Exploring Stratification Strategies for Population- Versus Randomization-Based Inference.

Stratification on important variables is a common practice in clinical trials, since ensuring cosmetic balance on known baseline covariates is often deemed to be a crucial requirement for the credibility of the experimental results. However, the actual benefits of stratification are still debated in the literature. Other authors have shown that it does not improve efficiency in large samples and improves it only negligibly in smaller samples. This paper investigates different subgroup analysis strategies, with a particular focus on the potential benefits in terms of inferential precision of prestratification versus both poststratification and post hoc regression adjustment. For each of these approaches, the pros and cons of population-based versus randomization-based inference are discussed. The effects of the presence of a treatment-by-covariate interaction and the variability in the patient responses are also taken into account. Our results show that, in general, prestratifying does not provide substantial benefit. On the contrary, it may be deleterious, in particular for randomization-based procedures in the presence of a chronological bias. Even when there is treatment-by-covariate interaction, prestratification may backfire by considerably reducing the inferential precision.

Optimal design for inference on the threshold of a biomarker.

Enrichment designs with a continuous biomarker require the estimation of a threshold to determine the subpopulation benefitting from the treatment. This article provides the optimal allocation for inference in a two-stage enrichment design for treatment comparisons when a continuous biomarker is suspected to affect patient response. Several design criteria, associated with different trial objectives, are optimized under balanced or Neyman allocation and under equality of the first two empirical biomarker's moments. Moreover, we propose a new covariate-adaptive randomization procedure that converges to the optimum with the fastest available rate. Theoretical and simulation results show that this strategy improves the efficiency of a two-stage enrichment clinical trial, especially with smaller sample sizes and under heterogeneous responses.

Randomization-based interval estimation in randomized clinical trials.

Randomization-based interval estimation takes into account the particular randomization procedure in the analysis and preserves the confidence level even in the presence of heterogeneity. It is distinguished from population-based confidence intervals with respect to three aspects: definition, computation, and interpretation. The article contributes to the discussion of how to construct a confidence interval for a treatment difference from randomization tests when analyzing data from randomized clinical trials. The discussion covers (i) the definition of a confidence interval for a treatment difference in randomization-based inference, (ii) computational algorithms for efficiently approximating the endpoints of an interval, and (iii) evaluation of statistical properties (ie, coverage probability and interval length) of randomization-based and population-based confidence intervals under a selected set of randomization procedures when assuming heterogeneity in patient outcomes. The method is illustrated with a case study.

Design and analysis of stratified clinical trials in the presence of bias.

BACKGROUND: Among various design aspects, the choice of randomization procedure have to be agreed on, when planning a clinical trial stratified by center. The aim of the paper is to present a methodological approach to evaluate whether a randomization procedure mitigates the impact of bias on the test decision in clinical trial stratified by center. METHODS: We use the weighted t test to analyze the data from a clinical trial stratified by center with a two-arm parallel group design, an intended 1:1 allocation ratio, aiming to prove a superiority hypothesis with a continuous normal endpoint without interim analysis and no adaptation in the randomization process. The derivation is based on the weighted t test under misclassification, i.e. ignoring bias. An additive bias model combing selection bias and time-trend bias is linked to different stratified randomization procedures. RESULTS: Various aspects to formulate stratified versions of randomization procedures are discussed. A formula for sample size calculation of the weighted t test is derived and used to specify the tolerated imbalance allowed by some randomization procedures. The distribution of the weighted t test under misclassification is deduced, taking the sequence of patient allocation to treatment, i.e. the randomization sequence into account. An additive bias model combining selection bias and time-trend bias at strata level linked to the applied randomization sequence is proposed. With these before mentioned components, the potential impact of bias on the type one error probability depending on the selected randomization sequence and thus the randomization procedure is formally derived and exemplarily calculated within a numerical evaluation study. CONCLUSION: The proposed biasing policy and test distribution are necessary to conduct an evaluation of the comparative performance of (stratified) randomization procedure in multi-center clinical trials with a two-arm parallel group design. It enables the choice of the best practice procedure. The evaluation stimulates the discussion about the level of evidence resulting in those kind of clinical trials.

