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Mendelian randomization (MR) analysis uses genotypes as instruments to estimate the causal effect of an exposure in the presence of unobserved confounders. The existing MR methods focus on the data generated from prospective cohort studies. We develop a procedure for studying binary outcomes under a case-control design. The proposed procedure is built upon two working models commonly used for MR analyses and adopts a quasi-empirical likelihood framework to address the ascertainment bias from case-control sampling. We derive various approaches for estimating the causal effect and hypothesis testing under the empirical likelihood framework. We conduct extensive simulation studies to evaluate the proposed methods. We find that the proposed empirical likelihood estimate is less biased than the existing estimates. Among all the approaches considered, the Lagrange multiplier (LM) test has the highest power, and the confidence intervals derived from the LM test have the most accurate coverage. We illustrate the use of our method in MR analysis of prostate cancer case-control data with vitamin D level as exposure and three single nucleotide polymorphisms as instruments.

Successful deployment of machine learning algorithms in healthcare requires careful assessments of their performance and safety. To date, the FDA approves locked algorithms prior to marketing and requires future updates to undergo separate premarket reviews. However, this negates a key feature of machine learning-the ability to learn from a growing dataset and improve over time. This paper frames the design of an approval policy, which we refer to as an automatic algorithmic change protocol (aACP), as an online hypothesis testing problem. As this process has obvious analogy with noninferiority testing of new drugs, we investigate how repeated testing and adoption of modifications might lead to gradual deterioration in prediction accuracy, also known as "biocreep" in the drug development literature. We consider simple policies that one might consider but do not necessarily offer any error-rate guarantees, as well as policies that do provide error-rate control. For the latter, we define two online error-rates appropriate for this context: bad approval count (BAC) and bad approval and benchmark ratios (BABR). We control these rates in the simple setting of a constant population and data source using policies aACP-BAC and aACP-BABR, which combine alpha-investing, group-sequential, and gate-keeping methods. In simulation studies, bio-creep regularly occurred when using policies with no error-rate guarantees, whereas aACP-BAC and aACP-BABR controlled the rate of bio-creep without substantially impacting our ability to approve beneficial modifications.

Effect modification means the magnitude or stability of a treatment effect varies as a function of an observed covariate. Generally, larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates, so a causal conclusion may be considerably firmer if this pattern is noted if it occurs. We propose a new strategy, called the submax-method, that combines exploratory, and confirmatory efforts to determine whether there is stronger evidence of causality-that is, greater insensitivity to unmeasured confounding-in some subgroups of individuals. It uses the joint distribution of test statistics that split the data in various ways based on certain observed covariates. For L binary covariates, the method splits the population L times into two subpopulations, perhaps first men and women, perhaps then smokers and nonsmokers, computing a test statistic from each subpopulation, and appends the test statistic for the whole population, makingmml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:mn2/mml:mnmml:miL/mml:mimml:mo+/mml:momml:mn1/mml:mn/mml:mathtest statistics in total. Although L binary covariates definemml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:msupmml:mn2/mml:mnmml:miL/mml:mi/mml:msup/mml:mathinteraction groups, onlymml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:mn2/mml:mnmml:miL/mml:mimml:mo+/mml:momml:mn1/mml:mn/mml:mathtests are performed, and at leastmml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:miL/mml:mimml:mo+/mml:momml:mn1/mml:mn/mml:mathof these tests use at least half of the data. The submax-method achieves the highest design sensitivity and the highest Bahadur efficiency of its component tests. Moreover, the form of the test is sufficiently tractable that its large sample power may be studied analytically. The simulation suggests that the submax method exhibits superior performance, in comparison with an approach using CART, when there is effect modification of moderate size. Using data from the NHANES I epidemiologic follow-up survey, an observational study of the effects of physical activity on survival is used to illustrate the method. The method is implemented in themml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:miR/mml:mi/mml:mathpackagemml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:misubmax/mml:mi/mml:mathwhich contains the NHANES example. An online Appendix provides simulation results and further analysis of the example.

Competing risks endpoints arise when patients can fail therapy from several causes. Analyzing these outcomes allows one to assess directly the benefit of treatment on a primary cause of failure in a clinical trial setting. Regression models can be used in clinical trials to adjust for residual imbalances in patient characteristics, improving the power to detect treatment differences. But, none of the competing risks methods currently available for use in group sequential trials adjust for covariates. We propose a group sequential test for treatment effect that, because it is based on the Fine-Gray model, permits adjustment for covariates. Our derivations show that its sequence of test statistics has an asymptotic distribution with an independent increments structure, which allows standard techniques such as O'Brien-Fleming designs and error spending functions to be employed to meet type I error rate and power specifications. We demonstrate the test in a reanalysis of BMT CTN 0402, a phase III clinical trial that evaluated an experimental treatment for the prevention of adverse outcomes following blood and marrow transplant. Moreover, using a simulation study of randomized group sequential trials, we demonstrate that the proposed method preserves the type I error rate and power at their nominal levels in the presence of influential covariates.

