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.

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).

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.

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.

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.

Maximizing power and minimizing treatment failures in clinical trials

Background Response-adaptive randomization procedures have a long history in the theoretical statistics literature over the past four decades. The main idea historically was to develop randomization procedures that place fewer patients on the inferior treatment. More recent research has changed the main focus to that of usual considerations in typical clinical trials: power, sample size, expected treatment failures, maintaining randomization, among others.

Methods We describe response-adaptive randomization procedures for simple clinical trials comparing two binomial success probabilities, including the randomized play-the-winner rule, the drop-the-loser rule, and a modification of the doubly-adaptive biased coin design. We treat as our principal goal minimizing expected treatment failures while preserving power and randomization. Based on some recent theoretical literature [1,8,14], the basic guidelines for selecting an appropriate procedure include targeting optimal allocation, having small variability, and preserving randomization. We use simulation to compare power and expected treatment failures according to these guidelines.

Results When the two treatments had high probabilities (>0.5) of success, the randomized play-the-winner rule was less powerful than complete randomization and the drop-the-loser rule by 1–3 percent with slightly larger expected number of treatment failures than the drop-the-loser rule. For all the success probabilities we examined, the drop-the-loser rule was within 1 percent of the power of complete randomization with a modest reduction of treatment failures. The doubly-adaptive biased coin design was as powerful or slightly more powerful than complete randomization in every case and expected treatment failures were always less, with modest reductions of the order of 0.3 percent to 8.3 percent.

Conclusions We conclude that the drop-the-loser rule and a modification of the doubly-adaptive biased coin design are the preferred procedures, and simulations show that these procedures yield a modest reduction in expected treatment failures while preserving power over complete randomization.

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

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.

A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes

BACKGROUND

Response-adaptive randomisation designs have been proposed to improve the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosenberger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size.

OBJECTIVES

The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the estimated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by redesigning a clinical trial on multiple myeloma.

METHODS

To handle continuous monitoring of data, we propose a Bayesian response-adaptive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simulation study to assess and compare the performance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive - either frequentist or fully Bayesian - designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior distribution of the log hazard ratio were computed. The method is then illustrated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts.

RESULTS

As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mixture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules.

CONCLUSIONS

Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

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.

Optimal sampling ratios in comparative diagnostic trials

A subjective sampling ratio between the case and the control groups is not always an efficient choice to maximize the power or to minimize the total required sample size in comparative diagnostic trials.We derive explicit expressions for an optimal sampling ratio based on a common variance structure shared by several existing summary statistics of the receiver operating characteristic curve. We propose a two-stage procedure to estimate adaptively the optimal ratio without pilot data. We investigate the properties of the proposed method through theoretical proofs, extensive simulation studies and a real example in cancer diagnostic studies.

Conditional Monte Carlo randomization tests for regression models

We discuss the computation of randomization tests for clinical trials of two treatments when the primary outcome is based on a regression model. We begin by revisiting the seminal paper of Gail, Tan, and Piantadosi (1988), and then describe a method based on Monte Carlo generation of randomization sequences. The tests based on this Monte Carlo procedure are design based, in that they incorporate the particular randomization procedure used. We discuss permuted block designs, complete randomization, and biased coin designs. We also use a new technique by Plamadeala and Rosenberger (2012) for simple computation of conditional randomization tests. Like Gail, Tan, and Piantadosi, we focus on residuals from generalized linear models and martingale residuals from survival models. Such techniques do not apply to longitudinal data analysis, and we introduce a method for computation of randomization tests based on the predicted rate of change from a generalized linear mixed model when outcomes are longitudinal. We show, by simulation, that these randomization tests preserve the size and power well under model misspecification.

Adaptive randomization for clinical trials

In February 2010, the U.S. Food and Drug Administration (FDA, 2010 ) drafted guidance that discusses the statistical, clinical, and regulatory aspects of various adaptive designs for clinical trials. An important class of adaptive designs is adaptive randomization, which is considered very briefly in subsection VI.B of the guidance. The objective of this paper is to review several important new classes of adaptive randomization procedures and convey information on the recent developments in the literature on this topic. Much of this literature has been focused on the development of methodology to address past criticisms and concerns that have hindered the broader use of adaptive randomization. We conclude that adaptive randomization is a very broad area of experimental design that has important application in modern clinical trials.