Randomization tests for multiarmed randomized clinical trials.

We examine the use of randomization-based inference for analyzing multiarmed randomized clinical trials, including the application of conditional randomization tests to multiple comparisons. The view is taken that the linkage of the statistical test to the experimental design (randomization procedure) should be recognized. A selected collection of randomization procedures generalized to multiarmed treatment allocation is summarized, and generalizations for two randomization procedures that heretofore were designed for only two treatments are developed. We explain the process of computing the randomization test and conditional randomization test via Monte Carlo simulation, developing an efficient algorithm that makes multiple comparisons possible that would not be possible using a standard algorithm, demonstrate the preservation of type I error rate, and explore the relationship of statistical power to the randomization procedure in the presence of a time trend and outliers. We distinguish between the interpretation of the p-value in the randomization test and in the population test and verify that the randomization test can be approximated by the population test on some occasions. Data from two multiarmed clinical trials from the literature are reanalyzed to illustrate the methodology.

Sociodemographic disparities in corticolimbic structures.

This study sought to examine the interactive relations of socioeconomic status and race to corticolimbic regions that may play a key role in translating stress to the poor health outcomes overrepresented among those of lower socioeconomic status and African American race. Participants were 200 community-dwelling, self-identified African American and White adults from the Healthy Aging in Neighborhoods of Diversity across the Life Span SCAN study. Brain volumes were derived using T1-weighted MP-RAGE images. Socioeconomic status by race interactions were observed for right medial prefrontal cortex (B = .26, p = .014), left medial prefrontal cortex (B = .26, p = .017), left orbital prefrontal cortex (B = .22, p = .037), and left anterior cingulate cortex (B = .27, p = .018), wherein higher socioeconomic status Whites had greater volumes than all other groups. Additionally, higher versus lower socioeconomic status persons had greater right and left hippocampal (B = -.15, p = .030; B = -.19, p = .004, respectively) and amygdalar (B = -.17, p = .015; B = -.21; p = .002, respectively) volumes. Whites had greater right and left hippocampal (B = -.17, p = .012; B = -.20, p = .003, respectively), right orbital prefrontal cortex (B = -.34, p < 0.001), and right anterior cingulate cortex (B = -.18, p = 0.011) volumes than African Americans. Among many factors, the higher levels of lifetime chronic stress associated with lower socioeconomic status and African American race may adversely affect corticolimbic circuitry. These relations may help explain race- and socioeconomic status-related disparities in adverse health outcomes.

Lifetime discrimination burden, racial discrimination, and subclinical cerebrovascular disease among African Americans.

OBJECTIVE: Explore interactive relations of lifetime discrimination burden and racial discrimination-chronic stressors among African Americans (AAs)-and age with MRI-assessed white matter lesion volume (WMLV), a prognostic indicator of poor clinical brain health outcomes. METHOD: AAs (N = 71; 60.6% female, mean age = 50) participating in the Healthy Aging in Neighborhoods of Diversity across the Life Span (HANDLS) SCAN study underwent quantitative magnetic resonance imaging coded for WMLV. Participants self-reported lifetime discrimination burden and racial discrimination approximately 5 years earlier. Multivariable regression models assessed interactions of linear and quadratic effects of discrimination and age with WMLV adjusted for sex and socioeconomic status. RESULTS: Findings revealed significant interactive relations of age and (a) quadratic, lifetime discrimination burden, B = .05, p = .014, ηpartial2 = .092, and (b) quadratic, racial discrimination, B = .03, p = .001, ηpartial2 = .155, with WMLV. Among older AA, increases in lifetime discrimination burden and racial discrimination were associated with increases in WMLV (ps < .03); in younger AA, decreasing levels of racial discrimination were related to increases in WMLV (p = .006). CONCLUSIONS: Among older AA, as lifetime discrimination burden and racial discrimination increased, so did WMLV. However, in younger AA, decreases in racial discrimination were associated with increased WMLV. Elucidation of complex mechanistic underpinnings, including potentially differential impacts of the acknowledgment versus suppression or underreporting of discriminatory experiences, among AA of different age cohorts, is critical to understanding the present pattern of findings. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Randomization: The forgotten component of the randomized clinical trial.

