Treatment comparisons based on two-dimensional safety and efficacy alternatives in oncology trials

Group sequential designs for clinical trials with bivariate endpoints

Although all clinical trials are designed and monitored using more than one endpoint, methods are needed to assure that decision criteria are chosen to reflect the clinically relevant tradeoffs that assure the trial's scientific integrity. This article presents a framework for the design and monitoring clinical trials in a bivariate outcome space. The framework uses a rectangular hyperbola to define a bivariate null curve that divides outcome space into regions of benefit and lack of benefit. The curve is shown to be a flexible mapping of bivariate space that allows a continuous tradeoff between the two endpoints in a manner that captures many previous bivariate designs. The curve is extended to a distance function in bivariate space that allows different decisions in each of the four quadrants that comprise bivariate space. The distance function forms a statistic ( δ ); the distribution of its estimate is derived and used as a basis for trial design and group sequential monitoring plans in bivariate space. A recursive form of the bivariate group sequential density is used to evaluate and control operating characteristics for the proposed design. The bivariate designs are shown to meet or exceed the usual standards for size and power. The proposed design is illustrated in the ongoing NHLBI-sponsored Kids-DOTT multinational randomized controlled trial comparing shortened versus conventional anticoagulation for the treatment of venous thromboembolism in patients less than 21 years of age. The proposed methods are broadly applicable to a wide range of clinical settings and trial designs.

A two-stage phase II clinical trial design with nested criteria for early stopping and efficacy

We propose a two-stage design for a single arm clinical trial with an early stopping rule for futility. This design employs different endpoints to assess early stopping and efficacy. The early stopping rule is based on a criteria determined more quickly than that for efficacy. These separate criteria are also nested in the sense that efficacy is a special case of, but usually not identical to, the early stopping endpoint. The design readily allows for planning in terms of statistical significance, power, expected sample size, and expected duration. This method is illustrated with a phase II design comparing rates of disease progression in elderly patients treated for lung cancer to rates found using a historical control. In this example, the early stopping rule is based on the number of patients who exhibit progression-free survival (PFS) at 2 months post treatment follow-up. Efficacy is judged by the number of patients who have PFS at 6 months. We demonstrate our design has expected sample size and power comparable with the Simon two-stage design but exhibits shorter expected duration under a range of useful parameter values.

Bivariate evaluation of thromboembolism and bleeding in clinical trials of anticoagulants in patients with atrial fibrillation

Clinical trials of antithrombotic therapy require a cohesive assessment of benefit and risk. A new graphical method to represent the bivariate relation of benefit and risk in trials of antithrombotic drugs is described and illustrated using published data from the four major registration clinical trials of non-vitamin K oral anticoagulants (NOACs) totalling 71,683 patients for prevention of thromboembolic events (TE) in patients with atrial fibrillation (RE-LY, ROCKET AF, ARISTOTLE, and ENGAGE-AF TIMI48). A curve representing a null hypothesis defines a region of benefit on a two-dimensional plane. Trial results are summarised by a rectangle defined by standard 95 % confidence intervals (CI) for thrombosis and bleeding risks. Benefit is judged by whether the confidence rectangle contains the null curve. The treatment effect is measured by the distance from the null curve to the opposing corners of the confidence rectangle (termed “corner distance (CD)”). Across trials NOACs reduced the absolute risk of TE compared to warfarin by 0.30 % (95 % CI: –0.56 % to –0.05 %) and reduced major bleeding by 0.88 % (95 % CI: –1.26 % to –0.51 %). Bivariate evaluation showed NOAC superiority to warfarin overall and elucidated dose differences; low dose edoxaban increased bivariate TE-bleeding risk 0.08 % (CD = –0.85 % to 0.78 %), whereas high dose edoxaban reduced risk 1.41 % (CD = –2.07 % to –0.70 %). In conclusion, bivariate evaluation facilitates visual assessment of the safety-efficacy profile of antithrombotic drugs. Its application to trials in atrial fibrillation found NOACs superior to warfarin without substantial differences between agents.

Supplementary Material to this article is available online at www.thrombosis-online.com.

Sources of Safety Data and Statistical Strategies for Design and Analysis: Clinical Trials

BACKGROUND

There has been an increased emphasis on the proactive and comprehensive evaluation of safety endpoints to ensure patient well-being throughout the medical product life cycle. In fact, depending on the severity of the underlying disease, it is important to plan for a comprehensive safety evaluation at the start of any development program. Statisticians should be intimately involved in this process and contribute their expertise to study design, safety data collection, analysis, reporting (including data visualization), and interpretation.

METHODS

In this manuscript, we review the challenges associated with the analysis of safety endpoints and describe the safety data that are available to influence the design and analysis of premarket clinical trials.

