Evaluating treatments when a gender by treatment interaction may exist

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.

The effects of safinamide according to gender in Chinese parkinsonian patients

The incidence and prevalence of Parkinson's disease (PD) is expected to raise dramatically over the next decades. Gender-related differences are not yet widely recognized, particularly regarding the response to dopaminergic medications. To analyse gender differences in the clinical effects of safinamide, compared to placebo, in Chinese PD patients of the pivotal XINDI trial. The XINDI study was a phase III, randomized, double-blind, placebo-controlled, multicenter trial. Patients were followed for 16 weeks receiving safinamide or placebo as add-on to levodopa. The primary efficacy endpoint was the change in the mean total daily OFF time. Secondary efficacy endpoints included total daily ON time, ON time with no/non-troublesome dyskinesia, Unified Parkinson's Disease Rating Scale and Parkinson's Disease Questionnaire-39 items. A post-hoc analysis was performed to describe the efficacy of safinamide in both genders on motor symptoms, motor fluctuations and quality of life. 128 (42%) out of 305 patients enrolled were women and 177 (58%) men. Our additional analyses of the XINDI study have shown that safinamide, compared to placebo, was associated with improvements in motor symptoms, motor fluctuations and quality of life in both genders, with some differences in the response that did not reach statistical significance, possibly due to sample size limitation and post-hoc design of the study. The changes from baseline at week 16 were > 50% higher in the females compared to males for the total daily OFF time (- 1.149 h vs - 0.764 h in males), the total daily ON time (1.283 h vs 0.441 h in males), the UPDRS total score (- 8.300 points vs - 5.253 points in males) and the UPDRS part II score (- 2.574 points vs - 1.016 points in males). The changes from baseline at week 16 were higher in the females compared to males in the "ADL" domain (- 6.965 points vs - 5.772 points in males), the "Emotional well-being" domain (- 6.243 points vs - 4.203 in males), the "Stigma" domain (- 6.185 points vs - 4.913 points in males) and the "Bodily discomfort" domain (- 5.196 points vs 1.099 points in males), while were higher in males in the "Mobility" score (- 6.523 points vs - 4.961 points in females) and the "Communication" score (- 3.863 points vs - 1.564 points in females). Safinamide was shown to improve PD symptoms and quality of life in both male and female Chinese patients. Possible differences in the response between genders need to be further studied in larger and different ethnic populations.

New insights into adaptive enrichment designs

The transition towards personalized medicine is happening and the new experimental framework is raising several challenges, from a clinical, ethical, logistical, regulatory, and statistical perspective. To face these challenges, innovative study designs with increasing complexity have been proposed. In particular, adaptive enrichment designs are becoming more attractive for their flexibility. However, these procedures rely on an increasing number of parameters that are unknown at the planning stage of the clinical trial, so the study design requires particular care. This review is dedicated to adaptive enrichment studies with a focus on design aspects. While many papers deal with methods for the analysis, the sample size determination and the optimal allocation problem have been overlooked. We discuss the multiple aspects involved in adaptive enrichment designs that contribute to their advantages and disadvantages. The decision-making process of whether or not it is worth enriching should be driven by clinical and ethical considerations as well as scientific and statistical concerns.

Exploration of Heterogeneous Treatment Effects via Concave Fusion

Understanding treatment heterogeneity is essential to the development of precision medicine, which seeks to tailor medical treatments to subgroups of patients with similar characteristics. One of the challenges of achieving this goal is that we usually do not have a priori knowledge of the grouping information of patients with respect to treatment effect. To address this problem, we consider a heterogeneous regression model which allows the coefficients for treatment variables to be subject-dependent with unknown grouping information. We develop a concave fusion penalized method for estimating the grouping structure and the subgroup-specific treatment effects, and derive an alternating direction method of multipliers algorithm for its implementation. We also study the theoretical properties of the proposed method and show that under suitable conditions there exists a local minimizer that equals the oracle least squares estimator based on a priori knowledge of the true grouping information with high probability. This provides theoretical support for making statistical inference about the subgroup-specific treatment effects using the proposed method. The proposed method is illustrated in simulation studies and illustrated with real data from an AIDS Clinical Trials Group Study.