"…The customary test for an observed difference…is based on an enumeration of the probabilities, on the initial hypothesis that two treatments do not differ in their effects,…of all the various results which would occur if the trial were repeated indefinitely with different random samples of the same size as those actually used." -Peter Armitage ("Sequential tests in prophylactic and therapeutic trials" in Quarterly Journal of Medicine, 1954;23(91):255-274). Randomization has been the hallmark of the clinical trial since Sir Bradford Hill adopted it in the 1946 streptomycin trial. An exploration of the early literature yields three rationales, ie, (i) the incorporation of randomization provides unpredictability in treatment assignments, thereby mitigating selection bias; (ii) randomization tends to ensure similarity in the treatment groups on known and unknown confounders (at least asymptotically); and (iii) the act of randomization itself provides a basis for inference when random sampling is not conducted from a population model. Of these three, rationale (iii) is often forgotten, ignored, or left untaught. Today, randomization is a rote exercise, scarcely considered in protocols or medical journal articles. Yet, the literature of the last century is rich with statistical articles on randomization methods and their consequences, authored by some of the pioneers of the biostatistics and statistics world. In this paper, we review some of this literature and describe very simple methods to rectify some of the oversight. We describe how randomization-based inference can be used for virtually any outcome of interest in a clinical trial. Special mention is made of nonstandard clinical trials situations.

Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule.

We introduce a non-myopic, covariate-adjusted response adaptive (CARA) allocation design for multi-armed clinical trials. The allocation scheme is a computationally tractable procedure based on the Gittins index solution to the classic multi-armed bandit problem and extends the procedure recently proposed in Villar et al. (2015). Our proposed CARA randomization procedure is defined by reformulating the bandit problem with covariates into a classic bandit problem in which there are multiple combination arms, considering every arm per each covariate category as a distinct treatment arm. We then apply a heuristically modified Gittins index rule to solve the problem and define allocation probabilities from the resulting solution. We report the efficiency, balance, and ethical performance of our approach compared to existing CARA methods using a recently published clinical trial as motivation. The net savings in terms of expected number of treatment failures is considerably larger and probably enough to make this design attractive for certain studies where known covariates are expected to be important, stratification is not desired, treatment failures have a high ethical cost, and the disease under study is rare. In a two-armed context, this patient benefit advantage comes at the expense of increased variability in the allocation proportions and a reduction in statistical power. However, in a multi-armed context, simple modifications of the proposed CARA rule can be incorporated so that an ethical advantage can be offered without sacrificing power in comparison with balanced designs.

ERDO - a framework to select an appropriate randomization procedure for clinical trials.

BACKGROUND: Randomization is considered to be a key feature to protect against bias in randomized clinical trials. Randomization induces comparability with respect to known and unknown covariates, mitigates selection bias, and provides a basis for inference. Although various randomization procedures have been proposed, no single procedure performs uniformly best. In the design phase of a clinical trial, the scientist has to decide which randomization procedure to use, taking into account the practical setting of the trial with respect to the potential of bias. Less emphasis has been placed on this important design decision than on analysis, and less support has been available to guide the scientist in making this decision. METHODS: We propose a framework that weights the properties of the randomization procedure with respect to practical needs of the research question to be answered by the clinical trial. In particular, the framework assesses the impact of chronological and selection bias on the probability of a type I error. The framework is applied to a case study with a 2-arm parallel group, single center randomized clinical trial with continuous endpoint, with no-interim analysis, 1:1 allocation and no adaptation in the randomization process. RESULTS: In so doing, we derive scientific arguments for the selection of an appropriate randomization procedure and develop a template which is illustrated in parallel by a case study. Possible extensions are discussed. CONCLUSION: The proposed ERDO framework guides the investigator through a template for the choice of a randomization procedure, and provides easy to use tools for the assessment. The barriers for the thorough reporting and assessment of randomization procedures could be further reduced in the future when regulators and pharmaceutical companies employ similar, standardized frameworks for the choice of a randomization procedure.

