Exact unconditional tests for testing non-inferiority in matched-pairs design

The problem of testing non-inferiority in a 2 x 2 matched-pairs sample is considered. Two exact unconditional tests based on the standard and the confidence interval p-values are proposed. Although tests of non-inferiority have two nuisance parameters under the null hypothesis, the exact tests are defined by reducing the dimension of nuisance parameter space from two to one using the monotonicity of the distribution. The exact sizes and powers of these tests and the existing asymptotic test are considered. The exact tests are found to be accurate in view of their size property. In addition, the exact test based on the confidence interval p-value is more powerful than the other exact test. It is shown that the asymptotic test is inaccurate, that is, its size exceeds the claimed nominal level alpha. Therefore, it recommends a cautious approach in use of the asymptotic test for the problem of testing non-inferiority, particularly when sample sizes are small or moderately large.     

Linear rank tests for doubly censored data

This paper establishes the asymptotic properties of the non-parametric maximum likelihood estimator of the survival function based on data censored both from the left and the right. We show that the sample mean based on the survival estimator converges to a normal distribution, and we derive non-parametric tests for the differences in survival functions. The methods are applied to a study of dementia associated with Parkinson's disease.     

A Monte Carlo approach for change-point detection in the Cox proportional hazards model

Detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis. The testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test. In the presence of random censoring and/or covariates, however, the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice. Moreover, a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged. In this paper, we consider maximal score tests for detecting change point(s) in the Cox proportional hazards model with censored data. We propose to use a simple Monte Carlo approach for assessing the statistical significance of tests. The proposed approach is applicable for testing a single change point in the Cox model with covariates and sample stratifications over various types of candidate regions, including discrete time-point sets or disjoint intervals. We also show that the proposed test statistics and the Monte Carlo procedure are well applicable under situations with multiple change points. Simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite-sample performance of the proposed approach.     

Tests for interaction in epidemiologic studies: a review and a study of power

Tests for statistical interaction have come into increasing use in epidemiologic analysis, with most based on either an additive or multiplicative model for joint effects. Further procedures have been proposed for testing the goodness-of-fit and comparing the fit of the latter models. This paper reviews the relationships between the various tests and model comparison methods, and, for the special case of two dichotomous risk factors, presents asymptotic power functions for tests of additivity and multiplicativity. For a range of sample sizes and factor effects, the powers of the tests are computed using both the asymptotic power function and simulation studies. The powers of the tests are very low in several commonly encountered situations. In addition, convergence to the asymptotic distribution appears slow for some of the statistics. The results also indicate that likelihood comparison procedures can provide a useful adjunct to the classical hypothesis-testing approach.     

Robust Mantel-Haenszel test under genetic model uncertainty allowing for covariates in case-control association studies

The trend test under the additive model is commonly used when a case-control genetic association study is carried out. However, for many complex diseases, the underlying genetic models are unknown and a mis-specification of the genetic model may result in a substantial loss of power. MAX3 has been proposed as an efficiency robust test against genetic model uncertainty which takes the maximum absolute value of the trend test statistics under the recessive, additive, and dominant models. Besides its popularity, little attention has been paid to the adjustment of covariates in this test and existing approaches all depend on the estimators of parameters of interest which may be seriously biased if the individuals are divided into a large number of partial tables stratified by covariates. In this article, we propose a modified MAX3 test based on the Mantel-Haenszel test (MHT). This new test avoids estimating the nuisance parameters induced by the covariates; thus, it is valid under both large and small numbers of partial tables while still enjoys the property of efficiency robustness. The asymptotic distribution of the test under the null hypothesis of no association is also derived; thus the corresponding asymptotic P-value of the statistic can be easily calculated. Besides, we prove that this new test can be equally derived through a conditional likelihood. As a result, the original MAX3 based on the trend tests or the matching trend tests can be treated as a special case and generally incorporated into the newly proposed test. Simulation results show that the modified MAX3 can keep the correct size under the null hypothesis and is more efficiency robustness than any single MHT optimal for a specified genetic model under the alternative hypothesis. Two real examples corresponding to the large and small number of partial tables scenarios, respectively, are analyzed using the proposed method. A type 2 diabetes mellitus data set is also analyzed to evaluate the performance of the proposed test under the GWAS criteria.     

