An adaptive design for updating the threshold value of a continuous biomarker

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.

Design considerations for two-stage enrichment clinical trials

When there is a predictive biomarker, enrichment can focus the clinical trial on a benefiting subpopulation. We describe a two-stage enrichment design, in which the first stage is designed to efficiently estimate a threshold and the second stage is a "phase III-like" trial on the enriched population. The goal of this paper is to explore design issues: sample size in Stages 1 and 2, and re-estimation of the Stage 2 sample size following Stage 1. By treating these as separate trials, we can gain insight into how the predictive nature of the biomarker specifically impacts the sample size. We also show that failure to adequately estimate the threshold can have disastrous consequences in the second stage. While any bivariate model could be used, we assume a continuous outcome and continuous biomarker, described by a bivariate normal model. The correlation coefficient between the outcome and biomarker is the key to understanding the behavior of the design, both for predictive and prognostic biomarkers. Through a series of simulations we illustrate the impact of model misspecification, consequences of poor threshold estimation, and requisite sample sizes that depend on the predictive nature of the biomarker. Such insight should be helpful in understanding and designing enrichment trials.

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.

IBIS: identify biomarker-based subgroups with a Bayesian enrichment design for targeted combination therapy

BACKGROUND

Combination therapies directed at multiple targets have potentially improved treatment effects for cancer patients. Compared to monotherapy, targeted combination therapy leads to an increasing number of subgroups and complicated biomarker-based efficacy profiles, making it more difficult for efficacy evaluation in clinical trials. Therefore, it is necessary to develop innovative clinical trial designs to explore the efficacy of targeted combination therapy in different subgroups and identify patients who are more likely to benefit from the investigational combination therapy.

METHODS

We propose a statistical tool called 'IBIS' to Identify BIomarker-based Subgroups and apply it to the enrichment design framework. The IBIS contains three main elements: subgroup division, efficacy evaluation and subgroup identification. We first enumerate all possible subgroup divisions based on biomarker levels. Then, Jensen-Shannon divergence is used to distinguish high-efficacy and low-efficacy subgroups, and Bayesian hierarchical model (BHM) is employed to borrow information within these two subsets for efficacy evaluation. Regarding subgroup identification, a hypothesis testing framework based on Bayes factors is constructed. This framework also plays a key role in go/no-go decisions and enriching specific population. Simulation studies are conducted to evaluate the proposed method.

RESULTS

The accuracy and precision of IBIS could reach a desired level in terms of estimation performance. In regard to subgroup identification and population enrichment, the proposed IBIS has superior and robust characteristics compared with traditional methods. An example of how to obtain design parameters for an adaptive enrichment design under the IBIS framework is also provided.

CONCLUSIONS

IBIS has the potential to be a useful tool for biomarker-based subgroup identification and population enrichment in clinical trials of targeted combination therapy.

A two-stage adaptive clinical trial design with data-driven subgroup identification at interim analysis

In this paper, we consider randomized controlled clinical trials comparing two treatments in efficacy assessment using a time to event outcome. We assume a relatively small number of candidate biomarkers available in the beginning of the trial, which may help define an efficacy subgroup which shows differential treatment effect. The efficacy subgroup is to be defined by one or two biomarkers and cut-offs that are unknown to the investigator and must be learned from the data. We propose a two-stage adaptive design with a pre-planned interim analysis and a final analysis. At the interim, several subgroup-finding algorithms are evaluated to search for a subgroup with enhanced survival for treated versus placebo. Conditional powers computed based on the subgroup and the overall population are used to make decision at the interim to terminate the study for futility, continue the study as planned, or conduct sample size recalculation for the subgroup or the overall population. At the final analysis, combination tests together with closed testing procedures are used to determine efficacy in the subgroup or the overall population. We conducted simulation studies to compare our proposed procedures with several subgroup-identification methods in terms of a novel utility function and several other measures. This research demonstrated the benefit of incorporating data-driven subgroup selection into adaptive clinical trial designs.

Lasso estimation of hierarchical interactions for analyzing heterogeneity of treatment effect

Individuals differ in how they respond to a given treatment. In an effort to predict the treatment response and analyze the heterogeneity of treatment effect, we propose a general modeling framework by identifying treatment-covariate interactions honoring a hierarchical condition. We construct a single-step l 1 norm penalty procedure that maintains the hierarchical structure of interactions in the sense that a treatment-covariate interaction term is included in the model only when either the covariate or both the covariate and treatment have nonzero main effects. We developed a constrained Lasso approach with two parameterization schemes that enforce the hierarchical interaction restriction differently. We solved the resulting constrained optimization problem using a spectral projected gradient method. We compared our methods to the unstructured Lasso using simulation studies including a scenario that violates the hierarchical condition (misspecified model). The simulations showed that our methods yielded more parsimonious models and outperformed the unstructured Lasso for correctly identifying nonzero treatment-covariate interactions. The superior performance of our methods are also corroborated by an application to a large randomized clinical trial data investigating a drug for treating congestive heart failure (N = 2569). Our methods provide a well-suited approach for doing secondary analysis in clinical trials to analyze heterogeneous treatment effects and to identify predictive biomarkers.

