Assessing the power of informative subsets of loci for population assignment: standard methods are upwardly biased

It is well known that statistical classification procedures should be assessed using data that are separate from those used to train the classifier. This principle is commonly overlooked when the classification procedure in question is population assignment using a set of genetic markers that were chosen specifically on the basis of their allele frequencies from amongst a larger number of candidate markers. This oversight leads to a systematic upward bias in the predicted accuracy of the chosen set of markers for population assignment. Three widely used software programs for selecting markers informative for population assignment suffer from this bias. The extent of this bias is documented through a small set of simulations. The relative effect of the bias is largest when screening many candidate loci from poorly differentiated populations. Simple unbiased methods are presented and their use encouraged.     

Exact Tests for Comparing Two Paired Proportions with Incomplete Data

Various asymptotic test procedures have been developed previously for testing the equality of two binomial proportions with partially incomplete paired data. Test procedures that discard incomplete observations have been shown to be less powerful than those procedures that utilize all available observations. On the other hand, asymptotic test procedures that utilize all available observations may not be reliable in small‐sample problems or sparse data structures. In this article, unconditional exact test procedures are proposed for testing the equality of two paired binomial proportions with partially incomplete paired data under a random mechanism. The proposed unconditional exact test methods are illustrated with real data from a neurological study. Empirical studies are conducted to investigate the performance of these and other test procedures with respect to size and power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analyzing Incomplete Data Subject to a Threshold using Empirical Likelihood Methods: An Application to a Pneumonia Risk Study in an ICU Setting

Summary .  The initial detection of ventilator-associated pneumonia (VAP) for inpatients at an intensive care unit needs composite symptom evaluation using clinical criteria such as the clinical pulmonary infection score (CPIS). When CPIS is above a threshold value, bronchoalveolar lavage (BAL) is performed to confirm the diagnosis by counting actual bacterial pathogens. Thus, CPIS and BAL results are closely related and both are important indicators of pneumonia whereas BAL data are incomplete. To compare the pneumonia risks among treatment groups for such incomplete data, we derive a method that combines nonparametric empirical likelihood ratio techniques with classical testing for parametric models. This technique augments the study power by enabling us to use any observed data. The asymptotic property of the proposed method is investigated theoretically. Monte Carlo simulations confirm both the asymptotic results and good power properties of the proposed method. The method is applied to the actual data obtained in clinical practice settings and compares VAP risks among treatment groups.     

Drawbacks to noninteger scoring for ordered categorical data

A proposal to improve trend tests by using noninteger scores is examined. It is concluded that despite improved power such tests are usually inferior to the simpler integer scored approach.     

An exact trend test for correlated binary data

The problem of testing a dose-response relationship in the presence of exchangeably correlated binary data has been addressed using a variety of models. Most commonly used approaches are derived from likelihood or generalized estimating equations and rely on large-sample theory to justify their inferences. However, while earlier work has determined that these methods may perform poorly for small or sparse samples, there are few alternatives available to those faced with such data. We propose an exact trend test for exchangeably correlated binary data when groups of correlated observations are ordered. This exact approach is based on an exponential model derived by Molenberghs and Ryan (1999) and Ryan and Molenberghs (1999) and provides natural analogues to Fisher's exact test and the binomial trend test when the data are correlated. We use a graphical method with which one can efficiently compute the exact tail distribution and apply the test to two examples.     

A class of permutation tests for stratified survival data

We propose a class of permutation tests for stratified survival data. The tests are derived using the framework of Fay and Shih (1998, Journal of the American Statistical Association 93, 387-396), which creates tests by permuting scores based on a functional of estimated distribution functions. Here the estimated distribution function for each possibly right-, left-, or interval-censored observation is based on a shrinkage estimator similar to the nonparametric empirical estimator of Ghosh, Lahiri, and Tiwari (1989, Communications in Statistics--Theory and Methods 18, 121-146), and permutation is carried out within strata. The proposed test with a weighted Mann-Whitney functional is similar to the permutation form of the stratified log-rank test when there is a large strata effect or the sample size in each stratum is large and is similar to the permutation form of the ordinary log-rank test when there is little strata effect. Thus, the proposed test unifies the advantages of both the stratified and ordinary log-rank tests. By changing the functional, we may obtain a stratified Prentice-Wilcoxon test or a difference in means test with similar unifying properties. We show through simulations the advantage of the proposed test over existing tests for uncensored and right-censored data.     

On the use of historical control data for trend test in carcinogenicity studies

Historical control data are often available in carcinogenicity studies and are included for testing dose effects in current studies. A new method is developed for incorporating the historical control information into a dose effect test. The method generalizes the test procedures proposed by Tarone (1982, Biometrics 38, 215-220) and Ibrahim and Ryan (1996, Biometrics 52, 1478-1485) by taking into account the variation resulting from parameter estimation based on historical data. Two examples are discussed for illustrating the proposed method.     

