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Changepoint detection methods are used in many areas of science and engineering, for example, in the analysis of copy number variation data to detect abnormalities in copy numbers along the genome. Despite the broad array of available tools, methodology for quantifying our uncertainty in the strength (or the presence) of given changepoints post-selection are lacking. Post-selection inference offers a framework to fill this gap, but the most straightforward application of these methods results in low-powered hypothesis tests and leaves open several important questions about practical usability. In this work, we carefully tailor post-selection inference methods toward changepoint detection, focusing on copy number variation data. To accomplish this, we study commonly used changepoint algorithms: binary segmentation, as well as two of its most popular variants, wild and circular, and the fused lasso. We implement some of the latest developments in post-selection inference theory, mainly auxiliary randomization. This improves the power, which requires implementations of Markov chain Monte Carlo algorithms (importance sampling and hit-and-run sampling) to carry out our tests. We also provide recommendations for improving practical useability, detailed simulations, and example analyses on array comparative genomic hybridization as well as sequencing data.

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid hypothesis tests for a low-dimensional regression parameter (e.g. the causal effect of an exposure A on an outcome Y) in high-dimensional models. So far there has been limited focus on model misspecification, although this is inevitable in high-dimensional settings. We propose tests of the null that are uniformly valid under sparsity conditions weaker than those typically invoked in the literature, assuming working models for the exposure and outcome are both correctly specified. When one of the models is misspecified, by amending the procedure for estimating the nuisance parameters, our tests continue to be valid; hence they are doubly robust. Our proposals are straightforward to implement using existing software for penalized maximum likelihood estimation and do not require sample-splitting. We illustrate them in simulations and an analysis of data obtained from the Ghent University Intensive Care Unit., Comment: 53 pages, 5 tables

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.

This paper addresses patient heterogeneity associated with prediction problems in biomedical applications. We propose a systematic hypothesis testing approach to determine the existence of patient subgroup structure and the number of subgroups in patient population if subgroups exist. A mixture of generalized linear models is considered to model the relationship between the disease outcome and patient characteristics and clinical factors, including targeted biomarker profiles. We construct a test statistic based on expectation maximization (EM) algorithm and derive its asymptotic distribution under the null hypothesis. An important computational advantage of the test is that the involved parameter estimates under the complex alternative hypothesis can be obtained through a small number of EM iterations, rather than optimizing the objective function. We demonstrate the finite sample performance of the proposed test in terms of type-I error rate and power, using extensive simulation studies. The applicability of the proposed method is illustrated through an application to a multi-center prostate cancer study.

In the analysis of next-generation sequencing technology, massive discrete data are generated from short read counts with varying biological coverage. Conducting conditional hypothesis testing such as Fisher’s Exact Test at every genomic region of interest thus leads to a heterogeneous multiple discrete testing problem. However, most existing multiple testing procedures for controlling the false discovery rate (FDR) assume that test statistics are continuous and become conservative for discrete tests. To overcome the conservativeness, in this article, we propose a novel multiple testing procedure for better FDR control on heterogeneous discrete tests. Our procedure makes decisions based on the marginal critical function (MCF) of randomized tests, which enables achieving a powerful and non-randomized multiple testing procedure. We provide upper bounds of the positive FDR (pFDR) and the positive false non-discovery rate (pFNR) corresponding to our procedure. We also prove that the set of detections made by our method contains every detection made by a naive application of the widely-used q-value method. We further demonstrate the improvement of our method over other existing multiple testing procedures by simulations and a real example of differentially methylated region (DMR) detection using whole-genome bisulfite sequencing (WGBS) data.

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.

Researchers in genetics and other life sciences commonly use permutation tests to evaluate differences between groups. Permutation tests have desirable properties, including exactness if data are exchangeable, and are applicable even when the distribution of the test statistic is analytically intractable. However, permutation tests can be computationally intensive. We propose both an asymptotic approximation and a resampling algorithm for quickly estimating small permutation p-values (e.g.

Functional data arise frequently in biomedical studies, where it is often of interest to investigate the association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not systematically studied. In this article, we first investigate the power performance of the Wald-type test with varying thresholds in selecting the number of PCs for the functional covariates, and show that the power is sensitive to the choice of thresholds. To circumvent the issue, we propose a new method of ordering and selecting principal components to construct test statistics. The proposed method takes into account both the association with the response and the variation along each eigenfunction. We establish its theoretical properties and assess the finite sample properties through simulations. Our simulation results show that the proposed test is more robust against the choice of threshold while being as powerful as, and often more powerful than, the existing method. We then apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study.

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependence that is often encoded in terms of partial correlation. Such a graph is inferred from the matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions does not offer a direct statistical significance quantification for the estimated links. In this article, we adopt a matrix normal distribution framework and formulate the brain connectivity analysis as a precision matrix hypothesis testing problem. Based on the separable spatial-temporal dependence structure, we develop oracle and data-driven procedures to test both the global hypothesis that all spatial locations are conditionally independent, and simultaneous tests for identifying conditional dependent spatial locations with false discovery rate control. Our theoretical results show that the data-driven procedures perform asymptotically as well as the oracle procedures and enjoy certain optimality properties. The empirical finite-sample performance of the proposed tests is studied via intensive simulations, and the new tests are applied on a real electroencephalography data analysis.