RESULTS

We share our recommendations for the statistical and graphical methodologies necessary to appropriately analyze, report, and interpret safety outcomes, and we discuss the advantages and disadvantages of safety data obtained from clinical trials compared to other sources.

CONCLUSIONS

Clinical trials are an important source of safety data that contribute to the totality of safety information available to generate evidence for regulators, sponsors, payers, physicians, and patients. This work is a result of the efforts of the American Statistical Association Biopharmaceutical Section Safety Working Group.

Generalized optimal design for two-arm, randomized phase II clinical trials with endpoints from the exponential dispersion family

For two-arm randomized phase II clinical trials, previous literature proposed an optimal design that minimizes the total sample sizes subject to multiple constraints on the standard errors of the estimated event rates and their difference. The original design is limited to trials with dichotomous endpoints. This paper extends the original approach to be applicable to phase II clinical trials with endpoints from the exponential dispersion family distributions. The proposed optimal design minimizes the total sample sizes needed to provide estimates of population means of both arms and their difference with pre-specified precision. Its applications on data from specific distribution families are discussed under multiple design considerations. Copyright © 2016 John Wiley & Sons, Ltd.

A comparative study of matched pair designs with two binary endpoints

We study matched pair designs with two binary endpoints under three different approaches. Power approximation and sample size calculation are derived under these situations and facilitated by R programs. An adaptive design with sample size re-estimation is also presented. Through extensive simulations, we provide general guidelines for practitioners to choose the best approach according to the ranges of the interested parameters in the sense of feasibility and robustness. Application to a cancer chemotherapy trial is illustrated.

Flexible designs for phase II comparative clinical trials involving two response variables

The aim of phase II clinical trials is to determine whether an experimental treatment is sufficiently promising and safe to justify further testing. The need for reduced sample size arises naturally in phase II clinical trials owing to both technical and ethical reasons, motivating a significant part of research in the field during recent years, while another significant part of the research effort is aimed at more complex therapeutic schemes that demand the consideration of multiple endpoints to make decisions. In this paper, our attention is restricted to phase II clinical trials in which two treatments are compared with respect to two dependent dichotomous responses proposing some flexible designs. These designs permit the researcher to terminate the clinical trial when high rates of favorable or unfavorable outcomes are observed early enough requiring in this way a small number of patients. From the mathematical point of view, the proposed designs are defined on bivariate sequences of multi-state trials, and the corresponding stopping rules are based on various distributions related to the waiting time until a certain number of events appear in these sequences. The exact distributions of interest, under a unified framework, are studied using the Markov chain embedding technique, which appears to be very useful in clinical trials for the sample size determination. Tables of expected sample size and power are presented. The numerical illustration showed a very good performance for these new designs.

Synthesis, characterization, and biological activity of poly(arginine)-derived cancer-targeting peptides in HepG2 liver cancer cells

The solid-phase synthesis, structural characterization, and biological evaluation of a small library of cancer-targeting peptides have been determined in HepG2 hepatoblastoma cells. These peptides are based on the highly specific Pep42 motif, which has been shown to target the glucose-regulated protein 78 receptors overexpressed and exclusively localized on the cell surface of tumors. In this study, Pep42 was designed to contain varying lengths (3-12) of poly(arginine) sequences to assess their influence on peptide structure and biology. Peptides were effectively synthesized by 9-fluorenylmethoxycarbonyl-based solid-phase peptide synthesis, in which the use of a poly(ethylene glycol) resin provided good yields (14-46%) and crude purities >95% as analyzed by liquid chromatography-mass spectrometry. Peptide structure and biophysical properties were investigated using circular dichroism spectroscopy. Interestingly, peptides displayed secondary structures that were contingent on solvent and length of the poly(arginine) sequences. Peptides exhibited helical and turn conformations, while retaining significant thermal stability. Structure-activity relationship studies conducted by flow cytometry and confocal microscopy revealed that the poly(arginine) derived Pep42 sequences maintained glucose-regulated protein 78 binding on HepG2 cells while exhibiting cell translocation activity that was contingent on the length of the poly(arginine) strand. In single dose (0.15 mM) and dose-response (0-1.5 mM) cell viability assays, peptides were found to be nontoxic in human HepG2 liver cancer cells, illustrating their potential as safe cancer-targeting delivery agents.

Optimal two-stage randomized multinomial designs for Phase II oncology trials

A new two-stage design is proposed that is suitable for early detection of the anticancer activity of experimental therapies in Phase II oncology trials. The endpoints of interest are response rate and early progression rate. The anticancer activity is defined by a positive signal in one endpoint and a non-negative signal in the other endpoint. The two endpoints are modeled by the multinomial distribution. The design is optimal in that it minimizes the patient exposure when the experimental therapies are inactive. The design parameters are found by a grid searching algorithm under type I and type II error rate constraints. Examples of the design are also presented in this paper.

