Saddlepoint p-values for a class of location-scale tests.

The main idea of this paper is to approximate the exact p-value of a class of non-parametric, two-sample location-scale tests. In this paper, the most famous non-parametric two-sample location-scale tests are formulated in a class of linear rank tests. The permutation distribution of this class is derived from a random allocation design. This allows us to approximate the exact p-value of the non-parametric two-sample location-scale tests of the considered class using the saddlepoint approximation method. The proposed method shows high accuracy in approximating the exact p-value compared to the normal approximation method. Moreover, the proposed method only requires a few calculations and time, as in the case of the simulated method. The procedures of the proposed method are clarified through four sets of real data that represent applications for a number of different fields. In addition, a simulation study compares the proposed method with the traditional methods to approximate the exact p-value of the specified class of the non-parametric two-sample location-scale tests.

Saddlepoint p-values for a class of location-scale tests under randomized block design.

This paper deals with a class of nonparametric two-sample location-scale tests. The purpose of this paper is to approximate the exact p-value of the considered class under a randomized block design. The exact p-value of the considered class is approximated by the saddlepoint approximation method, also by the traditional method which is the normal approximation method. The saddlepoint approximation method is more accurate than the normal approximation method in approximating the exact p-value, and does not take a lot of time like the simulation method. This accuracy is proved by applying the mentioned methods to two real data sets and a simulation study.

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.

A new approach for approximating the p-value of a class of bivariate sign tests.

Bivariate data are frequently encountered in many applied fields, including econometrics, engineering, physiology, biology, and medicine. For bivariate analysis, a wide range of non-parametric and parametric techniques can be applied. There are fewer requirements needed for non-parametric procedures than for parametric ones. In this paper, the saddlepoint approximation method is used to approximate the exact p-values of some non-parametric bivariate tests. The saddlepoint approximation is an approximation method used to approximate the mass or density function and the cumulative distribution function of a random variable based on its moment generating function. The saddlepoint approximation method is proposed in this article as an alternative to the asymptotic normal approximation. A comparison between the proposed method and the normal asymptotic approximation method is performed by conducting Monte Carlo simulation study and analyzing three numerical examples representing bivariate real data sets. In general, the results of the simulation study show the superiority of the proposed method over the asymptotic normal approximation method.

Weighted log-rank tests for censored data under Wei's urn design: saddlepoint approximation and confidence intervals.

The randomization designs in clinical trials provide probabilistic basis for the statistical inference of the permutation tests. One of the widely used designs to avoid the problems of imbalance and selection bias for one of the treatments is Wei's urn design. In this article, the saddlepoint approximation is suggested to approximate the p-values of the weighted log-rank class of two-sample tests under Wei's urn design. To show the accuracy of the proposed method and to clarify its procedure, two sets of real data are analyzed, and a simulation study is conducted using different sample sizes and three different life time distributions. Through the illustrative examples and simulation study, a comparison is made between the proposed method and the traditional method, which is the normal approximation method. All of these procedures confirmed that the proposed method is more accurate and efficient than the normal approximation method in approximating the exact p-value of the considered class of tests. As a result, the nominal 95% confidence intervals for the treatment effect are determined.

Weighted log-rank tests for left-truncated data under Wei's urn design: saddlepoint p-values and confidence intervals.

Left-truncated data are constructed from the time of an initial event and the time of the event of interest. That is to say, each individual represented by such data is exposed to an event prior to the event of interest, and both times are recorded. Weighted log-rank testing is commonly used for such data. In this paper, a saddlepoint approximation method is provided for computing p-values of the permutation distribution of tests from the weighted log-rank testing in the presence of left-truncated data and Wei's urn design. A simulation study is used to assess the efficiency of the saddlepoint approximation. The accuracy of the saddlepoint approximation in comparison to the normal approximation enables us to compute accurate confidence intervals for the treatment effect.

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.

Weighted log-rank tests for clustered censored data: Saddlepoint p-values and confidence intervals.

Clustered data with censored failure times frequently arise in clinical trials and tumorigenicity studies. For such data, the common and extensively used class of two-sample tests is the weighted log-rank tests. In this article, a double saddlepoint approximation is used to calculate the p-values of the null permutation distribution of these tests. This technique is demonstrated using three real clustered data sets. Comprehensive simulation studies are conducted to appraise the efficiency of the saddlepoint approximation. This approximation is far superior to the asymptotic normal approximation. This precision allows us to determine almost exact confidence intervals for the treatment impact.