In recent mutation studies, analyses based on protein domain positions are gaining popularity over gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents a large-scale simultaneous inference problem, with hundreds of hypothesis tests to consider at the same time. This article aims to select significant mutation counts while controlling a given level of Type I error via False Discovery Rate (FDR) procedures. One main assumption is that the mutation counts follow a zero-inflated model in order to account for the true zeros in the count model and the excess zeros. The class of models considered is the Zero-inflated Generalized Poisson (ZIGP) distribution. Furthermore, we assumed that there exists a cut-off value such that smaller counts than this value are generated from the null distribution. We present several data-dependent methods to determine the cut-off value. We also consider a two-stage procedure based on screening process so that the number of mutations exceeding a certain value should be considered as significant mutations. Simulated and protein domain data sets are used to illustrate this procedure in estimation of the empirical null using a mixture of discrete distributions. Overall, while maintaining control of the FDR, the proposed two-stage testing procedure has superior empirical power.

In comparing two treatments with the event time observations, the hazard ratio (HR) estimate is routinely used to quantify the treatment difference. However, this model dependent estimate may be difficult to interpret clinically especially when the proportional hazards (PH) assumption is violated. An alternative estimation procedure for treatment efficacy based on the restricted means survival time or t-year mean survival time (t-MST) has been discussed extensively in the statistical and clinical literature. On the other hand, a statistical test via the HR or its asymptotically equivalent counterpart, the logrank test, is asymptotically distribution-free. In this article, we assess the relative efficiency of the hazard ratio and t-MST tests with respect to the statistical power under various PH and non-PH models theoretically and empirically. When the PH assumption is valid, the t-MST test performs almost as well as the HR test. For non-PH models, the t-MST test can substantially outperform its HR counterpart. On the other hand, the HR test can be powerful when the true difference of two survival functions is quite large at end but not the beginning of the study. Unfortunately, for this case, the HR estimate may not have a simple clinical interpretation for the treatment effect due to the violation of the PH assumption.

Personalized medicine is the practice of tailoring treatment to account for patient heterogeneity (Chakraborty and Murphy, 2014). Health care providers have practiced personalized medicine by adjusting doses or prescriptions based on a patient’s medical history or demographics for centuries (Ashley, 2015). Precision medicine is an emerging field that aims to support personalized medicine decisions with reproducible research (Collins and Varmus, 2015). Such research is imperative, particularly when diseases are expressed with great heterogeneity across patients. A topic of interest in precision medicine is the individualized treatment regime (ITR): a set of decision rules for one or more decision time points that can be used to assign patients to treatment that is tailored by their patient-specific factors (Lavori and Dawson, 2014). One objective in precision medicine is to estimate the optimal ITR, or the ITR that maximizes the mean of some desirable outcome (Kosorok and Moodie, 2015). Crossover clinical trials are uniquely suited to precision medicine, because they allow for observing responses to multiple treatments for each patient. This paper introduces a method to estimate optimal ITRs using data from a crossover study by extending generalized outcome weighted learning (GOWL) (Chen et al., 2018) to deal with correlated outcomes. In a crossover study, patients are randomized to a sequence of treatments rather than a single treatment. Thus, multiple outcomes are observed, one per subject from each treatment period, and each subject acts as his or her own control for reduced between-subject variability (Wellek and Blettner, 2012). Such designs are popular in pilot studies, where only a small sample of individuals is available and/or affordable, because crossover designs at a lower sample size are able achieve the same level of power as a parallel design with a larger sample size. To concurrently address precision medicine aims with aims of hypothesis testing, it is imperative that ITR estimation methods be broadened to crossover designs in an accessible and easy to implement way in order to better take advantage of the additional data available in such crossover studies. There have been many developments in machine learning methods for answering precision medicine questions from parallel study designs. For example, Qian and Murphy (2011) indirectly estimate the decision rule using L1 penalized least squares; Zhang et al. (2012a) maximize a doubly robust augmented inverse probability weighted estimator for the population mean outcome; Athey and Wager (2017) maximize a doubly robust score that may take into account instrumental variables; Kallus (2018) employs a weighting algorithm similar to inverse probability weighting but minimize the worst case mean square error; Laber and Zhao (2015) propose the use of decision trees, which prove to be both flexible and easily interpretable; Zhao et al. (2012), Zhang et al. (2012b), Zhou et al. (2017), and Chen et al. (2018) directly estimate the decision rule by viewing the problem from a weighted classification standpoint. However, little work has been done to develop precision medicine methods that handle correlated observations in the single-stage decision setting such as those that arise from crossover designs. Kulasekera and Siriwardhana (2019) propose a weighted ranking algorithm to estimate a decision rule that maximizes either the expected outcome or the probability of selecting the best treatment, but they assume that there are no carryover effects present. Because the intended effect of the washout period can be difficult to achieve in practice (Wellek and Blettner, 2012), it is imperative that methods for crossover designs can be applied when carryover effects are present. In this paper, we show that the difference in response to two treatments from a 2 × 2 crossover trial can be used as the reward in the generalized outcome weighted learning (GOWL) objective function to estimate an optimal ITR. We introduce a plug-in estimator that can be used with the proposed method to account for carryover effects. Additionally, we show that using a crossover design with the proposed method results in improvements in misclassification rate and estimated value when compared to standard methods for a parallel design at the same sample size. As a clinical example, consider nutritional recommendations surrounding the intake of dietary fiber for the purpose of weight loss. Although increased fiber is recommended across the population for a myriad of health benefits (US Department of Agriculture, 2010), evidence of the impact of the consumption of dietary fiber for improved satiety and reduction in body weight is mixed (Halliday et al., 2018). Heterogeneity in response to dietary fiber may be leveraged to develop targeted fiber interventions to promote feelings of satiety. We use data from a crossover study in which Hispanic and African American adolescents who are overweight and obese were fed breakfast and lunch under a typical Western high sugar diet condition, and a high fiber diet condition. From these data, we estimate a decision rule with which clinical care providers can input patient characteristics, including demographics and clinical measures, and receive a recommendation to maximize the change in measures of perceived satiety from before breakfast to after lunch. This type of analysis could be useful in identifying a subgroup of at-risk adolescents for which targeting specific dietary recommendations is expected to lead to an increase in patient-reported satiety, thereby helping to decrease caloric intake in a population with great clinical need for effective, non-invasive weight loss strategies. The rest of this paper is organized as follows. In Section 2, we review outcome weighted learning (OWL) (Zhao et al., 2012) and present the proposed method for estimating an optimal ITR from a crossover study regardless of the presence of carryover effects. Section 3 establishes Fisher and global consistency. Section 4 demonstrates the performance of the proposed method in simulation studies, with results on misclassification rate and estimated value. Section 5 displays an analysis of data from a feeding trial with overweight and obese Hispanic and African American adolescents, and we conclude with a discussion in Section 6. Additional simulation results, feeding trial results and their discussion, and theoretical derivations may be found in the web based supporting materials.