Some Geometric Methods for Constructing Decision Criteria Based On Two-Dimensional Parameters

This paper reviews two types of geometric methods proposed in recent years for defining statistical decision rules based on 2-dimensional parameters that characterize treatment effect in a medical setting. A common example is that of making decisions, such as comparing treatments or selecting a best dose, based on both the probability of efficacy and the probability toxicity. In most applications, the 2-dimensional parameter is defined in terms of a model parameter of higher dimension including effects of treatment and possibly covariates. Each method uses a geometric construct in the 2-dimensional parameter space based on a set of elicited parameter pairs as a basis for defining decision rules. The first construct is a family of contours that partitions the parameter space, with the contours constructed so that all parameter pairs on a given contour are equally desirable. The partition is used to define statistical decision rules that discriminate between parameter pairs in term of their desirabilities. The second construct is a convex 2-dimensional set of desirable parameter pairs, with decisions based on posterior probabilities of this set for given combinations of treatments and covariates under a Bayesian formulation. A general framework for all of these methods is provided, and each method is illustrated by one or more applications.

A three-outcome design for randomized comparative phase II clinical trials

Randomized designs have been increasingly called for use in phase II oncology clinical trials to protect against potential patient selection bias. However, formal statistical comparison is rarely conducted due to the sample size restriction, despite its appeal. In this paper, we offer an approach to sample size reduction by extending the three-outcome design of Sargent et al. (Control Clin. Trials 2001; 22:117-125) for single-arm trials to randomized comparative trials. In addition to the usual two outcomes of a hypothesis testing (rejecting the null hypothesis or rejecting the alternative hypothesis), the three-outcome comparative design allows a third outcome of rejecting neither hypotheses when the testing result is in some 'grey area' and leaves the decision to the clinical judgment based on the overall evaluation of trial outcomes and other relevant factors. By allowing a reasonable region of uncertainty, the three-outcome design enables formal statistical comparison with considerably smaller sample size, compared to the standard two-outcome comparative design. Statistical formulation of the three-outcome comparative design is discussed for both the single-stage and two-stage trials. Sample sizes are tabulated for some common clinical scenarios.

An Adaptive Approach to Implementing Bivariate Group Sequential Clinical Trial Designs

In clinical trials, situations often arise where more than one response from each patient is of interest; and it is required that any decision to stop the study be based upon some or all of these measures simultaneously. Theory for the design of sequential experiments with simultaneous bivariate responses is described by Jennison and Turnbull (Jennison, C., Turnbull, B. W. (1993). Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints. Biometrics 49:741-752) and Cook and Farewell (Cook, R. J., Farewell, V. T. (1994). Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 50:1146-1152) in the context of one efficacy and one safety response. These expositions are in terms of normally distributed data with known covariance. The methods proposed require specification of the correlation, rho between test statistics monitored as part of the sequential test. It can be difficult to quantify rho and previous authors have suggested simply taking the lowest plausible value, as this will guarantee power. This paper begins with an illustration of the effect that inappropriate specification of rho can have on the preservation of trial error rates. It is shown that both the type I error and the power can be adversely affected. As a possible solution to this problem, formulas are provided for the calculation of correlation from data collected as part of the trial. An adaptive approach is proposed and evaluated that makes use of these formulas and an example is provided to illustrate the method. Attention is restricted to the bivariate case for ease of computation, although the formulas derived are applicable in the general multivariate case.

Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios

A Bayesian adaptive design is proposed for dose-finding in phase I/II clinical trials to incorporate the bivariate outcomes, toxicity and efficacy, of a new treatment. Without specifying any parametric functional form for the drug dose-response curve, we jointly model the bivariate binary data to account for the correlation between toxicity and efficacy. After observing all the responses of each cohort of patients, the dosage for the next cohort is escalated, deescalated, or unchanged according to the proposed odds ratio criteria constructed from the posterior toxicity and efficacy probabilities. A novel class of prior distributions is proposed through logit transformations which implicitly imposes a monotonic constraint on dose toxicity probabilities and correlates the probabilities of the bivariate outcomes. We conduct simulation studies to evaluate the operating characteristics of the proposed method. Under various scenarios, the new Bayesian design based on the toxicity-efficacy odds ratio trade-offs exhibits good properties and treats most patients at the desirable dose levels. The method is illustrated with a real trial design for a breast medical oncology study.