Summary This article investigates a generalized semiparametric varying-coefficient model for longitudinal data that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects. Different link functions can be selected to provide a rich family of models for longitudinal data. The model assumes that the time-varying effects are unspecified functions of time and the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. The estimation procedure is developed using local linear smoothing and profile weighted least squares estimation techniques. Hypothesis testing procedures are developed to test the parametric functions of the covariate-varying effects. The asymptotic distributions of the proposed estimators are established. A working formula for bandwidth selection is discussed and examined through simulations. Our simulation study shows that the proposed methods have satisfactory finite sample performance. The proposed methods are applied to the ACTG 244 clinical trial of HIV infected patients being treated with Zidovudine to examine the effects of antiretroviral treatment switching before and after HIV develops the T215Y/F drug resistance mutation. Our analysis shows benefits of treatment switching to the combination therapies as compared to continuing with ZDV monotherapy before and after developing the 215-mutation.

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.

Large assembled cohorts with banked biospecimens offer valuable opportunities to identify novel markers for risk prediction. When the outcome of interest is rare, an effective strategy to conserve limited biological resources while maintaining reasonable statistical power is the case cohort (CCH) sampling design, in which expensive markers are measured on a subset of cases and controls. However, the CCH design introduces significant analytical complexity due to outcome-dependent, finite-population sampling. Current methods for analyzing CCH studies focus primarily on the estimation of simple survival models with linear effects; testing and estimation procedures that can efficiently capture complex non-linear marker effects for CCH data remain elusive. In this article, we propose inverse probability weighted (IPW) variance component type tests for identifying important marker sets through a Cox proportional hazards kernel machine (CoxKM) regression framework previously considered for full cohort studies (Cai et al., 2011). The optimal choice of kernel, while vitally important to attain high power, is typically unknown for a given dataset. Thus, we also develop robust testing procedures that adaptively combine information from multiple kernels. The proposed IPW test statistics have complex null distributions that cannot easily be approximated explicitly. Furthermore, due to the correlation induced by CCH sampling, standard resampling methods such as the bootstrap fail to approximate the distribution correctly. We, therefore, propose a novel perturbation resampling scheme that can effectively recover the induced correlation structure. Results from extensive simulation studies suggest that the proposed IPW CoxKM testing procedures work well in finite samples. The proposed methods are further illustrated by application to a Danish CCH study of Apolipoprotein C-III markers on the risk of coronary heart disease.

In many practical cases of multiple hypothesis problems, it can be expected that the alternatives are not symmetrically distributed. If it is known a priori that the distributions of the alternatives are skewed, we show that this information yields high power procedures as compared to the procedures based on symmetric alternatives when testing multiple hypotheses. We propose a Bayesian decision theoretic rule for multiple directional hypothesis testing, when the alternatives are distributed as skewed, under a constraint on a mixed directional false discovery rate. We compare the proposed rule with a frequentist's rule of Benjamini and Yekutieli (2005) using simulations. We apply our method to a well-studied HIV dataset.

The field of neuroimaging dedicated to mapping connections in the brain is increasingly being recognized as key for understanding neurodevelopment and pathology. Networks of these connections are quantitatively represented using complex structures, including matrices, functions, and graphs, which require specialized statistical techniques for estimation and inference about developmental and disorder-related changes. Unfortunately, classical statistical testing procedures are not well suited to high-dimensional testing problems. In the context of global or regional tests for differences in neuroimaging data, traditional analysis of variance (ANOVA) is not directly applicable without first summarizing the data into univariate or low-dimensional features, a process that might mask the salient features of high-dimensional distributions. In this work, we consider a general framework for two-sample testing of complex structures by studying generalized within-group and between-group variances based on distances between complex and potentially high-dimensional observations. We derive an asymptotic approximation to the null distribution of the ANOVA test statistic, and conduct simulation studies with scalar and graph outcomes to study finite sample properties of the test. Finally, we apply our test to our motivating study of structural connectivity in autism spectrum disorder.

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods.

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.

Time-dependent receiver operating characteristic (ROC) curves and their area under the curve (AUC) are important measures to evaluate the prediction accuracy of biomarkers for time-to-event endpoints (e.g., time to disease progression or death). In this article, we propose a direct method to estimate AUC(t) as a function of time t using a flexible fractional polynomials model, without the middle step of modeling the time-dependent ROC. We develop a pseudo partial-likelihood procedure for parameter estimation and provide a test procedure to compare the predictive performance between biomarkers. We establish the asymptotic properties of the proposed estimator and test statistics. A major advantage of the proposed method is its ease to make inference and to compare the prediction accuracy across biomarkers, rendering our method particularly appealing for studies that require comparing and screening a large number of candidate biomarkers. We evaluate the finite-sample performance of the proposed method through simulation studies and illustrate our method in an application to AIDS Clinical Trials Group 175 data.

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.