Power and sample size calculation for paired right-censored data based on survival copula models

Sample size determination is essential during the planning phases of clinical trials. To calculate the required sample size for paired right-censored data, the structure of the within-paired correlations needs to be pre-specified. In this article, we consider using popular parametric copula models, including the Clayton, Gumbel, or Frank families, to model the distribution of joint survival times. Under each copula model, we derive a sample size formula based on the testing framework for rank-based tests and non-rank-based tests (i.e., logrank test and Kaplan–Meier statistic, respectively). We also investigate how the power or the sample size was affected by the choice of testing methods and copula model under different alternative hypotheses. In addition to this, we examine the impacts of paired-correlations, accrual times, follow-up times, and the loss to follow-up rates on sample size estimation. Finally, two real-world studies are used to illustrate our method and R code is available to the user.     

A pooled Bayes test of independence for sparse contingency tables from small areas

We study the association between bone mineral density (BMD) and body mass index (BMI) when contingency tables are constructed from the several U.S. counties, where BMD has three levels (normal, osteopenia and osteoporosis) and BMI has four levels (underweight, normal, overweight and obese). We use the Bayes factor (posterior odds divided by prior odds or equivalently the ratio of the marginal likelihoods) to construct the new test. Like the chi-squared test and Fisher's exact test, we have a direct Bayes test which is a standard test using data from each county. In our main contribution, for each county techniques of small area estimation are used to borrow strength across counties and a pooled test of independence of BMD and BMI is obtained using a hierarchical Bayesian model. Our pooled Bayes test is computed by performing a Monte Carlo integration using random samples rather than Gibbs samples. We have seen important differences among the pooled Bayes test, direct Bayes test and the Cressie-Read test that allows for some degree of sparseness, when the degree of evidence against independence is studied. As expected, we also found that the direct Bayes test is sensitive to the prior specifications but the pooled Bayes test is not so sensitive. Moreover, the pooled Bayes test has competitive power properties, and it is superior when the cell counts are small to moderate.     

Modified Wilcoxon–Mann–Whitney Test and Power Against Strong Null

The Wilcoxon–Mann–Whitney (WMW) test is a popular rank-based two-sample testing procedure for the strong null hypothesis that the two samples come from the same distribution. A modified WMW test, the Fligner–Policello (FP) test, has been proposed for comparing the medians of two populations. A fact that may be under-appreciated among some practitioners is that the FP test can also be used to test the strong null like the WMW. In this article, we compare the power of the WMW and FP tests for testing the strong null. Our results show that neither test is uniformly better than the other and that there can be substantial differences in power between the two choices. We propose a new, modified WMW test that combines the WMW and FP tests. Monte Carlo studies show that the combined test has good power compared to either the WMW and FP test. We provide a fast implementation of the proposed test in an open-source software. Supplementary materials for this article are available online.     

Global kernel estimator and test of varying‐coefficient autoregressive model

We propose a varying‐coefficient autoregressive model that contains additive models, varying‐ coefficient models, partially linear models and low‐dimensional interaction models as special cases. A global kernel backfitting method is proposed for the estimation and inference of parameters and unknown functions in this model. Key large‐sample results are established, including estimation consistency, asymptotic normality and the generalized likelihood ratio test for parameters and non‐parametric functions. The proposed methodology is examined by simulation studies and applied to examine the relationship between suicide news reports in the three leading newspapers and the daily number of suicides in Taiwan. The relationship between the media reporting and suicide incidence has been established and explored. The Canadian Journal of Statistics 47: 487–519; 2019 © 2019 Statistical Society of Canada     

Simultaneous estimation of Cronbach’s alpha coefficients

The simultaneous estimation of Cronbachs alpha coefficients from q populations under the compound symmetry assumption is considered. In a multi-sample scenario, it is suspected that all the Cronbachs alpha coefficients are identical. Consequently, the inclusion of non-sample information (NSI) on the homogeneity of Cronbachs alpha coefficients in the estimation process may improve precision. We propose improved estimators based on the linear shrinkage, preliminary test, and the Steins type shrinkage strategies, to incorporate available NSI into the estimation. Their asymptotic properties are derived and discussed using the concepts of bias and risk. Extensive Monte-Carlo simulations were conducted to investigate the performance of the estimators.     

Tests for noninferiority trials with binomial endpoints: A guide to modern and quasi‐exact methods for biomedical researchers

Applied statisticians and pharmaceutical researchers are frequently involved in the design and analysis of clinical trials where at least one of the outcomes is binary. Treatments are judged by the probability of a positive binary response. A typical example is the noninferiority trial, where it is tested whether a new experimental treatment is practically not inferior to an active comparator with a prespecified margin δ. Except for the special case of δ = 0, no exact conditional test is available although approximate conditional methods (also called second‐order methods) can be applied. However, in some situations, the approximation can be poor and the logical argument for approximate conditioning is not compelling. The alternative is to consider an unconditional approach. Standard methods like the pooled z‐test are already unconditional although approximate. In this article, we review and illustrate unconditional methods with a heavy emphasis on modern methods that can deliver exact, or near exact, results. For noninferiority trials based on either rate difference or rate ratio, our recommendation is to use the so‐called E‐procedure, based on either the score or likelihood ratio statistic. This test is effectively exact, computationally efficient, and respects monotonicity constraints in practice. We support our assertions with a numerical study, and we illustrate the concepts developed in theory with a clinical example in pulmonary oncology; R code to conduct all these analyses is available from the authors.     

Sample size calculation for the one‐sample log‐rank test

In this paper, an exact variance of the one‐sample log‐rank test statistic is derived under the alternative hypothesis, and a sample size formula is proposed based on the derived exact variance. Simulation results showed that the proposed sample size formula provides adequate power to design a study to compare the survival of a single sample with that of a standard population. Copyright © 2014 John Wiley & Sons, Ltd.     

A simulation study on the influence of ties on uniform scores test for circular data

Uniform scores test is a rank-based method that tests the homogeneity of k-populations in circular data problems. The influence of ties on the uniform scores test has been emphasized by several authors in several articles and books. Moreover, it is suggested that the uniform scores test should be used with caution if ties are present in the data. This paper investigates the influence of ties on the uniform scores test by computing the power of the test using average, randomization, permutation, minimum, and maximum methods to break ties. Monte Carlo simulation is performed to compute the power of the test under several scenarios such as having 5% or 10% of ties and tie group structures in the data. The simulation study shows no significant difference among the methods under the existence of ties but the test loses its power when there are many ties or complicated group structures. Thus, randomization or average methods are equally powerful to break ties when applying uniform scores test. Also, it can be concluded that k-sample uniform scores test can be used safely without sacrificing the power if there are only less than 5% of ties or at most two groups of a few ties.     

The effect of weight function on hypothesis testing in weighted sampling

In this paper the problem of statistical hypothesis testing under weighted sampling is considered for obtaining the most powerful test. Some simulated powers of tests, using the Monte Carlo method, are performed. Using a convenient sample of the specialist physicians of Social Security Organization of Ahvaz in Iran, two weighted samplings versus random sampling are tested. Among the three mentioned sampling, the size-biased sampling order 0.2 is more appropriate for the mechanism of data collection.