Adjusting O'Brien's test to control type I error for the generalized nonparametric Behrens-Fisher problem

Riluzole for Degenerative Cervical Myelopathy: A Secondary Analysis of the CSM-PROTECT Trial

Importance

The modified Japanese Orthopaedic Association (mJOA) scale is the most common scale used to represent outcomes of degenerative cervical myelopathy (DCM); however, it lacks consideration for neck pain scores and neglects the multidimensional aspect of recovery after surgery.

Objective

To use a global statistical approach that incorporates assessments of multiple outcomes to reassess the efficacy of riluzole in patients undergoing spinal surgery for DCM.

Design, Setting, and Participants

This was a secondary analysis of prespecified secondary end points within the Efficacy of Riluzole in Surgical Treatment for Cervical Spondylotic Myelopathy (CSM-PROTECT) trial, a multicenter, double-blind, phase 3 randomized clinical trial conducted from January 2012 to May 2017. Adult surgical patients with DCM with moderate to severe myelopathy (mJOA scale score of 8-14) were randomized to receive either riluzole or placebo. The present study was conducted from July to December 2023.

Intervention

Riluzole (50 mg twice daily) or placebo for a total of 6 weeks, including 2 weeks prior to surgery and 4 weeks following surgery.

Main Outcomes and Measures

The primary outcome measure was a difference in clinical improvement from baseline to 1-year follow-up, assessed using a global statistical test (GST). The 36-Item Short Form Health Survey Physical Component Score (SF-36 PCS), arm and neck pain numeric rating scale (NRS) scores, American Spinal Injury Association (ASIA) motor score, and Nurick grade were combined into a single summary statistic known as the global treatment effect (GTE).

Results

Overall, 290 patients (riluzole group, 141; placebo group, 149; mean [SD] age, 59 [10.1] years; 161 [56%] male) were included. Riluzole showed a significantly higher probability of global improvement compared with placebo at 1-year follow-up (GTE, 0.08; 95% CI, 0.00-0.16; P = .02). A similar favorable global response was seen at 35 days and 6 months (GTE for both, 0.07; 95% CI, -0.01 to 0.15; P = .04), although the results were not statistically significant. Riluzole-treated patients had at least a 54% likelihood of achieving better outcomes at 1 year compared with the placebo group. The ASIA motor score and neck and arm pain NRS combination at 1 year provided the best-fit parsimonious model for detecting a benefit of riluzole (GTE, 0.11; 95% CI, 0.02-0.16; P = .007).

Conclusions and Relevance

In this secondary analysis of the CSM-PROTECT trial using a global outcome technique, riluzole was associated with improved clinical outcomes in patients with DCM. The GST offered probability-based results capable of representing diverse outcome scales and should be considered in future studies assessing spine surgery outcomes.

A novel longitudinal rank-sum test for multiple primary endpoints in clinical trials: Applications to neurodegenerative disorders

Neurodegenerative disorders such as Alzheimer's disease (AD) present a significant global health challenge, characterized by cognitive decline, functional impairment, and other debilitating effects. Current AD clinical trials often assess multiple longitudinal primary endpoints to comprehensively evaluate treatment efficacy. Traditional methods, however, may fail to capture global treatment effects, require larger sample sizes due to multiplicity adjustments, and may not fully exploit multivariate longitudinal data. To address these limitations, we introduce the Longitudinal Rank Sum Test (LRST), a novel nonparametric rank-based omnibus test statistic. The LRST enables a comprehensive assessment of treatment efficacy across multiple endpoints and time points without multiplicity adjustments, effectively controlling Type I error while enhancing statistical power. It offers flexibility against various data distributions encountered in AD research and maximizes the utilization of longitudinal data. Extensive simulations and real-data applications demonstrate the LRST's performance, underscoring its potential as a valuable tool in AD clinical trials. Nonparametrics, Global test, rank-sum-type test, U-Statistics.