Current methods for detecting genetic associations lack full consideration of the background effects of environmental exposures. Recently proposed methods to account for environmental exposures have focused on logistic regressions with gene-environment interactions. In this report, we developed a test for genetic association, encompassing a broad range of risk models, including linear, logistic and probit, for specifying joint effects of genetic and environmental exposures. We obtained the test statistics by maximizing over a class of score tests, each of which involves modified standard tests of genetic association through a weight function. This weight function reflects the potential heterogeneity of the genetic effects by levels of environmental exposures under a particular model. Simulation studies demonstrate the robust power of these methods for detecting genetic associations under a wide range of scenarios. Applications of these methods are further illustrated using data from genome-wide association studies of type 2 diabetes with body mass index and of lung cancer risk with smoking.

Nested case-control sampling is a popular design for large epidemiological cohort studies due to its cost effectiveness. A number of methods have been developed for the estimation of the proportional hazards model with nested case-control data; however, the evaluation of modeling assumption is less attended. In this paper, we propose a class of goodness-of-fit test statistics for testing the proportional hazards assumption based on nested case-control data. The test statistics are constructed based on asymptotically mean-zero processes derived from Samuelsen’s maximum pseudo-likelihood estimation method. In addition, we develop an innovative resampling scheme to approximate the asymptotic distribution of the test statistics while accounting for the dependent sampling scheme of nested case-control design. Numerical studies are conducted to evaluate the performance of our proposed approach, and an application to the Wilms’ Tumor Study is given to illustrate the methodology.

This paper derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the paper are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications., Comment: Some typos were corrected from the published version

The log-rank test has been widely used to test treatment effects under the Cox model for censored time-to-event outcomes, though it may lose power substantially when the model's proportional hazards assumption does not hold. In this article, we consider an extended Cox model that uses B-splines or smoothing splines to model a time-varying treatment effect and propose score test statistics for the treatment effect. Our proposed new tests combine statistical evidence from both the magnitude and the shape of the time-varying hazard ratio function, and thus are omnibus and powerful against various types of alternatives. In addition, the new testing framework is applicable to any choice of spline basis functions, including B-splines, and smoothing splines. Simulation studies confirm that the proposed tests performed well in finite samples and were frequently more powerful than conventional tests alone in many settings. The new methods were applied to the HIVNET 012 Study, a randomized clinical trial to assess the efficacy of single-dose Nevirapine against mother-to-child HIV transmission conducted by the HIV Prevention Trial Network.

Motivated by the problem of construction gene co-expression network, we propose a statistical framework for estimating high-dimensional partial correlation matrix by a three-step approach. We first obtain a penalized estimate of a partial correlation matrix using ridge penalty. Next we select the non-zero entries of the partial correlation matrix by hypothesis testing. Finally we reestimate the partial correlation coefficients at these non-zero entries. In the second step, the null distribution of the test statistics derived from penalized partial correlation estimates has not been established. We address this challenge by estimating the null distribution from the empirical distribution of the test statistics of all the penalized partial correlation estimates. Extensive simulation studies demonstrate the good performance of our method. Application on a yeast cell cycle gene expression data shows that our method delivers better predictions of the protein-protein interactions than the Graphic Lasso.