Beneficial Effects of Dry Needling for Treatment of Chronic Myofascial Pain Persist for 6 Weeks After Treatment Completion.

BACKGROUND: Dry needling is an effective treatment for reducing pain associated with active myofascial trigger points (a-MTrPs) in the short term. The duration of the benefits of this treatment have not been fully assessed. OBJECTIVE: To determine whether the benefits of dry needling (DN) of a-MTrPs are sustained 6 weeks posttreatment. DESIGN: Follow-up of a prospective study. SETTING: University. PARTICIPANTS: A total of 45 patients (13 male and 32 female) with cervical pain >3 months and a-MTrPs in the upper trapezius who completed 3 DN treatments and who were evaluated 6 weeks posttreatment. INTERVENTIONS: None. MAIN OUTCOME MEASURES: Primary outcomes were changes from baseline to follow-up in scores for the verbal analogue scale (VAS), Brief Pain Inventory (BPI), and MTrP status. MTrPs were rated as active (spontaneously painful), latent (painful only on compression), and nonpalpable nodule. Responders were patients whose MTrP status changed from active to latent or nonpalpable nodule (resolved). Secondary outcomes were pain pressure threshold (PPT), Profile of Mood States, Oswestry Disability Index (ODI), MOS 36-Item Short-Form Health Survey (SF-36), and cervical range of motion. RESULTS: Pain measures remained significantly improved 6 weeks posttreatment (P < .003), as did the SF-36 physical functioning score (0.01) and ODI (P = .002). Side bending and PPT for subjects with unilateral MTrPs had sustained improvement (P = .002). The number of subjects with sustained MTrP response at 6 weeks was significant (P < .001). Comparing responders to nonresponders, the changes in VAS and BPI were statistically significant (P = .006, P = .03) but the change in PPT was not. Patients with higher baseline VAS scores had a higher risk of not responding to DN; those with a greater drop in VAS score from baseline had a higher probability of sustained response. A 1-unit decrease in VAS at baseline resulted in a 6.3-fold increase in the odds of being a responder versus a nonresponder (P = .008). CONCLUSIONS: In this study, there was sustained reduction of pain scores after completion of DN, which is more likely with a greater drop in VAS score. Patients with higher baseline VAS scores are less likely to respond to DN. Early intervention toward significant pain reduction is likely to be associated with sustained clinical response. LEVEL OF EVIDENCE: IV.

Differential Associations of Socioeconomic Status With Global Brain Volumes and White Matter Lesions in African American and White Adults: the HANDLS SCAN Study.

OBJECTIVE: The aim of the study was to examine interactive relations of race and socioeconomic status (SES) to magnetic resonance imaging (MRI)-assessed global brain outcomes with previously demonstrated prognostic significance for stroke, dementia, and mortality. METHODS: Participants were 147 African Americans (AAs) and whites (ages 33-71 years; 43% AA; 56% female; 26% below poverty) in the Healthy Aging in Neighborhoods of Diversity across the Life Span SCAN substudy. Cranial MRI was conducted using a 3.0 T unit. White matter (WM) lesion volumes and total brain, gray matter, and WM volumes were computed. An SES composite was derived from education and poverty status. RESULTS: Significant interactions of race and SES were observed for WM lesion volume (b = 1.38; η = 0.036; p = .028), total brain (b = 86.72; η = 0.042; p < .001), gray matter (b = 40.16; η = 0.032; p = .003), and WM (b = 46.56; η = 0.050; p < .001). AA participants with low SES exhibited significantly greater WM lesion volumes than white participants with low SES. White participants with higher SES had greater brain volumes than all other groups (albeit within normal range). CONCLUSIONS: Low SES was associated with greater WM pathology-a marker for increased stroke risk-in AAs. Higher SES was associated with greater total brain volume-a putative global indicator of brain health and predictor of mortality-in whites. Findings may reflect environmental and interpersonal stressors encountered by AAs and those of lower SES and could relate to disproportionate rates of stroke, dementia, and mortality.