Semiparametric regression modeling of the global percentile outcome

When no single outcome is sufficient to capture the multidimensional impairments of a disease, investigators often rely on multiple outcomes for comprehensive assessment of global disease status. Methods for assessing covariate effects on global disease status include the composite outcome and global test procedures. One global test procedure is the O'Brien's rank-sum test, which combines information from multiple outcomes using a global rank-sum score. However, existing methods for the global rank-sum do not lend themselves to regression modeling. We consider sensible regression strategies for the global percentile outcome (GPO), under the transformed linear model and the monotonic index model. Posing minimal assumptions, we develop estimation and inference procedures that account for the special features of the GPO. Asymptotics are established using U-statistic and U-process techniques. We illustrate the practical utilities of the proposed methods via extensive simulations and application to a Parkinson's disease study.

Directional-sum test for nonparametric Behrens-Fisher problem with applications to the dietary intervention trial

For a nonparametric Behrens-Fisher problem, a directional-sum test is proposed based on division-combination strategy. A one-layer wild bootstrap procedure is given to calculate its statistical significance. We conduct simulation studies with data generated from lognormal, t and Laplace distributions to show that the proposed test can control the type I error rates properly and is more powerful than the existing rank-sum and maximum-type tests under most of the considered scenarios. Applications to the dietary intervention trial further show the performance of the proposed test.

Use of composite outcomes to assess risk-benefit in clinical trials

Before a novel treatment can be deemed a clinical success, an assessment of its risk-benefit profile must be made. One of the inherent challenges for this assessment comes from the multiplicity that arises from comparing treatment groups across multiple outcomes. Composite outcomes that summarize a patient's clinical status, or severity, across a prioritized list of safety and efficacy outcomes have become increasing popular. In this article, we review these approaches and illustrate through examples some of the challenges and complexities of a composite derived from prioritized outcomes, such as the win ratio. These challenges include the difficult tension between the analytical validity that comes from choosing a pre-specified outcome and an evaluation that is responsive to unexpected safety events that arise during the course of a trial. Other challenges include a sensitivity of the resulting test statistic to the underlying censoring distribution and other nuisance parameters. Approaches that resolve some of the difficulties of the analytical challenges associated with prioritized outcomes are then discussed. Ultimately, a composite outcome of net clinical benefit is another decision tool, but one to be used alongside more traditional analyses of efficacy and safety, and with the broader perspective that investigators, the data safety monitoring board, and regulators bring to an evaluation of risk-benefit.

Methods for the analysis of multiple endpoints in small populations: A review

While current guidelines generally recommend single endpoints for primary analyses of confirmatory clinical trials, it is recognized that certain settings require inference on multiple endpoints for comprehensive conclusions on treatment effects. Furthermore, combining treatment effect estimates from several outcome measures can increase the statistical power of tests. Such an efficient use of resources is of special relevance for trials in small populations. This paper reviews approaches based on a combination of test statistics or measurements across endpoints as well as multiple testing procedures that allow for confirmatory conclusions on individual endpoints. We especially focus on feasibility in trials with small sample sizes and do not solely rely on asymptotic considerations. A systematic literature search in the Scopus database, supplemented by a manual search, was performed to identify research papers on analysis methods for multiple endpoints with relevance to small populations. The identified methods were grouped into approaches that combine endpoints into a single measure to increase the power of statistical tests and methods to investigate differential treatment effects in several individual endpoints by multiple testing.