Summary Many papers have introduced adaptive clinical trial methods that allow modifications to the sample size based on interim estimates of treatment effect. There has been extensive commentary on type I error control and efficiency considerations, but little research on estimation after an adaptive hypothesis test. We evaluate the reliability and precision of different inferential procedures in the presence of an adaptive design with pre-specified rules for modifying the sampling plan. We extend group sequential orderings of the outcome space based on the stage at stopping, likelihood ratio statistic, and sample mean to the adaptive setting in order to compute median-unbiased point estimates, exact confidence intervals, and P-values uniformly distributed under the null hypothesis. The likelihood ratio ordering is found to average shorter confidence intervals and produce higher probabilities of P-values below important thresholds than alternative approaches. The bias adjusted mean demonstrates the lowest mean squared error among candidate point estimates. A conditional error-based approach in the literature has the benefit of being the only method that accommodates unplanned adaptations. We compare the performance of this and other methods in order to quantify the cost of failing to plan ahead in settings where adaptations could realistically be pre-specified at the design stage. We find the cost to be meaningful for all designs and treatment effects considered, and to be substantial for designs frequently proposed in the literature.

The case series method is useful in studying the relationship between time-varying exposures, such as infections, and acute events observed during the observation periods of individuals. It provides estimates of the relative incidences of events in risk periods (e.g., 30-day period after infections) relative to the baseline periods. When the times of exposure onsets are not known precisely, application of the case series model ignoring exposure onset measurement error leads to biased estimates. Bias-correction is necessary in order to understand the true directions and effect sizes associated with exposure risk periods, although uncorrected estimators have smaller variance. Thus, inference via hypothesis testing based on uncorrected test statistics, if valid, is potentially more powerful. Furthermore, the tests can be implemented in standard software and do not require additional auxiliary data. In this work, we examine the validity and power of naive hypothesis testing, based on applying the case series analysis to the imprecise data without correcting for the error. Based on simulation studies and theoretical calculations, we determine the validity and relative power of common hypothesis tests of interest in case series analysis. In particular, we illustrate that the tests for the global null hypothesis, the overall null hypotheses associated with all risk periods or all age effects are valid. However, tests of individual risk period parameters are not generally valid. Practical guidelines are provided and illustrated with data from patients on dialysis.

When faced with categorical predictors and a continuous response, the objective of an analysis often consists of two tasks: finding which factors are important and determining which levels of the factors differ significantly from one another. Often times, these tasks are done separately using Analysis of Variance (ANOVA) followed by a post hoc hypothesis testing procedure such as Tukey's Honestly Significant Difference test. When interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem. When testing for differences between two levels of a factor, claiming no difference would refer not only to equality of main effects, but also to equality of each interaction involving those levels. This structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models. This article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity-type constraint on the model. An appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero. It is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand. We also discuss the application to estimating interactions in the unreplicated case. Simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint. The method is also illustrated using a real data example.

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic datasets and an human acute lymphoblastic leukemia gene expression dataset, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN., Comment: 34 pages, 10 figures; Accepted for biometrics

Case–parent trio studies concerned with children affected by a disease and their parents aim to detect single nucleotide polymorphisms (SNPs) showing a preferential transmission of alleles from the parents to their affected offspring. A popular statistical test for detecting such SNPs associated with disease in this study design is the genotypic transmission/disequilibrium test (gTDT) based on a conditional logistic regression model, which usually needs to be fitted by an iterative procedure. In this article, we derive exact closed-form solutions for the parameter estimates of the conditional logistic regression models when testing for an additive, a dominant, or a recessive effect of a SNP, and show that such analytic parameter estimates also exist when considering gene–environment interactions with binary environmental variables. Because the genetic model underlying the association between a SNP and a disease is typically unknown, it might further be beneficial to use the maximum over the gTDT statistics for the possible effects of a SNP as test statistic. We therefore propose a procedure enabling a fast computation of the test statistic and the permutation-based p-value of this MAX gTDT. All these methods are applied to whole-genome scans of the case–parent trios from the International Cleft Consortium. These applications show our procedures dramatically reduce the required computing time compared to the conventional iterative methods allowing, for example, the analysis of hundreds of thousands of SNPs in a few minutes instead of several hours.

Pilot phases of a randomized clinical trial often suggest that a parametric model may be an accurate description of the trial's longitudinal trajectories. However, parametric models are often not used for fear that they may invalidate tests of null hypotheses of equality between the experimental groups. Existing work has shown that when, for some types of data, certain parametric models are used, the validity for testing the null is preserved even if the parametric models are incorrect. Here, we provide a broader and easier to check characterization of parametric models that can be used to (i) preserve nonparametric validity of testing the null hypothesis, i.e., even when the models are incorrect, and (ii) increase power compared to the non- or semiparametric bounds when the models are close to correct. We demonstrate our results in a clinical trial of depression in Alzheimer's patients.