Case-mix adjustment and enabled reporting of the health care experiences of adults with disabilities

OBJECTIVES

To develop activity limitation clusters for case-mix adjustment of health care ratings and as a population profiler, and to develop a cognitively accessible report of statistically reliable quality and access measures comparing the health care experiences of adults with and without disabilities, within and across health delivery organizations.

DESIGN

Observational study.

SETTING

Three California Medicaid health care organizations.

PARTICIPANTS

Adults (N = 1086) of working age enrolled for at least 1 year in Medicaid because of disability.

INTERVENTIONS

Not applicable.

MAIN OUTCOME MEASURES

Principal components analysis created 4 clusters of activity limitations that we used to characterize case mix. We identified and calculated 28 quality measures using responses from a proposed enabled version of the Consumer Assessment of Healthcare Providers and Systems (CAHPS) survey. We calculated scores for overall care as the weighted mean of the case-mix adjusted ratings.

RESULTS

Disability caused a greater bias on health plan ratings and specialist ratings than did demographic factors. Proxy respondents rated care the same as self-respondents. Telephone and mail administration were equivalent for service reports, but telephone respondents tended to offer more positive global ratings. Plan-level reliability estimates for new composites on shared decision making and advice on healthy living are .79 and .87, respectively. Plan-level reliability estimates for a new composite measure on family planning did not discriminate between health plans because respondents rated all health plans poorly. Approximately 125 respondents per site are necessary to detect group differences.

CONCLUSIONS

Self-reported activity limitations incorporating standard questions from the American Community Survey can be used to create a disability case-mix index and to construct profiles of a population's activity limitations. The enabled comparative report, which we call the Assessment of Health Plans and Providers by People with Activity Limitations, is more cognitively accessible than typical CAHPS report templates for state Medicaid plans. The CAHPS Medicaid reporting tools may provide misleading ratings of health plan and physician quality by people with disabilities because the mean ratings do not account for systematic biases associated with disability. More testing on larger populations would help to quantify the strength of various reporting biases.

Sequential monitoring of randomization tests: stratified randomization

In many clinical trials, it is desirable to establish a sequential monitoring plan, whereby the test statistic is computed at an interim point or points in the trial and a decision is made whether to stop early due to evidence of treatment efficacy. In this article, we will set up a sequential monitoring plan for randomization-based inference under the permuted block design, stratified block design, and stratified urn design. We will also propose a definition of information fraction in these settings and discuss its calculation under these different designs.

Sequential designs for logistic phase I clinical trials

Both parametric and nonparametric sequential designs and estimation methods are implemented in phase I clinical trials. In this article, we take a systematic approach, consisting of a start-up design, a follow-on design, a sequential dose-finding design, and an estimation method, to find an efficient estimate of the maximum tolerated dose under the assumption that the dose-response curve has a true underlying logistic distribution. In particular, for the problem of the nonexistence of the maximum likelihood estimates of the logistic parameters, a constraint on the probability of an undetermined maximum likelihood estimator (MLE) is incorporated into the parametric sequential designs. In addition, this approach can also be extended to incorporate ethical considerations, which prohibit an administered dose from exceeding the maximum acceptable dose. Comparison based on simulation studies between the systematic designs and nonparametric designs are described both for continuous dose spaces and discrete dose spaces, respectively.

Response-adaptive randomization for clinical trials with continuous outcomes

We provide an explicit asymptotic method to evaluate the performance of different response-adaptive randomization procedures in clinical trials with continuous outcomes. We use this method to investigate four different response-adaptive randomization procedures. Their performance, especially in power and treatment assignment skewing to the better treatment, is thoroughly evaluated theoretically. These results are then verified by simulation. Our analysis concludes that the doubly adaptive biased coin design procedure targeting optimal allocation is the best one for practical use. We also consider the effect of delay in responses and nonstandard responses, for example, Cauchy distributed response. We illustrate our procedure by redesigning a real clinical trial.