Robust multivariate nonparametric tests for detection of two-sample location shift in clinical trials

This article presents and investigates performance of a series of robust multivariate nonparametric tests for detection of location shift between two multivariate samples in randomized controlled trials. The tests are built upon robust estimators of distribution locations (medians, Hodges-Lehmann estimators, and an extended U statistic) with both unscaled and scaled versions. The nonparametric tests are robust to outliers and do not assume that the two samples are drawn from multivariate normal distributions. Bootstrap and permutation approaches are introduced for determining the p-values of the proposed test statistics. Simulation studies are conducted and numerical results are reported to examine performance of the proposed statistical tests. The numerical results demonstrate that the robust multivariate nonparametric tests constructed from the Hodges-Lehmann estimators are more efficient than those based on medians and the extended U statistic. The permutation approach can provide a more stringent control of Type I error and is generally more powerful than the bootstrap procedure. The proposed robust nonparametric tests are applied to detect multivariate distributional difference between the intervention and control groups in the Thai Healthy Choices study and examine the intervention effect of a four-session motivational interviewing-based intervention developed in the study to reduce risk behaviors among youth living with HIV.

Added Value of Computer-aided CT Image Features for Early Lung Cancer Diagnosis with Small Pulmonary Nodules: A Matched Case-Control Study

Purpose To test whether computer-aided diagnosis (CAD) approaches can increase the positive predictive value (PPV) and reduce the false-positive rate in lung cancer screening for small nodules compared with human reading by thoracic radiologists. Materials and Methods A matched case-control sample of low-dose computed tomography (CT) studies in 186 participants with 4-20-mm noncalcified lung nodules who underwent biopsy in the National Lung Screening Trial (NLST) was selected. Variables used for matching were age, sex, smoking status, chronic obstructive pulmonary disease status, body mass index, study year of the positive screening test, and screening results. Studies before lung biopsy were randomly split into a training set (70 cancers plus 70 benign controls) and a validation set (20 cancers plus 26 benign controls). Image features from within and outside dominant nodules were extracted. A CAD algorithm developed from the training set and a random forest classifier were applied to the validation set to predict biopsy outcomes. Receiver operating characteristic analysis was used to compare the prediction accuracy of CAD with the NLST investigator's diagnosis and readings from three experienced and board-certified thoracic radiologists who used contemporary clinical practice guidelines. Results In the validation cohort, the area under the receiver operating characteristic curve for CAD was 0.9154. By default, the sensitivity, specificity, and PPV of the NLST investigators were 1.00, 0.00, and 0.43, respectively. The sensitivity, specificity, PPV, and negative predictive value of CAD and the three radiologists' combined reading were 0.95, 0.88, 0.86, and 0.96 and 0.70, 0.69, 0.64, and 0.75, respectively. Conclusion CAD could increase PPV and reduce the false-positive rate in the early diagnosis of lung cancer. © RSNA, 2017 Online supplemental material is available for this article.

Bayesian Hierarchical Joint Modeling Using Skew-Normal/Independent Distributions

The multiple longitudinal outcomes collected in many clinical trials are often analyzed by multilevel item response theory (MLIRT) models. The normality assumption for the continuous outcomes in the MLIRT models can be violated due to skewness and/or outliers. Moreover, patients' follow-up may be stopped by some terminal events (e.g., death or dropout) which are dependent on the multiple longitudinal outcomes. We proposed a joint modeling framework based on the MLIRT model to account for three data features: skewness, outliers, and dependent censoring. Our method development was motivated by a clinical study for Parkinson's disease.

Composite End Points in Clinical Trials of Heart Failure Therapy

Composite end points are popular outcomes in clinical trials of heart failure therapies. For example, a global rank composite is typically analyzed using a Mann–Whitney U test, and the results are summarized by the mean of ranks and a corresponding P value. The mean of ranks is uninformative, and a clinically meaningful estimate of the treatment effect is needed to communicate study results and facilitate an assessment of heterogeneity (the consistency of the effect across outcomes). The probability index is intuitive for clinicians, easy to calculate, and may be applied to various composites. We suggest a simple and familiar plot to assess heterogeneity across outcomes, which should be routine when analyzing composites. We think that the probability index provides an immediate and simple solution to an overt problem.