Summary. For group-randomized trials, randomization inference based on rank statistics provides robust, exact inference against nonnormal distributions. However, in a matched-pair design, the currently available rank-based statistics lose significant power compared to normal linear mixed model (LMM) test statistics when the LMM is true. In this article, we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed Mann-Whitney-Wilcoxon statistics under certain assumptions. This test is almost as powerful as the LMM even when the LMM is true, but it is much more powerful for heavy tailed distributions. A simulation study is conducted to examine the power.

Summary We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate of n−2 can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.

Summary We consider a problem of testing mixture proportions using two-sample data, one from group one and the other from a mixture of groups one and two with unknown proportion, λ, for being in group two. Various statistical applications, including microarray study, infectious epidemiological studies, case–control studies with contaminated controls, clinical trials allowing “nonresponders,” genetic studies for gene mutation, and fishery applications can be formulated in this setup. Under the assumption that the log ratio of probability (density) functions from the two groups is linear in the observations, we propose a generalized score test statistic to test the mixture proportion. Under some regularity conditions, it is shown that this statistic converges to a weighted chi-squared random variable under the null hypothesis of λ= 0, where the weight depends only on the sampling fraction of both groups. The permutation method is used to provide more reliable finite sample approximation. Simulation results and two real data applications are presented.

We consider the problem of evaluating a statistical hypothesis when some model characteristics are nonidentifiable from observed data. Such a scenario is common in meta-analysis for assessing publication bias and in longitudinal studies for evaluating a covariate effect when dropouts are likely to be nonignorable. One possible approach to this problem is to fix a minimal set of sensitivity parameters conditional upon which hypothesized parameters are identifiable. Here, we extend this idea and show how to evaluate the hypothesis of interest using an infimum statistic over the whole support of the sensitivity parameter. We characterize the limiting distribution of the statistic as a process in the sensitivity parameter, which involves a careful theoretical analysis of its behavior under model misspecification. In practice, we suggest a nonparametric bootstrap procedure to implement this infimum test as well as to construct confidence bands for simultaneous pointwise tests across all values of the sensitivity parameter, adjusting for multiple testing. The methodology's practical utility is illustrated in an analysis of a longitudinal psychiatric study.

Regression models are often used to test for cause-effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, because commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this article, we focus on hypothesis tests of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such hypothesis tests have correct type I error for large samples. Our main result is that for a surprisingly large class of commonly used regression models, standard regression-based hypothesis tests (but using robust variance estimators) are guaranteed to have correct type I error for large samples, even when the models are incorrectly specified. To the best of our knowledge, this robustness of such model-based hypothesis tests to incorrectly specified models was previously unknown for Poisson regression models and for other commonly used models we consider. Our results have practical implications for understanding the reliability of commonly used, model-based tests for analyzing randomized trials.

We provide a method for obtaining confidence intervals, point estimates, and p-values for the primary effect size parameter at the end of a two-arm group sequential clinical trial in which adaptive changes have been implemented along the way. The method is based on applying the adaptive hypothesis testing procedure of Müller and Schäfer (2001, Biometrics 57, 886-891) to a sequence of dual tests derived from the stage-wise adjusted confidence interval of Tsiatis, Rosner, and Mehta (1984, Biometrics 40, 797-803). In the nonadaptive setting this confidence interval is known to provide exact coverage. In the adaptive setting exact coverage is guaranteed provided the adaptation takes place at the penultimate stage. In general, however, all that can be claimed theoretically is that the coverage is guaranteed to be conservative. Nevertheless, extensive simulation experiments, supported by an empirical characterization of the conditional error function, demonstrate convincingly that for all practical purposes the coverage is exact and the point estimate is median unbiased. No procedure has previously been available for producing confidence intervals and point estimates with these desirable properties in an adaptive group sequential setting. The methodology is illustrated by an application to a clinical trial of deep brain stimulation for Parkinson's disease.

Summary. Spatial clustering is commonly modeled by a Bayesian method under the framework of generalized linear mixed effect models (GLMMs). Spatial clusters are commonly detected by a frequentist method through hypothesis testing. In this article, we provide a frequentist method for assessing spatial properties of GLMMs. We propose a strategy that detects spatial clusters through parameter estimates of spatial associations, and assesses spatial aspects of model improvement through iterated residuals. Simulations and a case study show that the proposed method is able to consistently and efficiently detect the locations and magnitudes of spatial clusters.

In this article, we consider comparing the areas under correlated receiver operating characteristic (ROC) curves of diagnostic biomarkers whose measurements are subject to a limit of detection (LOD), a source of measurement error from instruments' sensitivity in epidemiological studies. We propose and examine the likelihood ratio tests with operating characteristics that are easily obtained by classical maximum likelihood methodology.