Treatment evaluation for a data-driven subgroup in adaptive enrichment designs of clinical trials

Adaptive enrichment designs (AEDs) of clinical trials allow investigators to restrict enrollment to a promising subgroup based on an interim analysis. Most of the existing AEDs deal with a small number of predefined subgroups, which are often unknown at the design stage. The newly developed Simon design offers a great deal of flexibility in subgroup selection (without requiring pre-defined subgroups) but does not provide a procedure for estimating and testing treatment efficacy for the selected subgroup. This article proposes a 2-stage AED which does not require predefined subgroups but requires a prespecified algorithm for choosing a subgroup on the basis of baseline covariate information. Having a prespecified algorithm for subgroup selection makes it possible to use cross-validation and bootstrap methods to correct for the resubstitution bias in estimating treatment efficacy for the selected subgroup. The methods are evaluated and compared in a simulation study mimicking actual clinical trials of human immunodeficiency virus infection.

Use of auxiliary covariates in estimating a biomarker-adjusted treatment effect model with clinical trial data

A biomarker-adjusted treatment effect (BATE) model describes the effect of one treatment versus another on a subpopulation of patients defined by a biomarker. Such a model can be estimated from clinical trial data without relying on additional modeling assumptions, and the estimator can be made more efficient by incorporating information on the main effect of the biomarker on the outcome of interest. Motivated by an HIV trial known as THRIVE, we consider the use of auxiliary covariates, which are usually available in clinical trials and have been used in overall treatment comparisons, in estimating a BATE model. Such covariates can be incorporated using an existing augmentation technique. For a specific type of estimating functions for difference-based BATE models, the optimal augmentation depends only on the joint main effects of marker and covariates. For a ratio-based BATE model, this result holds in special cases but not in general; however, simulation results suggest that the augmentation based on the joint main effects of marker and covariates is virtually equivalent to the theoretically optimal augmentation, especially when the augmentation terms are estimated from data. Application of these methods and results to the THRIVE data yields new insights on the utility of baseline CD4 cell count and viral load as predictive or treatment selection markers.

Group sequential designs with prospectively planned rules for subpopulation enrichment

We propose a class of randomized trial designs aimed at gaining the advantages of wider generalizability and faster recruitment while mitigating the risks of including a population for which there is greater a priori uncertainty. We focus on testing null hypotheses for the overall population and a predefined subpopulation. Our designs have preplanned rules for modifying enrollment criteria based on data accrued at interim analyses. For example, enrollment can be restricted if the participants from a predefined subpopulation are not benefiting from the new treatment. Our designs have the following features: the multiple testing procedure fully leverages the correlation among statistics for different populations; the asymptotic familywise Type I error rate is strongly controlled; for outcomes that are binary or normally distributed, the decision rule and multiple testing procedure are functions of the data only through minimal sufficient statistics. Our designs incorporate standard group sequential boundaries for each population of interest; this may be helpful in communicating the designs, because many clinical investigators are familiar with such boundaries, which can be summarized succinctly in a single table or graph. We demonstrate these designs through simulations of a Phase III trial of a new treatment for stroke. User-friendly, free software implementing these designs is described. Copyright © 2016 John Wiley & Sons, Ltd.

The Use of Covariates and Random Effects in Evaluating Predictive Biomarkers Under a Potential Outcome Framework

Predictive or treatment selection biomarkers are usually evaluated in a subgroup or regression analysis with focus on the treatment-by-marker interaction. Under a potential outcome framework (Huang, Gilbert and Janes [Biometrics68 (2012) 687-696]), a predictive biomarker is considered a predictor for a desirable treatment benefit (defined by comparing potential outcomes for different treatments) and evaluated using familiar concepts in prediction and classification. However, the desired treatment benefit is un-observable because each patient can receive only one treatment in a typical study. Huang et al. overcome this problem by assuming monotonicity of potential outcomes, with one treatment dominating the other in all patients. Motivated by an HIV example that appears to violate the monotonicity assumption, we propose a different approach based on covariates and random effects for evaluating predictive biomarkers under the potential outcome framework. Under the proposed approach, the parameters of interest can be identified by assuming conditional independence of potential outcomes given observed covariates, and a sensitivity analysis can be performed by incorporating an unobserved random effect that accounts for any residual dependence. Application of this approach to the motivating example shows that baseline viral load and CD4 cell count are both useful as predictive biomarkers for choosing antiretroviral drugs for treatment-naive patients.