A simple significance test for quantile regression

Where OLS regression seeks to model the mean of a random variable as a function of observed variables, quantile regression seeks to model the quantiles of a random variable as functions of observed variables. Tests for the dependence of the quantiles of a random variable upon observed variables have only been developed through the use of computer resampling or based on asymptotic approximations resting on distributional assumptions. We propose an exceedingly simple but heretofore undocumented likelihood ratio test within a logistic regression framework to test the dependence of a quantile of a random variable upon observed variables. Simulated data sets are used to illustrate the rationale, ease, and utility of the hypothesis test. Simulations have been performed over a variety of situations to estimate the type I error rates and statistical power of the procedure. Results from this procedure are compared to (1) previously proposed asymptotic tests for quantile regression and (2) bootstrap techniques commonly used for quantile regression inference. Results show that this less computationally intense method has appropriate type I error control, which is not true for all competing procedures, comparable power to both previously proposed asymptotic tests and bootstrap techniques, and greater computational ease. We illustrate the approach using data from 779 adolescent boys age 12-18 from the Third National Health and Nutrition Examination Survey (NHANES III) to test hypotheses regarding age, ethnicity, and their interaction upon quantiles of waist circumference.     

Tests for equivalence or non-inferiority for paired binary data.

Assessment of therapeutic equivalence or non-inferiority between two medical diagnostic procedures often involves comparisons of the response rates between paired binary endpoints. The commonly used and accepted approach to assessing equivalence is by comparing the asymptotic confidence interval on the difference of two response rates with some clinical meaningful equivalence limits. This paper investigates two asymptotic test statistics, a Wald-type (sample-based) test statistic and a restricted maximum likelihood estimation (RMLE-based) test statistic, to assess equivalence or non-inferiority based on paired binary endpoints. The sample size and power functions of the two tests are derived. The actual type I error and power of the two tests are computed by enumerating the exact probabilities in the rejection region. The results show that the RMLE-based test controls type I error better than the sample-based test. To establish an equivalence between two treatments with a symmetric equivalence limit of 0.15, a minimal sample size of 120 is needed. The RMLE-based test without the continuity correction performs well at the boundary point 0. A numerical example illustrates the proposed procedures.     

A hybrid procedure for detecting global treatment effects in multivariate clinical trials: theory and applications to fMRI studies

In multivariate clinical trials, a key research endpoint is ascertaining whether a candidate treatment is more efficacious than an established alternative. This global endpoint is clearly of high practical value for studies, such as those arising from neuroimaging, where the outcome dimensions are not only numerous but they are also highly correlated and the available sample sizes are typically small. In this paper, we develop a two-stage procedure testing the null hypothesis of global equivalence between treatments effects and demonstrate its application to analysing phase II neuroimaging trials. Prior information such as suitable statistics of historical data or suitably elicited expert clinical opinions are combined with data collected from the first stage of the trial to learn a set of optimal weights. We apply these weights to the outcome dimensions of the second-stage responses to form the linear combination z and t tests statistics while controlling the test's false positive rate. We show that the proposed tests hold desirable asymptotic properties and characterise their power functions under wide conditions. In particular, by comparing the power of the proposed tests with that of Hotelling's T(2), we demonstrate their advantages when sample sizes are close to the dimension of the multivariate outcome. We apply our methods to fMRI studies, where we find that, for sufficiently precise first stage estimates of the treatment effect, standard single-stage testing procedures are outperformed.     

A noniterative sample size procedure for tests based on t distributions

A noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending Guenther's 6 approach for the one sample and two sample t tests. The generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance (ANCOVA) and the mixed effects model for repeated measures in randomized clinical trials. The sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms, which are functions of the covariates in the model. But it does not require specifying the covariate distribution. The noniterative procedure is suitable for superiority tests, noninferiority tests, and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer. The method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials. We also derive accurate power formulae for ANCOVA and mixed effects model for repeated measures, and the formula for ANCOVA is exact for normally distributed covariates. Numerical examples demonstrate the accuracy of the proposed methods particularly in small samples.     

Partial F‐tests with multiply imputed data in the linear regression framework via coefficient of determination

Tests for regression coefficients such as global, local, and partial F‐tests are common in applied research. In the framework of multiple imputation, there are several papers addressing tests for regression coefficients. However, for simultaneous hypothesis testing, the existing methods are computationally intensive because they involve calculation with vectors and (inversion of) matrices. In this paper, we propose a simple method based on the scalar entity, coefficient of determination, to perform (global, local, and partial) F‐tests with multiply imputed data. The proposed method is evaluated using simulated data and applied to suicide prevention data. Copyright © 2014 John Wiley & Sons, Ltd.     