An optimal Wilcoxon-Mann-Whitney test of mortality and a continuous outcome

We consider a two-group randomized clinical trial, where mortality affects the assessment of a follow-up continuous outcome. Using the worst-rank composite endpoint, we develop a weighted Wilcoxon-Mann-Whitney test statistic to analyze the data. We determine the optimal weights for the Wilcoxon-Mann-Whitney test statistic that maximize its power. We derive a formula for its power and demonstrate its accuracy in simulations. Finally, we apply the method to data from an acute ischemic stroke clinical trial of normobaric oxygen therapy.

A rank test for bivariate time-to-event outcomes when one event is a surrogate

In many clinical settings, improving patient survival is of interest but a practical surrogate, such as time to disease progression, is instead used as a clinical trial's primary endpoint. A time-to-first endpoint (e.g., death or disease progression) is commonly analyzed but may not be adequate to summarize patient outcomes if a subsequent event contains important additional information. We consider a surrogate outcome very generally as one correlated with the true endpoint of interest. Settings of interest include those where the surrogate indicates a beneficial outcome so that the usual time-to-first endpoint of death or surrogate event is nonsensical. We present a new two-sample test for bivariate, interval-censored time-to-event data, where one endpoint is a surrogate for the second, less frequently observed endpoint of true interest. This test examines whether patient groups have equal clinical severity. If the true endpoint rarely occurs, the proposed test acts like a weighted logrank test on the surrogate; if it occurs for most individuals, then our test acts like a weighted logrank test on the true endpoint. If the surrogate is a useful statistical surrogate, our test can have better power than tests based on the surrogate that naively handles the true endpoint. In settings where the surrogate is not valid (treatment affects the surrogate but not the true endpoint), our test incorporates the information regarding the lack of treatment effect from the observed true endpoints and hence is expected to have a dampened treatment effect compared with tests based on the surrogate alone. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Bayesian multiple imputation for missing multivariate longitudinal data from a Parkinson's disease clinical trial

In Parkinson's disease (PD) clinical trials, Parkinson's disease is studied using multiple outcomes of various types (e.g. binary, ordinal, continuous) collected repeatedly over time. The overall treatment effects across all outcomes can be evaluated based on a global test statistic. However, missing data occur in outcomes for many reasons, e.g. dropout, death, etc., and need to be imputed in order to conduct an intent-to-treat analysis. We propose a Bayesian method based on item response theory to perform multiple imputation while accounting for multiple sources of correlation. Sensitivity analysis is performed under various scenarios. Our simulation results indicate that the proposed method outperforms standard methods such as last observation carried forward and separate random effects model for each outcome. Our method is motivated by and applied to a Parkinson's disease clinical trial. The proposed method can be broadly applied to longitudinal studies with multiple outcomes subject to missingness.

Global rank tests for multiple, possibly censored, outcomes

Clinical trials often collect multiple outcomes on each patient, as the treatment may be expected to affect the patient on many dimensions. For example, a treatment for a neurological disease such as ALS is intended to impact several dimensions of neurological function as well as survival. The assessment of treatment on the basis of multiple outcomes is challenging, both in terms of selecting a test and interpreting the results. Several global tests have been proposed, and we provide a general approach to selecting and executing a global test. The tests require minimal parametric assumptions, are flexible about weighting of the various outcomes, and are appropriate even when some or all of the outcomes are censored. The test we propose is based on a simple scoring mechanism applied to each pair of subjects for each endpoint. The pairwise scores are then reduced to a summary score, and a rank-sum test is applied to the summary scores. This can be seen as a generalization of previously proposed nonparametric global tests (e.g., O'Brien, 1984). We discuss the choice of optimal weighting schemes based on power and relative importance of the outcomes. As the optimal weights are generally unknown in practice, we also propose an adaptive weighting scheme and evaluate its performance in simulations. We apply the methods to analyze the impact of a treatment on neurological function and death in an ALS trial.

