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

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.

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.

Saddlepoint p-values for a class of nonparametric tests for the current status and panel count data under generalized permuted block design

<abstract><p>Current status and panel count data appear in many applied fields, including medicine, clinical trials, epidemiology, econometrics, demography, engineering and public health. Therefore, in this article, we use the saddlepoint approximation method to approximate the exact p-value of a number of nonparametric tests for the current status and panel count data under a generalized permuted block design. The saddlepoint approximation is referred to as higher-order approximation and it is more accurate than the methods that lead to approximations that are accurate to the first order, such as the asymptotic normal approximation method. To verify the accuracy and efficiency of the saddlepoint approximation method, a simulation study is conducted. The simulation study results confirm that the saddlepoint approximation method is more powerful than the existing approximation method. Furthermore, number of real current status and panel count data sets are analyzed and displayed as illustrative examples.</p></abstract>