Nonlinear associations between plasma cholesterol levels and neuropsychological function.

OBJECTIVE: Although both high and low levels of total and low-density lipoprotein (LDL) cholesterol have been associated with poor neuropsychological function, little research has examined nonlinear effects. We examined quadratic relations of cholesterol to performance on a comprehensive neuropsychological battery. METHOD: Participants were 190 older adults (53% men, ages 54-83) free of major medical, neurologic, and psychiatric disease. Measures of fasting plasma total and high-density lipoprotein (HDL) cholesterol were assayed, and LDL cholesterol was calculated. Participants completed neuropsychological measures of attention, executive function, memory, visuospatial judgment, and manual speed and dexterity. Multiple regression analyses examined cholesterol levels as quadratic predictors of each measure of cognitive performance, with age (dichotomized as <70 vs. 70+) as an effect modifier. RESULTS: A significant quadratic effect of Total Cholesterol² × Age was identified for Logical Memory II (b = -.0013, p = .039), such that the 70+ group performed best at high and low levels of total cholesterol than at midrange total cholesterol (U-shaped) and the <70 group performed worse at high and low levels of total cholesterol than at midrange total cholesterol (inverted U shape). Similarly, significant U- and J-shaped effects of LDL Cholesterol² × Age were identified for Visual Reproduction II (b = -.0020, p = .026) and log of the Trail Making Test, Part B (b = .0001, p = .044). Quadratic associations between HDL cholesterol and cognitive performance were nonsignificant. CONCLUSIONS: Results indicate differential associations between cholesterol and neuropsychological function across different ages and domains of function. High and low total and LDL cholesterol may confer both risk and benefit for suboptimal cognitive function at different ages. (PsycINFO Database Record

On the use of randomization tests following adaptive designs.

Randomization tests (sometimes referred to as "re-randomization" tests) are used in clinical trials, either as an assumption-free confirmation of parametric analyses, or as an independent analysis based on the principle of randomization-based inference. In the context of adaptive randomization, either restricted or response-adaptive procedures, it is unclear how accurate such Monte Carlo approximations are, or how many Monte Carlo sequences to generate. In this paper, we describe several randomization procedures for which there is a known exact or asymptotic distribution of the randomization test. For a special class of procedures, called [Formula: see text], and binary responses, the exact test statistic has a simple closed form. For the limited subset of existing procedures with known exact and asymptotic distributions, we can use these as a benchmark for the accuracy of Monte Carlo randomization techniques. We conclude that Monte Carlo tests are very accurate, and require minimal computation time. For simple tests with binary response in the class of [Formula: see text] procedures, the exact distribution provides the best test, but Monte Carlo approximations can be used when the exact distribution is difficult to compute.

Novel Use of Ultrasound Elastography to Quantify Muscle Tissue Changes After Dry Needling of Myofascial Trigger Points in Patients With Chronic Myofascial Pain.