Bartlett‐type corrections and bootstrap adjustments of likelihood‐based inference methods for network meta‐analysis

In network meta‐analyses that synthesize direct and indirect comparison evidence concerning multiple treatments, multivariate random effects models have been routinely used for addressing between‐studies heterogeneities. Although their standard inference methods depend on large sample approximations (eg, restricted maximum likelihood estimation) for the number of trials synthesized, the numbers of trials are often moderate or small. In these situations, standard estimators cannot be expected to behave in accordance with asymptotic theory; in particular, confidence intervals cannot be assumed to exhibit their nominal coverage probabilities (also, the type I error probabilities of the corresponding tests cannot be retained). The invalidity issue may seriously influence the overall conclusions of network meta‐analyses. In this article, we develop several improved inference methods for network meta‐analyses to resolve these problems. We first introduce 2 efficient likelihood‐based inference methods, the likelihood ratio test–based and efficient score test–based methods, in a general framework of network meta‐analysis. Then, to improve the small‐sample inferences, we developed improved higher‐order asymptotic methods using Bartlett‐type corrections and bootstrap adjustment methods. The proposed methods adopt Monte Carlo approaches using parametric bootstraps to effectively circumvent complicated analytical calculations of case‐by‐case analyses and to permit flexible application to various statistical models network meta‐analyses. These methods can also be straightforwardly applied to multivariate meta‐regression analyses and to tests for the evaluation of inconsistency. In numerical evaluations via simulations, the proposed methods generally performed well compared with the ordinary restricted maximum likelihood–based inference method. Applications to 2 network meta‐analysis datasets are provided.     

An age-adjusted bootstrap-based Poly-k test

The assumption of an asymptotic normal distribution of some test statistics may be invalid in certain dose-response trend tests. For instance, the survival-adjusted Cochran-Armitage test, known as the Poly-k test, is asymptotically standard normal under the null hypothesis. However, the asymptotic normality is not valid if there is a deviation from the tumour onset distribution that is assumed in this test or if the competing risks survival rates differ across groups. We develop an age-adjusted bootstrap-based method to assess the significance of assumed asymptotic normal tests for animal carcinogenicity data. The proposed method differs from conventional bootstrap methods in the aspect of preserving the mortality rate in each dose group under the null hypothesis of equal tumour incidence rates among the groups. We investigate an empirical distribution of the Poly-3 (P3) trend test statistic using the proposed age-adjusted bootstrap-based method and compare it with the P3 test statistic referenced to the assumed standard normal distribution. A simulation study is conducted to evaluate the robustness of these tests to various Weibull-family tumour onset distributions. The proposed method is applied to National Toxicology Program data sets to evaluate a dose-related trend of a test substance on the incidence of neoplasms.     

Graphical model checking with correlated response data

Correlated response data arise often in biomedical studies. The generalized estimation equation (GEE) approach is widely used in regression analysis for such data. However, there are few methods available to check the adequacy of regression models in GEE. In this paper, a graphical method is proposed based on Cook and Weisberg's marginal model plot. A bootstrap method is applied to obtain the reference band to assess statistical uncertainties in comparing two marginal mean functions. We also propose using the generalized additive model (GAM) in a similar fashion. The proposed two methods are easy to implement by taking advantage of existing smoothing and GAM softwares for independent data. The usefulness of the methodology is demonstrated through application to a correlated binary data set drawn from a clinical trial, the Lung Health Study.     

A new association test using haplotype similarity

Association tests based on multi-marker haplotypes may be more powerful than those based on single markers. The existing association tests based on multi-marker haplotypes include Pearson's chi2 test which tests for the difference of haplotype distributions in cases and controls, and haplotype-similarity based methods which compare the average similarity among cases with that of the controls. In this article, we propose new association tests based on haplotype similarities. These new tests compare the average similarities within cases and controls with the average similarity between cases and controls. These methods can be applied to either phase-known or phase-unknown data. We compare the performance of the proposed methods with Pearson's chi2 test and the existing similarity-based tests by simulation studies under a variety of scenarios and by analyzing a real data set. The simulation results show that, in most cases, the new proposed methods are more powerful than both Pearson's chi2 test and the existing similarity-based tests. In one extreme case where the disease mutant induced at a very rare haplotype (相似文献   

Testing for change-point in the covariate effects based on the Cox regression model

Models with change-point in covariates have wide applications in cancer research with the response being the time to a certain event. A Cox model with change-point in covariate is considered at which the pattern of the change-point effects can be flexibly specified. To test for the existence of the change-point effects, three statistical tests, namely, the maximal score, maximal normalized score, and maximal Wald tests are proposed. The asymptotic properties of the test statistics are established. Monte Carlo approaches to simulate the critical values are suggested. A large-scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change-points and various alternative hypothesis settings. Each of the proposed methods provides a natural estimate for the location of the change-point, but it is found that the performance of the maximal score test can be sensitive to the true location of the change-point in some cases, while the performance of the maximal Wald test is very satisfactory in general even in cases with moderate sample size. For illustration, the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer, respectively.     