Testing for efficacy in adaptive clinical trials with enrichment

Adaptive design of clinical trials has attracted considerable interest because of its potential of reducing costs and saving time in the clinical development process. In this paper, we consider the problem of assessing the effectiveness of a test treatment over a control by a two-arm randomized clinical trial in a potentially heterogenous patient population. In particular, we study enrichment designs that use accumulating data from a clinical trial to adaptively determine patient subpopulation in which the treatment effect is eventually assessed. A hypothesis testing procedure and a lower confidence limit are presented for the treatment effect in the selected patient subgroups. The performances of the new methods are compared with existing approaches through a simulation study.

Assessing the heterogeneity of treatment effects via potential outcomes of individual patients

There is growing interest in understanding the heterogeneity of treatment effects (HTE), which has important implications in treatment evaluation and selection. The standard approach to assessing HTE (i.e. subgroup analyses based on known effect modifiers) is informative about the heterogeneity between subpopulations but not within. It is arguably more informative to assess HTE in terms of individual treatment effects, which can be defined by using potential outcomes. However, estimation of HTE based on potential outcomes is challenged by the lack of complete identifiability. The paper proposes methods to deal with the identifiability problem by using relevant information in baseline covariates and repeated measurements. If a set of covariates is sufficient for explaining the dependence between potential outcomes, the joint distribution of potential outcomes and hence all measures of HTE will then be identified under a conditional independence assumption. Possible violations of this assumption can be addressed by including a random effect to account for residual dependence or by specifying the conditional dependence structure directly. The methods proposed are shown to reduce effectively the uncertainty about HTE in a trial of human immunodeficiency virus.

Confidence intervals for the selected population in randomized trials that adapt the population enrolled

It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence during the trial that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95% coverage probability, uniformly over a large class Q of possible data generating distributions. Our method involves computing the minimum factor c by which a standard confidence interval must be expanded in order to have, asymptotically, at least 95% coverage probability, uniformly over Q. Computing the expansion factor c is not trivial, since it is not a priori clear, for a given decision rule, for which data generating distribution leads to the worst-case coverage probability. We give an algorithm that computes c, and then prove an optimality property for the resulting confidence interval procedure.

Optimizing randomized trial designs to distinguish which subpopulations benefit from treatment

It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes to the population enrolled, care must be taken to ensure strong control of the familywise Type I error rate. Our main contribution is a general method for constructing randomized trial designs that allow changes to the population enrolled based on interim data using a prespecified decision rule, for which the asymptotic, familywise Type I error rate is strongly controlled at a specified level α. As a demonstration of our method, we prove new, sharp results for a simple, two-stage enrichment design. We then compare this design to fixed designs, focusing on each design's ability to determine the overall and subpopulation-specific treatment effects.

After inclusion, information and inference: reporting on clinical trials results after 15 years of monitoring inclusion of women

OBJECTIVE

The objectives of this report are to review the publications resulting from National Institutes of Health (NIH)-funded phase 3 trials monitored by NIH for inclusion and to address the quality of the research conducted and the validity of the sex/gender-specific or sex/gender difference analyses reported.

METHODS

For intervention trials enrolling both women and men, this review links reports to NIH of completed enrollment to publications of trial results. Each publication was then reviewed for a variety of reported characteristics based on established measures of quality, bearing on whether or not the research will permit valid analyses of sex/gender differences.

RESULTS

Publications from 268 trials reported an overall average enrollment of 37% (±6% standard deviation [SD]) women, at an increasing rate over the years 1995-2010. Only 28% of the publications either made some reference to sex/gender-specific results in the text or provided detailed results including sex/gender-specific estimates of effect or tests of interaction.