Due to competition among individual trees and other exogenous factors that change the growth environment, each tree grows following its own growth trend with some structural changes in growth over time. In the present article, a new method is proposed to detect a structural change in the growth process. We formulate the method as a simple statistical test for signal detection without constructing any specific model for the structural change. To evaluate the p-value of the test, the tube method is developed because the regular distribution theory is insufficient. Using two sets of tree diameter growth data sampled from planted forest stands of Cryptomeria japonica in Japan, we conduct an analysis of identifying the effect of thinning on the growth process as a structural change. Our results demonstrate that the proposed method is useful to identify the structural change caused by thinning. We also provide the properties of the method in terms of the size and power of the test.

MICE--multiple-peak identification, characterization, and estimation--is a procedure for estimating a lower bound of the number of frequency peaks and for estimating the frequency peak parameters. The leading application is protein structure determination using nuclear magnetic resonance (NMR) experiments. NMR frequency data are multiple-peak data, where each frequency peak corresponds to two connected atoms in the three-dimensional protein structure. We analyze the NMR frequency data through a series of steps: a preliminary step for separating the signal from the background followed by identification of local maxima up to a noise-level-dependent threshold, estimation of the frequency peak parameters using an iterative algorithm, and detection of mixtures of peaks using hypothesis testing.

There is an increasing interest in the use of two-stage case-control studies to reduce genotyping costs in the search for genes underlying common disorders. Instead of analyzing the data from the second stage separately, a more powerful test can be performed by combining the data from both stages. However, standard tests cannot be used because only the markers that are significant in the first stage are selected for the second stage and the test statistics at both stages are dependent because they partly involve the same data. Theoretical approximations are not available for commonly used test statistics and in this specific context simulations can be problematic because of the computational burden. We therefore derived a cost-effective, that is, accurate but fast in terms of central processing unit (CPU) time, approximation for the distribution of Pearson's statistic on 2 xm contingency tables in two-stage design with combined data. We included this approximation in an iterative method for designing optimal two-stage studies. Simulations supported the accuracy of our approximation. Numerical results confirmed that the use of two-stage designs reduces the genotyping burden substantially. Compared to not combining data, combining the data decreases the required sample sizes on average by 15% and the genotyping burden by 5%.

Clinical trial designs involving correlated data often arise in biomedical research. The intracluster correlation needs to be taken into account to ensure the validity of sample size and power calculations. In contrast to the fixed-sample designs, we propose a flexible trial design with adaptive monitoring and inference procedures. The total sample size is not predetermined, but adaptively re-estimated using observed data via a systematic mechanism. The final inference is based on a weighted average of the block-wise test statistics using generalized estimating equations, where the weight for each block depends on cumulated data from the ongoing trial. When there are no significant treatment effects, the devised stopping rule allows for early termination of the trial and acceptance of the null hypothesis. The proposed design updates information regarding both the effect size and within-cluster correlation based on the cumulated data in order to achieve a desired power. Estimation of the parameter of interest and its confidence interval are proposed. We conduct simulation studies to examine the operating characteristics and illustrate the proposed method with an example.

Summary. We derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods. These methods are based on estimating functions motivated by a working “mixed-Poisson” assumption under which conditioning can eliminate subject-specific random effects. Robust pseudoscore test statistics are obtained via “sandwich” variance estimation. The relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time-homogeneous Poisson model. The robustness and empirical power of the semiparametric approach are assessed through simulation. Adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two-period crossover trial of patients with bronchial asthma.

In clinical studies, multiple superiority/equivalence testing procedures can be applied to classify a new treatment as superior, equivalent (same therapeutic effect), or inferior to each set of standard treatments. Previous stepwise approaches (Dunnett and Tamhane, 1997, Statistics in Medicine16, 2489-2506; Kwong, 2001, Journal of Statistical Planning and Inference 97, 359-366) are only appropriate for balanced designs. Unfortunately, the construction of similar tests for unbalanced designs is far more complex, with two major difficulties: (i) the ordering of test statistics for superiority may not be the same as the ordering of test statistics for equivalence; and (ii) the correlation structure of the test statistics is not equi-correlated but product-correlated. In this article, we seek to develop a two-stage testing procedure for unbalanced designs, which are very popular in clinical experiments. This procedure is a combination of step-up and single-step testing procedures, while the familywise error rate is proved to be controlled at a designated level. Furthermore, a simulation study is conducted to compare the average powers of the proposed procedure to those of the single-step procedure. In addition, a clinical example is provided to illustrate the application of the new procedure.