Small-sample degrees of freedom for multi-component significance tests with multiple imputation for missing data

When performing multi-component significance tests with multiply-imputeddatasets, analysts can use a Wald-like test statistic and areference F-distribution. The currently employed degrees offreedom in the denominator of this F-distribution are derivedassuming an infinite sample size. For modest complete-data samplesizes, this degrees of freedom can be unrealistic; for example,it may exceed the complete-data degrees of freedom. This paperpresents an alternative denominator degrees of freedom thatis always less than or equal to the complete-data denominatordegrees of freedom, and equals the currently employed denominatordegrees of freedom for infinite sample sizes. Its advantagesover the currently employed degrees of freedom are illustratedwith a simulation.     

An Exact Paired Rank Test

An exact rank test for two dependent samples based on overall mid‐ranks is discussed which can be applied to metric as well as to ordinal data. The exact conditional distribution of the test statistic given the observed vector of rank differences is determined. A recursion formula is given as well as a fast shift algorithm in SAS/IML code. Moreover, it is demonstrated that the paired rank test can be more powerful than other tests for paired samples by means of a simulation study. Finally, the test is applied to a psychiatric trial with longitudinal ordinal data.     

Estimating the Power of the Gehan Test

A bootstrap method suggested by COLLINGS and HAMILTON (1988) to estimate the power of the two-sample Wilcoxon test is adapted to use for estimating the power of the Gehan test. A Monte Carlo simulation study is done to determine how well the method works in this case.     

A sampling study of the size and power of tests for paired survival data

The paired-t, sign, and signed rank tests were compared for samples from a bivariate exponential distribution. Each is a valid α-level test. One test was not uniformly more powerful than the others for all sample sizes, α levels, correlations, and alternative hypotheses considered, but the signed rank test did well consistently. It was always preferable to the sign test and never was appreciably worse than the paired-t test. The relative performance of the tests depends on α as well as the sample size.     

Accounting for nonignorable verification bias in assessment of diagnostic tests

A "gold" standard test, providing definitive verification of disease status, may be quite invasive or expensive. Current technological advances provide less invasive, or less expensive, diagnostic tests. Ideally, a diagnostic test is evaluated by comparing it with a definitive gold standard test. However, the decision to perform the gold standard test to establish the presence or absence of disease is often influenced by the results of the diagnostic test, along with other measured, or not measured, risk factors. If only data from patients who received the gold standard test were used to assess the test performance, the commonly used measures of diagnostic test performance--sensitivity and specificity--are likely to be biased. Sensitivity would often be higher, and specificity would be lower, than the true values. This bias is called verification bias. Without adjustment for verification bias, one may possibly introduce into the medical practice a diagnostic test with apparent, but not truly, high sensitivity. In this article, verification bias is treated as a missing covariate problem. We propose a flexible modeling and computational framework for evaluating the performance of a diagnostic test, with adjustment for nonignorable verification bias. The presented computational method can be utilized with any software that can repetitively use a logistic regression module. The approach is likelihood-based, and allows use of categorical or continuous covariates. An explicit formula for the observed information matrix is presented, so that one can easily compute standard errors of estimated parameters. The methodology is illustrated with a cardiology data example. We perform a sensitivity analysis of the dependency of verification selection process on disease.     

Statistical Methods for Ordered Categorical Data Based on a Constrained Odds Model

The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann‐Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.     

A simple permutation-type method for testing circular uniformity with correlated angular measurements

A simple method is provided for testing uniformity on the circle that allows dependence among repeated angular measurements on the same subject. Our null hypothesis is that the distribution of repeated angles is unaffected by rotation. This null can be evaluated with any test of uniformity by using a null reference distribution obtained by simulation, where each subject's vector of angles is rotated by a random amount. A new weighted version of the univariate Rayleigh test of circular uniformity is proposed.     

Power and sample size estimation for the clustered wilcoxon test

The Wilcoxon rank sum test is widely used for two-group comparisons of nonnormal data. An assumption of this test is independence of sampling units both within and between groups, which will be violated in the clustered data setting such as in ophthalmological clinical trials, where the unit of randomization is the subject, but the unit of analysis is the individual eye. For this purpose, we have proposed the clustered Wilcoxon test to account for clustering among multiple subunits within the same cluster (Rosner, Glynn, and Lee, 2003, Biometrics 59, 1089-1098; 2006, Biometrics 62, 1251-1259). However, power estimation is needed to plan studies that use this analytic approach. We have recently published methods for estimating power and sample size for the ordinary Wilcoxon rank sum test (Rosner and Glynn, 2009, Biometrics 65, 188-197). In this article we present extensions of this approach to estimate power for the clustered Wilcoxon test. Simulation studies show a good agreement between estimated and empirical power. These methods are illustrated with examples from randomized trials in ophthalmology. Enhanced power is achieved with use of the subunit as the unit of analysis instead of the cluster using the ordinary Wilcoxon rank sum test.     

A Matrix Formulation for Nonparametric Permutation Tests

Many of the common permutation tests, particularly those from survival analysis, are special cases of a more general methodology. They are based on a single covariance matrix which is simple and can be derived by elementary means. It is, however, surprisingly hard to find a complete treatment of this covariance matrix in the literature. Such a treatment is given here together with a discussion of the permutation tests' uses in data analysis.