Time‐varying coefficients models for recurrent event data when different varying coefficients admit different degrees of smoothness: application to heart disease modeling

We consider a class of semiparametric marginal rate models for analyzing recurrent event data. In these models, both time‐varying and time‐free effects are present, and the estimation of time‐varying effects may result in non‐smooth regression functions. A typical approach for avoiding this problem and producing smooth functions is based on kernel methods. The traditional kernel‐based approach, however, assumes a common degree of smoothness for all time‐varying regression functions, which may result in suboptimal estimators if the functions have different levels of smoothness. In this paper, we extend the traditional approach by introducing different bandwidths for different regression functions. First, we establish the asymptotic properties of the suggested estimators. Next, we demonstrate the superiority of our proposed method using two finite‐sample simulation studies. Finally, we illustrate our methodology by analyzing a real‐world heart disease dataset. Copyright © 2016 John Wiley & Sons, Ltd.     

Covariance estimators for generalized estimating equations (GEE) in longitudinal analysis with small samples

Generalized estimating equations (GEE) is a general statistical method to fit marginal models for longitudinal data in biomedical studies. The variance–covariance matrix of the regression parameter coefficients is usually estimated by a robust “sandwich” variance estimator, which does not perform satisfactorily when the sample size is small. To reduce the downward bias and improve the efficiency, several modified variance estimators have been proposed for bias‐correction or efficiency improvement. In this paper, we provide a comprehensive review on recent developments of modified variance estimators and compare their small‐sample performance theoretically and numerically through simulation and real data examples. In particular, Wald tests and t‐tests based on different variance estimators are used for hypothesis testing, and the guideline on appropriate sample sizes for each estimator is provided for preserving type I error in general cases based on numerical results. Moreover, we develop a user‐friendly R package “geesmv” incorporating all of these variance estimators for public usage in practice. Copyright © 2015 John Wiley & Sons, Ltd.     

Graphical approaches using a Bonferroni mixture of weighted Simes tests

Graphical approaches to multiple testing procedures are very flexible and easy to communicate with non‐statisticians. The availability of the R package gMCP further propelled the application of graphical approaches in randomized clinical trials. Bretz et al. (Biometrical Journal 2011; 53:894–913) introduced a class of nonparametric testing procedures based on a Bonferroni mixture of weighted Simes tests for intersection hypotheses. Such approaches are extremely useful when the conditions for the Simes test are known to hold for hypotheses within certain subsets but may not hold for hypotheses across subsets. We describe the calculation of adjusted p‐values for such approaches, which is currently not available in the gMCP package. We also optimize the generation of the weights for each intersection hypothesis in the closure of a graph‐based multiple testing procedure, which can dramatically reduce the computing time for simulation‐based power calculations. We show the validity of the Simes test for comparing several treatments with a control, performing noninferiority and superiority tests, or testing the treatment effect in an overall and a subpopulation for the normal, binary, count, and time‐to‐event data. The proposed method is illustrated using an example for designing a confirmatory clinical trial. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact approaches for testing hypotheses based on the intra‐class kappa coefficient

Testing involving the intra‐class kappa coefficient is commonly performed in order to assess agreement involving categorical ratings. A number of procedures have been proposed, which make use of the limiting null distribution as the sample size goes to infinity in order to compute the observed significance. As with many tests based on asymptotic null distributions, these tests are associated with problematic type I error control for selected sample sizes and points in the parameter space. We propose and study a collection of exact testing approaches for both the one‐sample and K‐sample scenarios. For the one‐sample case, p‐values are obtained using the exact distribution of the test statistic conditional on a sufficient statistic. In addition, unconditional approaches are considered on the basis of maximization across the nuisance parameter space. Numerical evaluation reveals advantages with the exact unconditional procedures. Copyright © 2014 John Wiley & Sons, Ltd.     

The nonparametric Behrens-Fisher problem with dependent replicates

Purely nonparametric methods are developed for general two-sample problems in which each experimental unit may have an individual number of possibly correlated replicates. In particular, equality of the variances, or higher moments, of the distributions of the data is not assumed, even under the null hypothesis of no treatment effect. Thus, a solution for the so-called nonparametric Behrens-Fisher problem is proposed for such models. The methods are valid for metric, count, ordered categorical, and even dichotomous data in a unified way. Point estimators of the treatment effects as well as their asymptotic distributions will be studied in detail. For small sample sizes, the distributions of the proposed test statistics are approximated using Satterthwaite-Welch-type t-approximations. Extensive simulation studies show favorable performance of the new methods, in particular, in small sample size situations. A real data set illustrates the application of the proposed methods.