparametric ones. In this article, the saddlepoint approximation method is proposed as an alternative to the asymptotic normal approximation method to carry out statistical inference for a number of nonparametric tests for an important type of data that appears frequently in many clinical studies such as cancer and tumorigenicity studies. In clinical trials, there are many strategies through which treatments are assigned to patients. Equal allocation of both treatments is a largely prevalent approach in clinical trials to eliminate experimental bias and increase power. Accordingly, the statistical analysis is carried out based on the truncated binomial design, which is one of the designs that achieve a perfect balance between the two treatments. To clarify the accuracy of the proposed approximation method, two sets of real data are analyzed, and for the same purpose, a comprehensive simulation study is carried out.

Log-rank tests for censored clustered data under generalized randomized block design: Saddlepoint approximation

The weighted log-rank class is the common and widely used class of two-sample tests for clustered data. Clustered data with censored failure times often arise in tumorigenicity investigations and clinical trials. The randomized block design is a significant design that reduces both unintentional bias and selection bias. Accordingly, the p-values of the null permutation distribution of weighted log-rank class for clustered data are approximated using the double saddlepoint approximation technique. Comprehensive simulation studies are carried out to appraise the accuracy of the saddlepoint approximation. This approximation exhibits a significant improvement in precision over the asymptotic approximation. This precision motivates us to determine the approximated confidence intervals for the treatment impact.

Fast approximation of small p-values in permutation tests by partitioning the permutations

Researchers in genetics and other life sciences commonly use permutation tests to evaluate differences between groups. Permutation tests have desirable properties, including exactness if data are exchangeable, and are applicable even when the distribution of the test statistic is analytically intractable. However, permutation tests can be computationally intensive. We propose both an asymptotic approximation and a resampling algorithm for quickly estimating small permutation p-values (e.g., <10-6) for the difference and ratio of means in two-sample tests. Our methods are based on the distribution of test statistics within and across partitions of the permutations, which we define. In this article, we present our methods and demonstrate their use through simulations and an application to cancer genomic data. Through simulations, we find that our resampling algorithm is more computationally efficient than another leading alternative, particularly for extremely small p-values (e.g., <10-30). Through application to cancer genomic data, we find that our methods can successfully identify up- and down-regulated genes. While we focus on the difference and ratio of means, we speculate that our approaches may work in other settings.