CONCLUSIONS

Efforts at including women in clinical research have increased the information captured relative to women's health. Sex/gender-specific information has been captured and should be available to other researchers for further analysis, including individual patient data meta-analyses. Improved reporting and disseminating sex/gender-specific results will allow sex/gender-specific inferences and healthcare decisions.

The true lift model

In database marketing, data mining has been used extensively to find the optimal customer targets so as to maximize return on investment. In particular, using marketing campaign data, models are typically developed to identify characteristics of customers who are most likely to respond. While these models are helpful in identifying the likely responders, they may be targeting customers who have decided to take the desirable action or not regardless of whether they receive the campaign contact (e.g. mail, call). Based on many years of business experience, we identify the appropriate business objective and its associated mathematical objective function. We point out that the current approach is not directly designed to solve the appropriate business objective. We then propose a new methodology to identify the customers whose decisions will be positively influenced by campaigns. The proposed methodology is easy to implement and can be used in conjunction with most commonly used supervised learning algorithms. An example using simulated data is used to illustrate the proposed methodology. This paper may provide the database marketing industry with a simple but significant methodological improvement and open a new area for further research and development.

Bayesian subset analysis: application to studying treatment-by-gender interactions

Evaluating treatment effects within subsets of patients plays a major part of the analysis of many major clinical trials. Clinicians are often impressed by the heterogeneity of patient populations in clinical trials and hence are interested in examining subset effects. Statisticians generally discourage subset analysis or suggest that clinicians 'do subset analysis but do not believe it'. This advice, however, is a sign of the inadequacy of the analytic methods generally used for subset analysis. Separate analysis of many subsets, and basing conclusions on whether the observed treatment difference achieves significance at the 0.05 level, is likely to yield erroneous conclusions. Making the separate analysis of subsets dependent on demonstration of a statistically significant treatment-by-subset interaction is also not an effective analytic strategy because of the limited power of interaction tests. This paper describes a Bayesian approach to subset analysis developed by Simon, Dixon and Freidlin. The method avoids many of the problems of subset analysis because it is not 'separate' analysis of subsets. Instead, subset-specific treatment effects are estimated as an average of observed within-subset differences and overall differences; the two components are weighted by the a priori estimate of the likelihood of qualitative treatment by subset interactions. Hence, the Bayesian method proposed permits subset analyses incorporating the assumption that qualitative interactions are unlikely. The methodology is applied to the problem of designing and analysing clinical trials to estimate treatment effects for males and females.

Predictive factors for local recurrence in 2006 patients with surgically resected small breast cancer

BACKGROUND

Analyses of predictive factors for local recurrences are important, as an increasing number of patients with early breast cancer opt for a breast-conserving procedure. This study investigates whether factors predictive of local recurrence differ between patients treated with conservative or radical surgery.

PATIENTS AND METHODS

Two thousands and six patients with invasive breast carcinoma (< or =25 mm) were included. Of these patients, 717 were treated conservatively (lumpectomy and breast irradiation) and 1289 were treated with total mastectomy. All patients had axillary dissection and received lymph node irradiation if axillary nodes were positive. Most patients did not receive adjuvant chemotherapy or additive hormonal treatments. The mean duration of follow-up was 20 years. The main end point was the total local recurrence rate. The risk factors of local recurrence were estimated by multivariate analyses and interaction tests were used for intergroup comparisons.

RESULTS

Statistically significant predictive factors for mastectomized patients were histological grade, extensive axillary node involvement (10 nodes or more), and inner quadrant tumors, which were of borderline significance. Young age, however, was not a prognostic indicator for local recurrence. The main statistically significant factor for patients treated with a conservative approach was young age (< or =40 years). These younger patients had a five-fold increased risk of developing a breast recurrence compared with patients older than 60 years.

CONCLUSIONS

Younger patients with early breast cancer treated with breast-conserving surgery should in particular be followed up at regular intervals so that any sign of local failure can be diagnosed early.