In this article, we consider problems with correlated data that can be summarized in a 2 x 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. Lui (1998, Biometrics54, 706-711) considered confidence interval estimation of rate ratio based on Fieller-type, Wald-type, and logarithmic transformation statistics. We reexamine the same problem under the context of confidence interval construction on false-negative rate ratio in diagnostic performance when combining two diagnostic tests. We propose a score statistic for testing the null hypothesis of nonunity false-negative rate ratio. Score test-based confidence interval construction for false-negative rate ratio will also be discussed. Simulation studies are conducted to compare the performance of the new derived score test statistic and existing statistics for small to moderate sample sizes. In terms of confidence interval construction, our asymptotic score test-based confidence interval estimator possesses significantly shorter expected width with coverage probability being close to the anticipated confidence level. In terms of hypothesis testing, our asymptotic score test procedure has actual type I error rate close to the pre-assigned nominal level. We illustrate our methodologies with real examples from a clinical laboratory study and a cancer study.

Summary. In this article, we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match-pairs design. Using the ratio of two proportions as the equivalence measure, we derive sample size formulas based on a score statistic for two types of analyses: hypothesis testing and confidence interval estimation. Depending on the purpose of a study, these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level. Our empirical results confirm that these score methods are reliable in terms of true size, coverage probability, and skewness. A liver scan detection study is used to illustrate the proposed methods.

Summary. Using genetic recombination data to make inferences about chiasmata on the tetrad during meiosis is a classic problem dating back to Weinstein's paper in 1936 (Genetics21, 155–199). In the last few years, Weinstein's methods have been revived and applied to new problems, but a number of important statistical issues remain unresolved. Recently, we developed improved statistical methods for studying the frequency distribution of the number of chiasmata (Yu and Feingold, 2001, Biometrics57, 427–434). In the current article, we develop methods for the complementary issue of studying the spatial distribution of chiasmata. Somewhat different statistical approaches are needed for the spatial problem than for the frequency problem because different scientific questions are of interest. We explore the properties of the maximum likelihood estimate (MLE) for chiasma spatial distributions and propose improvements to the estimation procedures. We develop a class of statistical tests for comparing chiasma patterns in tetrads that have undergone normal meiosis and tetrads that have had a nondisjunction event. Finally, we propose an EM algorithm to find the MLE when the observed data is ambiguous, as is often the case in human datasets. We apply our improved methods to reanalyze a dataset from the literature studying the association between crossover location and meiotic nondisjunction of chromosome 21.

Summary. The problem of inferring kinship structure among a sample of individuals using genetic markers is considered with the objective of developing hypothesis tests for genetic relatedness with nearly optimal properties. The class of tests considered are those that are constrained to be permutation invariant, which in this context defines tests whose properties do not depend on the labeling of the individuals. This is appropriate when all individuals are to be treated identically from a statistical point of view. The approach taken is to derive tests that are provably most powerful for a permutation invariant alternative hypothesis that is, in some sense, close to a null hypothesis of mutual independence. This is analagous to the locally most powerful test commonly used in parametric inference. Although the resulting test statistic is a U-statistic, normal approximation theory is found to be inapplicable because of high skewness. As an alternative it is found that a conditional procedure based on the most powerful test statistic can calculate accurate significance levels without much loss in power. Examples are given in which this type of test proves to be more powerful than a number of alternatives considered in the literature, including Queller and Goodknight's (1989) estimate of genetic relatedness, the average number of shared alleles (Blouin, 1996), and the number of feasible sibling triples (Almudevar and Field, 1999).

We present a method for comparing the survival functions of quality-adjusted lifetime from two treatments. This test statistic becomes the ordinary log-rank test when quality-adjusted lifetime is the same as the survival time. Simulation experiments are conducted to examine the behavior of our proposed test statistic under both null and alternative hypotheses. In addition, we apply our method to a breast cancer trial for comparing the distribution of quality-adjusted lifetime between two treatment regimes.

Summary. The accelerated hazards regression model is introduced to study the relationship between survival times and covariates through a scale change between hazard functions. The model is also compared with several other popular classes of regression models for censored survival data in statistical literature. Test statistics are proposed and studied to assess the model's adequacy. Actual data from a randomized clinical trial of biodegradable carmustine polymer for treatment of brain cancer are analyzed to demonstrate the potential application of the regression model and the proposed test statistics.

The association analysis between the disease and genetic alleles is one of the simple methods for localizing the susceptibility locus in the genes. For revealing the association, several statistical tests have been proposed without discussing explicitly the alternative hypotheses. We therefore specify two types of alternative hypotheses (i.e., there is only one susceptibility allele in the locus, and there is an extension or shortening of alleles associated with the disease) and derive exact tests for the respective hypotheses. We also propose to combine these two tests when the prior knowledge is not sufficient enough to specify one of these two hypotheses. In particular, these ideas are extended to the haplotype analysis of three-way association between the disease and bivariate allele frequencies at two closely linked loci. As a by-product, a factorization of the probability distribution of the three-way cell frequencies under the null hypothesis of no three-way interaction is obtained.