Optimized adaptive enrichment designs for three-arm trials: learning which subpopulations benefit from different treatments

We consider the problem of designing a confirmatory randomized trial for comparing two treatments versus a common control in two disjoint subpopulations. The subpopulations could be defined in terms of a biomarker or disease severity measured at baseline. The goal is to determine which treatments benefit which subpopulations. We develop a new class of adaptive enrichment designs tailored to solving this problem. Adaptive enrichment designs involve a preplanned rule for modifying enrollment based on accruing data in an ongoing trial. At the interim analysis after each stage, for each subpopulation, the preplanned rule may decide to stop enrollment or to stop randomizing participants to one or more study arms. The motivation for this adaptive feature is that interim data may indicate that a subpopulation, such as those with lower disease severity at baseline, is unlikely to benefit from a particular treatment while uncertainty remains for the other treatment and/or subpopulation. We optimize these adaptive designs to have the minimum expected sample size under power and Type I error constraints. We compare the performance of the optimized adaptive design versus an optimized nonadaptive (single stage) design. Our approach is demonstrated in simulation studies that mimic features of a completed trial of a medical device for treating heart failure. The optimized adaptive design has $25\%$ smaller expected sample size compared to the optimized nonadaptive design; however, the cost is that the optimized adaptive design has $8\%$ greater maximum sample size. Open-source software that implements the trial design optimization is provided, allowing users to investigate the tradeoffs in using the proposed adaptive versus standard designs.

Cumulative use of salivary markers with an adaptive design improves detection of periodontal disease over fixed biomarker thresholds

OBJECTIVE

Aim was to analyze the diagnostic ability of cumulative risk score (CRS), which uses salivary levels of Porphyromonas gingivalis, interleukin (IL)-1β, and matrix metalloproteinase (MMP)-8 in an adaptive design, compared to previously reported thresholds of each marker alone.

MATERIALS AND METHODS

Oral and general health information of 463 participants were included in the analysis. Having the percentage of bleeding on probing (BOP) > 25%, having at least two sites with probing pocket depth (PPD) of 4-5 mm or having at least one tooth with alveolar bone loss (ABL) of at least 1/3 of the root length were accepted as outcome variables. Being above the salivary threshold concentrations of P. gingivalis, IL-1β, and MMP-8 and CRS values were used as explanatory variables. Receiver operating characteristics (ROC) producing an area under the curve (AUC) and multinomial regression analysis were used in statistical analysis.

RESULTS

CRS provided AUCs larger than any other tested biomarker threshold. Sensitivity and specificity of CRS for detecting clinical markers of periodontitis were acceptable, and a strong association was observed between the highest CRS score and having at least two sites with PPD of 4-5 mm.

CONCLUSION

CRS brings additional power over fixed thresholds of single biomarkers in detecting periodontitis.

Point estimation following two-stage adaptive threshold enrichment clinical trials

Recently, several study designs incorporating treatment effect assessment in biomarker-based subpopulations have been proposed. Most statistical methodologies for such designs focus on the control of type I error rate and power. In this paper, we have developed point estimators for clinical trials that use the two-stage adaptive enrichment threshold design. The design consists of two stages, where in stage 1, patients are recruited in the full population. Stage 1 outcome data are then used to perform interim analysis to decide whether the trial continues to stage 2 with the full population or a subpopulation. The subpopulation is defined based on one of the candidate threshold values of a numerical predictive biomarker. To estimate treatment effect in the selected subpopulation, we have derived unbiased estimators, shrinkage estimators, and estimators that estimate bias and subtract it from the naive estimate. We have recommended one of the unbiased estimators. However, since none of the estimators dominated in all simulation scenarios based on both bias and mean squared error, an alternative strategy would be to use a hybrid estimator where the estimator used depends on the subpopulation selected. This would require a simulation study of plausible scenarios before the trial.

Auxiliary variable-enriched biomarker-stratified design

Clinical trials in the era of precision medicine require assessment of biomarkers to identify appropriate subgroups of patients for targeted therapy. In a biomarker-stratified design (BSD), biomarkers are measured on all patients and used as stratification variables. However, such a trial can be both inefficient and costly, especially when the prevalence of the subgroup of primary interest is low and the cost of assessing the biomarkers is high. Efficiency can be improved and costs reduced by using enriched biomarker-stratified designs, in which patients of primary interest, typically the biomarker-positive patients, are oversampled. We consider a special type of enrichment design, an auxiliary variable-enriched design (AEBSD), in which enrichment is based on some inexpensive auxiliary variable that is positively correlated with the true biomarker. The proposed AEBSD reduces the total cost of the trial compared with a standard BSD when the prevalence rate of true biomarker positivity is small and the positive predictive value (PPV) of the auxiliary biomarker is larger than the prevalence rate. In addition, for an AEBSD, we can immediately randomize the patients selected in the screening process without waiting for the result of the true biomarker test, reducing the treatment waiting time. We propose an adaptive Bayesian method to adjust the assumed PPV while the trial is ongoing. Numerical studies and an example illustrate the approach. An R package is available.