Robust Bayesian hierarchical model using normal/independent distributions

The multilevel item response theory (MLIRT) models have been increasingly used in longitudinal clinical studies that collect multiple outcomes. The MLIRT models account for all the information from multiple longitudinal outcomes of mixed types (e.g., continuous, binary, and ordinal) and can provide valid inference for the overall treatment effects. However, the continuous outcomes and the random effects in the MLIRT models are often assumed to be normally distributed. The normality assumption can sometimes be unrealistic and thus may produce misleading results. The normal/independent (NI) distributions have been increasingly used to handle the outlier and heavy tail problems in order to produce robust inference. In this article, we developed a Bayesian approach that implemented the NI distributions on both continuous outcomes and random effects in the MLIRT models and discussed different strategies of implementing the NI distributions. Extensive simulation studies were conducted to demonstrate the advantage of our proposed models, which provided parameter estimates with smaller bias and more reasonable coverage probabilities. Our proposed models were applied to a motivating Parkinson's disease study, the DATATOP study, to investigate the effect of deprenyl in slowing down the disease progression.

Effect of creatine monohydrate on clinical progression in patients with Parkinson disease: a randomized clinical trial

IMPORTANCE

There are no treatments available to slow or prevent the progression of Parkinson disease, despite its global prevalence and significant health care burden. The National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson Disease program was established to promote discovery of potential therapies.

OBJECTIVE

To determine whether creatine monohydrate was more effective than placebo in slowing long-term clinical decline in participants with Parkinson disease.

DESIGN, SETTING, AND PATIENTS

The Long-term Study 1, a multicenter, double-blind, parallel-group, placebo-controlled, 1:1 randomized efficacy trial. Participants were recruited from 45 investigative sites in the United States and Canada and included 1741 men and women with early (within 5 years of diagnosis) and treated (receiving dopaminergic therapy) Parkinson disease. Participants were enrolled from March 2007 to May 2010 and followed up until September 2013.

INTERVENTIONS

Participants were randomized to placebo or creatine (10 g/d) monohydrate for a minimum of 5 years (maximum follow-up, 8 years).

MAIN OUTCOMES AND MEASURES

The primary outcome measure was a difference in clinical decline from baseline to 5-year follow-up, compared between the 2 treatment groups using a global statistical test. Clinical status was defined by 5 outcome measures: Modified Rankin Scale, Symbol Digit Modalities Test, PDQ-39 Summary Index, Schwab and England Activities of Daily Living scale, and ambulatory capacity. All outcomes were coded such that higher scores indicated worse outcomes and were analyzed by a global statistical test. Higher summed ranks (range, 5-4775) indicate worse outcomes.

RESULTS

The trial was terminated early for futility based on results of a planned interim analysis of participants enrolled at least 5 years prior to the date of the analysis (n = 955). The median follow-up time was 4 years. Of the 955 participants, the mean of the summed ranks for placebo was 2360 (95% CI, 2249-2470) and for creatine was 2414 (95% CI, 2304-2524). The global statistical test yielded t1865.8 = -0.75 (2-sided P = .45). There were no detectable differences (P < .01 to partially adjust for multiple comparisons) in adverse and serious adverse events by body system.

CONCLUSIONS AND RELEVANCE

Among patients with early and treated Parkinson disease, treatment with creatine monohydrate for at least 5 years, compared with placebo did not improve clinical outcomes. These findings do not support the use of creatine monohydrate in patients with Parkinson disease.

TRIAL REGISTRATION

clinicaltrials.gov Identifier: NCT00449865.

Parkinson's disease severity and use of dopaminergic medications

BACKGROUND

The effects of dopaminergic therapy in parkinson's disease (PD) can vary depending on the class of medication selected.

OBJECTIVE

The aim of this post hoc study was to determine if the class of dopaminergic therapy correlated with disease severity in persons with early, treated PD.

METHODS

A non-parametric global statistical test (GST) was used to assess the status of participants treated with dopamine agonist (DA) monotherapy, levodopa (LD) monotherapy or combined LD and DA therapy on multiple PD outcomes encompassing motor, cognitive, psychiatric and autonomic function, as well as disability and quality of life.