Summary. In this paper, a semiparametric bivariate linear regression model for survival and quality-adjusted survival is investigated. Even with a parametric specification for the joint distribution, maximum likelihood is not applicable because of induced informative censoring. We propose inference procedures based on estimating functions. The estimators are consistent and asymptotically normal. Hypothesis tests and confidence intervals may be constructed with easy-to-implement resampling techniques. Simultaneous regression modeling of survival and quality-adjusted survival has not been studied formally. Our methodology gives parameter estimates that are highly interpretable in the context of a cost-effectiveness analysis. The usefulness of the proposal is illustrated with a breast cancer dataset.

Estimation of tetrad crossover frequency distributions from genetic recombination data is a classic problem dating back to Weinstein (1936, Genetics 21, 155-199). But a number of important issues, such as how to specify the maximum number of crossovers, how to construct confidence intervals for crossover probabilities, and how to obtain correct p-values for hypothesis tests, have never been adequately addressed. In this article, we obtain some properties of the maximum likelihood estimate (MLE) for crossover probabilities that imply guidelines for choosing the maximum number of crossovers. We give these results for both normal meiosis and meiosis with nondisjunction. We also develop an accelerated EM algorithm to find the MLE more efficiently. We propose bootstrap-based methods to find confidence intervals and p-values and conduct simulation studies to check the validity of the bootstrap approach.

SUMMARY. It is proposed that the orientation of elongate objects, such as bones, may be used to identify the flow direction of ancient river deposits. If true, elongate objects could be of great value when ancient bedforms such as ripples and dunes are not visible. Two sandstone quarries were investigated wherein the paleoflow direction was determined from both bedforms and elongate dinosaur bones. A mixture of two von Mises distributions captures the observation that elongate bones transported under unidirectional flow conditions will align both parallel and perpendicular to the flow direction. Likelihood ratio tests for a mixture of two von Mises distributions are given. The power of these tests is investigated by simulation since the direction of dinosaur bones agrees with the primary bedforms if the hypothesis test comparing the dominant mean direction of the bones to the paleoflow direction fails to reject. The likelihood ratio test on the dominant mean direction has reasonable power. If the two mean directions in the mixture distribution are ir apart, a more powerful likelihood ratio test can be used. The likelihood ratio test on the hypothesis that the two mean directions are exactly ir apart is useful in determining if the assumptions of the more powerful test are satisfied.

This article is concerned with the analysis of recurrent events in the presence of a terminal event such as death. We consider the mean frequency function, defined as the marginal mean of the cumulative number of recurrent events over time. A simple nonparametric estimator for this quantity is presented. It is shown that the estimator, properly normalized, converges weakly to a zero-mean Gaussian process with an easily estimable covariance function. Nonparametric statistics for comparing two mean frequency functions and for combining data on recurrent events and death are also developed. The asymptotic null distributions of these statistics, together with consistent variance estimators, are derived. The small-sample properties of the proposed estimators and test statistics are examined through simulation studies. An application to a cancer clinical trial is provided.

Summary. In group testing, the test unit consists of a group of individuals. If the group test is positive, then one or more individuals in the group are assumed to be positive. A group observation in binomial group testing can be, say, the test result (positive or negative) for a pool of blood samples that come from several different individuals. It has been shown that, when the proportion (p) of infected individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of those infected. We extend the potential applications of group testing to hypothesis-testing problems wherein one wants to test for a relationship between p and a classification or quantitative covariable. Asymptotic relative efficiencies (AREs) of tests based on group testing versus the usual individual testing are obtained. The Pitman ARE strongly favors group testing in many cases. Small-sample results from simulation studies are given and are consistent with the large-sample (asymptotic) findings. We illustrate the potential advantages of group testing in hypothesis testing using HIV-1 seroprevalence data.

SUMMARY. We introduce two test procedures for comparing two survival distributions on the basis of randomly right-censored data consisting of both paired and unpaired observations. Our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data. One generalization adapts the Prentice-Wilcoxon score, while the other adapts the Akritas score. The use of these particular scoring systems in pooled rank tests with randomly right-censored paired data has been advocated by several researchers. Our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores. Permutation versions of tests for right-censored paired data and for two independent right-censored samples that use the proposed scoring systems are obtained as special cases of our test procedures. Simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log-logistic distributions for the survival times. We also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data. The tests are applied to skin graft data previously reported elsewhere.

Locating quantitative trait loci (QTL), or genomic regions associated with known molecular markers, is of increasing interest in a wide variety of applications ranging from human genetics to agricultural genetics. The hope of locating QTL (or genes) affecting a quantitative trait is that it will lead to characterization and possible manipulations of these genes. However, the complexity of both statistical and genetic issues surrounding the location of these regions calls into question the asymptotic statistical results supplying the distribution of the test statistics employed. Coupled with the power of current-day computing, permutation theory was reintroduced for the purpose of estimating the distribution of any test statistic used to test for the location of QTL. Permutation techniques have offered an attractive alternative to significance measures based on asymptotic theory. The ideas of permutation testing are extended in this application to include confidence intervals for the thresholds and p-values estimated in permutation testing procedures. The confidence intervals developed account for the Monte Carlo error associated with practical applications of permutation testing and lead to an effective method of determining an efficient permutation sample size.