Decision-theoretic designs for dose-finding clinical trials with multiple outcomes

A decision-theoretic framework is proposed for designing sequential dose-finding trials with multiple outcomes. The optimal strategy is solvable theoretically via backward induction. However, for dose-finding studies involving k doses, the computational complexity is the same as the bandit problem with k-dependent arms, which is computationally prohibitive. We therefore provide two computationally compromised strategies, which is of practical interest as the computational complexity is greatly reduced: one is closely related to the continual reassessment method (CRM), and the other improves CRM and approximates to the optimal strategy better. In particular, we present the framework for phase I/II trials with multiple outcomes. Applications to a pediatric HIV trial and a cancer chemotherapy trial are given to illustrate the proposed approach. Simulation results for the two trials show that the computationally compromised strategy can perform well and appear to be ethical for allocating patients. The proposed framework can provide better approximation to the optimal strategy if more extensive computing is available.

A Geometric Approach to Comparing Treatments for Rapidly Fatal Diseases

In therapy of rapidly fatal diseases, early treatment efficacy often is characterized by an event, "response," which is observed relatively quickly. Since the risk of death decreases at the time of response, it is desirable not only to achieve a response, but to do so as rapidly as possible. We propose a Bayesian method for comparing treatments in this setting based on a competing risks model for response and death without response. Treatment effect is characterized by a two-dimensional parameter consisting of the probability of response within a specified time and the mean time to response. Several target parameter pairs are elicited from the physician so that, for a reference covariate vector, all elicited pairs embody the same improvement in treatment efficacy compared to a fixed standard. A curve is fit to the elicited pairs and used to determine a two-dimensional parameter set in which a new treatment is considered superior to the standard. Posterior probabilities of this set are used to construct rules for the treatment comparison and safety monitoring. The method is illustrated by a randomized trial comparing two cord blood transplantation methods.

A nonparametric comparison of the effectiveness of treatments: a multivariate toxicity-penalized approach

In cancer clinical trials, the amount of treatment dose actually received by a patient may be limited by severe toxicity or lack of efficacy. A nonparametric approach is proposed for comparing the effectiveness of treatments based on the bivariate relationship defined by the doses at which efficacy and toxicity are observed to occur. Simulation studies are used to contrast the performance of the new procedure with the usual method of comparing percentages of patients who have effective results. Data from a randomized clinical trial of patients with metastatic nonseminomatous germ cell tumors are used to illustrate the method.

Two-treatment comparison based on joint toxicity and efficacy ordered alternatives in cancer trials

The primary goal of anticancer treatments is to attain efficacy, however toxicity could affect the course of the therapy. Methods have been proposed for comparing two treatments on the basis of the joint distribution for safety and efficacy outcomes, but they do not take into account the cumulative doses of drugs (chemotherapy) or radiation (radiotherapy) received by each patient. Moreover, these methods assume a parametric form for the joint distribution. In this paper we define a multi-dimensional parameter including toxicity and efficacy outcomes and the dose at which one, none or both occur. Each patient is classified into an ordered category depending on the order of occurrence of these two criteria: the sooner the patient benefits from efficacy and/or the later he/she experiences toxicity, the better is the treatment. We then apply likelihood ratio tests with ordered alternatives. This procedure requires constrained maximum likelihood estimation via isotonic regression. A large set of simulations compares the proposed tests to other more usual tests and the results show a good power and a satisfactory type I error control. Our approach is illustrated with a multi-centre randomized clinical trial involving patients with metastatic non-seminomatous germ cell tumours.

Ethical issues in oncology biostatistics

A medical statistician's routine professional activities are likely to have important ethical consequences. This is due in part to the fact that good medical practice and scientifically valid medical research both require as precursors high quality statistical design and data analysis. In this paper I discuss various ethical issues that I have encountered while working as a biostatistician at M.D. Anderson Cancer Center. I describe particular experiences and the ethical issues involved. Topics include medical decision making, benefit-harm trade-offs, safety monitoring, adaptive randomization, informed consent, and publication bias.

Optimal two-stage designs for clinical trials based on safety and efficacy

In clinical trials designed to evaluate treatment efficacy, it is common practice to terminate a treatment arm in which the observed rate of an adverse event is unacceptably high. This practice may be formalized by a group-sequential test based on a multivariate outcome including both adverse and efficacy events. Recently, Thall and Cheng proposed a family of tests for randomized trials of an experimental treatment versus a standard where patient outcome is bivariate with entries characterizing efficacy and safety. The test is motivated by the idea that clinically meaningful improvements over the standard may be characterized by a two-dimensional parameter quantifying trade-offs between efficacy and safety. We provide optimal two-stage designs based on this test that minimize either the mean sample size under the null hypothesis of no treatment difference, or the maximum sample size if the trial continues to a second stage. A more general group-sequential version of the design also is described, an illustration is provided, and application to the special case of single-arm phase II trials is discussed.