RESULTS

The outcomes measured at the beginning of the study showed lower disease burden for participants on initial DA monotherapy compared to those taking combined LD and DA therapy after controlling for age, education, taking cog-meds and amantadine.

CONCLUSION

This observation suggests that clinicians treating early PD patients favor combined LD and DA therapy in patients with more disabling features over DA monotherapy. As such, studies of PD progression in treated PD patients may be affected by the class of symptomatic dopaminergic therapy.

Formulating appropriate statistical hypotheses for treatment comparison in clinical trial design and analysis

We discuss the problem of properly defining treatment superiority through the specification of hypotheses in clinical trials. The need to precisely define the notion of superiority in a one-sided hypothesis test problem has been well recognized by many authors. Ideally designed null and alternative hypotheses should correspond to a partition of all possible scenarios of underlying true probability models P={P(ω):ω∈Ω} such that the alternative hypothesis Ha={P(ω):ω∈Ωa} can be inferred upon the rejection of null hypothesis Ho={P(ω):ω∈Ω(o)} However, in many cases, tests are carried out and recommendations are made without a precise definition of superiority or a specification of alternative hypothesis. Moreover, in some applications, the union of probability models specified by the chosen null and alternative hypothesis does not constitute a completed model collection P (i.e., H(o)∪H(a) is smaller than P). This not only imposes a strong non-validated assumption of the underlying true models, but also leads to different superiority claims depending on which test is used instead of scientific plausibility. Different ways to partition P fro testing treatment superiority often have different implications on sample size, power, and significance in both efficacy and comparative effectiveness trial design. Such differences are often overlooked. We provide a theoretical framework for evaluating the statistical properties of different specification of superiority in typical hypothesis testing. This can help investigators to select proper hypotheses for treatment comparison inclinical trial design.

Generalized F test and generalized deviance test in two-way ANOVA models for randomized trials

We consider the problem of detecting treatment effects in a randomized trial in the presence of an additional covariate. By reexpressing a two-way analysis of variance (ANOVA) model in a logistic regression framework, we derive generalized F tests and generalized deviance tests, which provide better power in detecting common location-scale changes of treatment outcomes than the classical F test. The null distributions of the test statistics are independent of the nuisance parameters in the models, so the critical values can be easily determined by Monte Carlo methods. We use simulation studies to demonstrate how the proposed tests perform compared with the classical F test. We also use data from a clinical study to illustrate possible savings in sample sizes.

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow-up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random-effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in 'BUGS' language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD.

Design innovations and baseline findings in a long-term Parkinson's trial: the National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson's Disease Long-Term Study-1

Based on the preclinical data and the results of a phase II futility study, creatine was selected for an efficacy trial in Parkinson's disease (PD). We present the design rationale and a description of the study cohort at baseline. A randomized, multicenter, double-blind, parallel-group, placebo-controlled phase III study of creatine (10 g daily) in participants with early, treated PD, the Long-term Study-1 (LS-1), is being conducted by the National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson's Disease network. The study utilizes a global statistical test (GST) encompassing five clinical rating scales to provide a multidimensional assessment of disease progression. A total of 1,741 PD participants from 45 sites in the United States and Canada were randomized 1:1 to either 10 g of creatine/day or matching placebo. Participants are being evaluated for a minimum of 5 years. The LS-1 baseline cohort includes participants treated with dopaminergic therapy and generally mild PD. LS-1 represents the largest cohort of patients with early treated PD ever enrolled in a clinical trial. The GST approach should provide high power to test the hypothesis that daily administration of creatine (10 g/day) is more effective than placebo in slowing clinical decline in PD between baseline and the 5-year follow-up visit against the background of dopaminergic therapy and best PD care.