OBJECTIVES: To compare a mechanical heterogeneity index derived from ultrasound vibration elastography with physical findings before and after dry-needling treatment of spontaneously painful active myofascial trigger points in the upper trapezius muscle. METHODS: Forty-eight patients with chronic myofascial pain enrolled in a prospective interventional trial of 3 weekly dry-needling treatments for active myofascial trigger points. Trigger points were evaluated at baseline and at treatment completion using palpation, the pressure-pain threshold, and the mechanical heterogeneity index. Thirty patients were reevaluated at 8 weeks. Trigger points that "responded" changed to tissue that was no longer spontaneously painful, with or without the presence of a palpable nodule. Trigger points that "resolved" changed to tissue without a palpable nodule. The mechanical heterogeneity index was defined as the proportion of the upper trapezius muscle that appeared mechanically stiffer on elastography. Statistical significance for comparisons was determined at P < .05. RESULTS: Following 3 dry needle treatments, the mechanical heterogeneity index decreased significantly for the 38 myofascial trigger points (79% of 48) that responded to treatment. Among these, the baseline mechanical heterogeneity index was significantly lower for the 13 trigger points (27% of 38) that resolved, but the decrease after 3 dry needle treatments did not reach significance. The pressure-pain threshold improved significantly for both groups. At 8 weeks, the mechanical heterogeneity index decreased significantly for the 22 trigger points (73% of 30) that responded and for the 10 (45% of 22) that resolved. The pressure-pain threshold improvement was significant for trigger points that responded but did not reach significance for resolved trigger points. CONCLUSIONS: The mechanical heterogeneity index identifies changes in muscle tissue properties that correlate with changes in the myofascial trigger point status after dry needling.

Exact optimum coin bias in Efron's randomization procedure.

Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efron's coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples.

Inference for blocked randomization under a selection bias model.

We provide an asymptotic test to analyze randomized clinical trials that may be subject to selection bias. For normally distributed responses, and under permuted block randomization, we derive a likelihood ratio test of the treatment effect under a selection bias model. A likelihood ratio test of the presence of selection bias arises from the same formulation. We prove that the test is asymptotically chi-square on one degree of freedom. These results correlate well with the likelihood ratio test of Ivanova et al. (2005, Statistics in Medicine 24, 1537-1546) for binary responses, for which they established by simulation that the asymptotic distribution is chi-square. Simulations also show that the test is robust to departures from normality and under another randomization procedure. We illustrate the test by reanalyzing a clinical trial on retinal detachment.

Fasting glucose and glucose tolerance as potential predictors of neurocognitive function among nondiabetic older adults.

INTRODUCTION: Significant evidence has demonstrated that Type 2 diabetes mellitus and related precursors are associated with diminished neurocognitive function and risk of dementia among older adults. However, very little research has examined relations of glucose regulation to neurocognitive function among older adults free of these conditions. The primary aim of this investigation was to examine associations among fasting glucose, glucose tolerance, and neurocognitive function among nondiabetic older adults. The secondary aim was to examine age, gender, and education as potential effect modifiers. METHOD: The study employed a cross-sectional, correlational study design. Participants were 172 older adults with a mean age of 64.43 years (SD = 13.09). The sample was 58% male and 87% White. Participants completed an oral glucose tolerance test as part of a larger study. Trained psychometricians administered neuropsychological tests that assessed performance in the domains of response inhibition, nonverbal memory, verbal memory, attention and working memory, visuoconstructional abilities, visuospatial abilities, psychomotor speed and executive function, and motor speed and manual dexterity. Linear multiple regressions were run to test study aims. RESULTS: No significant main effects of fasting glucose and 2-hour glucose emerged for performance on any neurocognitive test; however, significant interactions were present. Higher fasting glucose was associated with poorer short-term verbal memory performance among men, but unexpectedly better response inhibition and long-term verbal memory performance for participants over age 70. Higher 2-hour glucose values were associated with reduced divided attention performance among participants with less than a high school education. CONCLUSIONS: Mixed findings suggest that glucose levels may be both beneficial and deleterious to neurocognition among nondiabetic older adults. Additional studies with healthy older adults are needed to confirm this unexpected pattern of associations; however, findings have implications for the importance of maintaining healthy glucose levels in older adulthood.