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.

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 p-values of weighted log-rank tests based on censored clustered data under block Efron's biased-coin design

Clustered survival data frequently occurs in biomedical research fields and clinical trials. The log-rank tests are used for two independent samples of clustered data tests. We use the block Efron's biased-coin randomization (design) to assign patients to treatment groups in a clinical trial by forcing a sequential experiment to be balanced. In this article, 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 demonstrates 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.

Sparse One-Grab Sampling with Probabilistic Guarantees

Sampling is an important and effective strategy in analyzing "big data," whereby a smaller subset of a dataset is used to estimate the characteristics of its entire population. The main goal in sampling is often to achieve a significant gain in the computational time. However, a major obstacle towards this goal is the assessment of the smallest sample size needed to ensure, with a high probability, a faithful representation of the entire dataset, especially when the data set is compiled of a large number of diverse structures (e.g., clusters). To address this problem, we propose a method referred to as the Sparse Withdrawal of Inliers in a First Trial (SWIFT) that determines the smallest sample size of a subset of a dataset sampled in one grab, with the guarantee that the subset provides a sufficient number of samples from each of the underlying structures necessary for the discovery and inference. The latter is established with high probability, and the lower bound of the smallest sample size depends on probabilistic guarantees. In addition, we derive an upper bound on the smallest sample size that allows for detection of the structures and show that the two bounds are very close to each other in a variety of scenarios. We show that the problem can be modeled using either a hypergeometric or a multinomial probability mass function (pmf), and derive accurate mathematical bounds to determine a tight approximation to the sample size, leading thus to a sparse sampling strategy. The key features of the proposed method are: (i) sparseness of the sampled subset for analyzing data, where the level of sparseness is independent of the population size; (ii) no prior knowledge of the distribution of data, or the number of underlying structures in the data; and (iii) robustness in the presence of overwhelming number of outliers. We evaluate the method thoroughly in terms of accuracy, its behavior against different parameters, and its effectiveness in reducing the computational cost in various applications of computer vision, such as subspace clustering and structure from motion.