Simultaneous confidence intervals on multivariate non-inferiority

We discuss the analysis of non-inferiority trials based on a multi-armed design with multiple correlated endpoints. We consider five different scenarios: (1) global non-inferiority; (2) non-inferiority for subsets of comparisons; (3) global non-inferiority for a treatment group; (4) global non-inferiority for an endpoint; and (5) local non-inferiority. We describe and compare related approaches, which are based on the union-intersection and intersection-union test principles - alone and in combination. Because non-inferiority thresholds for many differently scaled endpoints are rarely available in practice, the approaches described focus on the estimation of simultaneous confidence limits and their post hoc interpretation on non-inferiority. We discuss and demonstrate pros and cons by means of a real data example.

Basal-like breast cancer displays distinct patterns of promoter methylation

Recent microarray profiling studies on breast cancer have identified distinct subtypes that are associated with different clinical outcomes. Promoter hypermethylation of several known or putative tumor suppressor genes occurs frequently during the pathogenesis of breast cancer. We proposed that immunohistopathologic subtypes of breast cancer are likely to contain distinct promoter methylation patterns. A panel of 10 gene promoters was assessed by quantitative multiplex methylation-specific PCR in 114 invasive ductal carcinomas from Korea representing the three major subtypes [57 luminal, 24 human epidermal growth factor 2 (HER2), and 33 basal-like] based on immunohistochemical findings of estrogen receptor, progesterone receptor, HER2, cytokeratin 5/6 and epidermal growth factor receptor. The median methylation levels of HIN1, RASSF1A and TWIST, and the average methylation ratio were significantly lower in basal-like subtype compared to luminal or HER2 subtypes. In contrast, BRCA1 methylation level was significantly higher in basal-like subtype than in luminal subtype. The methylation status of a panel of four genes (APC1, CDH, BRCA1 and RAR-β) in luminal and HER2 subtypes were dissimilar, where HER2 tumors showed a significantly higher level of methylation compared to luminal tumors. These results suggest that gene methylation in breast cancer can potentially serve as epigenetic biomarkers and may contribute further to current breast cancer classification.

A Rank-Based Test for Comparison of Multidimensional Outcomes

For comparison of multiple outcomes commonly encountered in biomedical research, Huang et al. (2005) improved O'Brien's (1984) rank-sum tests through the replacement of the ad hoc variance by the asymptotic variance of the test statistics. The improved tests control the Type I error rate at the desired level and gain power when the differences between the two comparison groups in each outcome variable fall into the same direction. However, they may lose power when the differences are in different directions (e.g., some are positive and some are negative). These tests and the popular Bonferroni correction failed to show important significant difference when applied to compare heart rates from a clinical trial to evaluate the effect of a procedure to remove the cardioprotective solution HTK. We propose an alternative test statistic, taking the maximum of the individual rank-sum statistics, which controls the type I error and maintains satisfactory power regardless of the directions of the differences. Simulation studies show the proposed test to be of higher power than other tests in certain alternative parameter space of interest. Furthermore, when used to analyze the heart rates data the proposed test yields more satisfactory results.

Using global statistical tests in long-term Parkinson's disease clinical trials

Parkinson's disease (PD) impairments are multidimensional, making it difficult to choose a single primary outcome when evaluating treatments to stop or lessen the long-term decline in PD. We review commonly used multivariate statistical methods for assessing a treatment's global impact, and we highlight the novel Global Statistical Test (GST) methodology. We compare the GST to other multivariate approaches using data from two PD trials. In one trial where the treatment showed consistent improvement on all primary and secondary outcomes, the GST was more powerful than other methods in demonstrating significant improvement. In the trial where treatment induced both improvement and deterioration in key outcomes, the GST failed to demonstrate statistical evidence even though other techniques showed significant improvement. Based on the statistical properties of the GST and its relevance to overall treatment benefit, the GST appears particularly well suited for a disease like PD where disability and impairment reflect dysfunction of diverse brain systems and where both disease and treatment side effects impact quality of life. In future long term trials, use of GST for primary statistical analysis would allow the assessment of clinically relevant outcomes rather than the artificial selection of a single primary outcome.

A Weighted Rank-Sum Procedure for Comparing Samples with Multiple Endpoints

For comparing the distribution of two samples with multiple endpoints, O'Brien (1984) proposed rank-sum-type test statistics. Huang et al. (2005) extended these statistics to the general nonparametric Behrens-Fisher hypothesis problem and obtained improved test statistics by replacing the ad hoc variance with the asymptotic variance of the rank-sum statistics. In this paper we generalize the work of O'Brien (1984) and Huang et al. (2005) and propose a weighted rank-sum statistic. We show that the weighted rank-sum statistic is asymptotically normally distributed, permitting the computation of power, p-values and confidence intervals. We further demonstrate via simulation that the weighted rank-sum statistic is efficient in controlling the type I error rate and under certain alternatives, is more powerful than the statistics of O'Brien (1984) and Huang et al.(2005).

A rank-based sample size method for multiple outcomes in clinical trials

O'Brien (Biometrics 1984; 40:1079-1087) introduced a rank-sum-type global statistical test to summarize treatment's effect on multiple outcomes and to determine whether a treatment is better than others. This paper presents a sample size computation method for clinical trial design with multiple primary outcomes, and O'Brien's test or its modified test (Biometrics 2005; 61:532-539) is used for the primary analysis. A new measure, the global treatment effect (GTE), is introduced to summarize treatment's efficacy from multiple primary outcomes. Computation of the GTE under various settings is provided. Sample size methods are presented based on prespecified GTE both when pilot data are available and when no pilot data are available. The optimal randomization ratio is given for both cases. We compare our sample size method with the Bonferroni adjustment for multiple tests. Since ranks are used in our derivation, sample size formulas derived here are invariant to any monotone transformation of the data and are robust to outliers and skewed distributions. When all outcomes are binary, we show how sample size is affected by the success probabilities of outcomes. Simulation shows that these sample size formulas provide good control of type I error and statistical power. An application to a Parkinson's disease clinical trial design is demonstrated. Splus codes to compute sample size and the test statistic are provided.

Robust step-down tests for multivariate independent group designs

A composite step-down procedure, in which a set of step-down tests are summarized collectively with Fisher's combination statistic, was considered to test for multivariate mean equality in two-group designs. An approximate degrees of freedom (ADF) composite procedure based on trimmed/Winsorized estimators and a non-pooled estimate of error variance is proposed, and compared to a composite procedure based on trimmed/Winsorized estimators and a pooled estimate of error variance. The step-down procedures were also compared to Hotelling's T (2) and Johansen's ADF global procedure based on trimmed estimators in a simulation study. Type I error rates of the pooled step-down procedure were sensitive to covariance heterogeneity in unbalanced designs; error rates were similar to those of Hotelling's T (2) across all of the investigated conditions. Type I error rates of the ADF composite step-down procedure were insensitive to covariance heterogeneity and less sensitive to the number of dependent variables when sample size was small than error rates of Johansen's test. The ADF composite step-down procedure is recommended for testing hypotheses of mean equality in two-group designs except when the data are sampled from populations with different degrees of multivariate skewness.

Nonparametric bayes testing of changes in a response distribution with an ordinal predictor

In certain biomedical studies, one may anticipate changes in the shape of a response distribution across the levels of an ordinal predictor. For instance, in toxicology studies, skewness and modality might change as dose increases. To address this issue, we propose a Bayesian nonparametric method for testing for distribution changes across an ordinal predictor. Using a dynamic mixture of Dirichlet processes, we allow the response distribution to change flexibly at each level of the predictor. In addition, by assigning mixture priors to the hyperparameters, we can obtain posterior probabilities of no effect of the predictor and identify the lowest dose level for which there is an appreciable change in distribution. The method also provides a natural framework for performing tests across multiple outcomes. We apply our method to data from a genotoxicity experiment.