Modification of the sample size and the schedule of interim analyses in survival trials based on data inspections

A landscape of methodology and implementation of adaptive designs in cancer clinical trials

BACKGROUND

The use of adaptive designs in cancer trials has considerably increased worldwide in recent years, along with the release of various guidelines for their application. This systematic review aims to comprehensively summarize the key methodological and executive features of adaptive designs in cancer clinical trials.

METHODS

A comprehensive search from PubMed, EMBASE, and the Cochrane Central Register of Controlled Trials was conducted to screen eligible clinical trials that employed adaptive designs and were conducted in cancer patients. The methodological and executive characteristics of adaptive designs were the main measurements extracted. Descriptive analyses, primarily consisting of frequency and percentage, were employed to analyzed and reported the data.

RESULTS

A total of 180 cancer clinical trials with adaptive designs were identified. The first three most common type of adaptive design was the group sequential design (n=114, 63.3 %), adaptive dose-finding design (n=22, 12.2 %), and adaptive platform design (n=16, 8.9 %). The results showed that 4.4 % (n=8) of trials conducted post hoc modifications, and around 29.4 % (n=53) did not provide the methods for controlling type I errors. Among phase II or above trials, 79.9 % (112/140) applied the surrogate endpoint as the primary outcome in these trials. Importantly, 27.2 % (49/180) of trials did not report clear information on the independent data monitoring committee (iDMC), and 13.3 % (n=24) without clear information on interim analyses. Interim analyses suggested 34.4 % (62/180) of trials being stopped for futility, 10.6 % (n=19) for efficacy, and 2.2 % (n=4) for safety concerns in the early stage.

CONCLUSIONS

This study emphasizes adaptive designs in cancer trials face significant challenges in their design or strict implementation according to protocol, which might significantly compromise the validity and integrity of trials. It is thus important for researchers, sponsors, and policymakers to actively oversee and guide their application.

Confirmatory adaptive group sequential designs for single-arm phase II studies with multiple time-to-event endpoints

Existing methods concerning the assessment of long-term survival outcomes in one-armed trials are commonly restricted to one primary endpoint. Corresponding adaptive designs suffer from limitations regarding the use of information from other endpoints in interim design changes. Here we provide adaptive group sequential one-sample tests for testing hypotheses on the multivariate survival distribution derived from multi-state models, while making provision for data-dependent design modifications based on all involved time-to-event endpoints. We explicitly elaborate application of the methodology to one-sample tests for the joint distribution of (i) progression-free survival (PFS) and overall survival (OS) in the context of an illness-death model, and (ii) time to toxicity and time to progression while accounting for death as a competing event. Large sample distributions are derived using a counting process approach. Small sample properties are studied by simulation. An already established multi-state model for non-small cell lung cancer is used to illustrate the adaptive procedure.

Adaptive group sequential survival comparisons based on log-rank and pointwise test statistics

Whereas the theory of confirmatory adaptive designs is well understood for uncensored data, implementation of adaptive designs in the context of survival trials remains challenging. Commonly used adaptive survival tests are based on the independent increments structure of the log-rank statistic. This implies some relevant limitations: On the one hand, essentially only the interim log-rank statistic may be used for design modifications (such as data-dependent sample size recalculation). Furthermore, the treatment arm allocation ratio in these classical methods is assumed to be constant throughout the trial period. Here, we propose an extension of the independent increments approach to adaptive survival tests that addresses some of these limitations. We present a confirmatory adaptive two-sample log-rank test that allows rejection regions and sample size recalculation rules to be based not only on the interim log-rank statistic, but also on point-wise survival rate estimates, simultaneously. In addition, the possibility is opened to adapt the treatment arm allocation ratio after each interim analysis in a data-dependent way. The ability to include point-wise survival rate estimators in the rejection region of a test for comparing survival curves might be attractive, e.g., for seamless phase II/III designs. Data-dependent adaptation of the allocation ratio could be helpful in multi-arm trials in order to successively steer recruitment into the study arms with the greatest chances of success. The methodology is motivated by the LOGGIC Europe Trial from pediatric oncology. Distributional properties are derived using martingale techniques in the large sample limit. Small sample properties are studied by simulation.

Endometrial Cancer Lymphadenectomy Trial (ECLAT) (pelvic and para-aortic lymphadenectomy in patients with stage I or II endometrial cancer with high risk of recurrence; AGO-OP.6)

BACKGROUND

The impact of comprehensive pelvic and para-aortic lymphadenectomy on survival in patients with stage I or II endometrial cancer with a high risk of recurrence is not reliably documented. The side effects of this procedure, including lymphedema and lymph cysts, are evident.

PRIMARY OBJECTIVE

Evaluation of the effect of comprehensive pelvic and para-aortic lymphadenectomy in the absence of bulky nodes on 5 year overall survival of patients with endometrial cancer (International Federation of Gynecology and Obstetrics (FIGO) stages I and II) and a high risk of recurrence.

STUDY HYPOTHESIS

Comprehensive pelvic and para-aortic lymphadenectomy will increase 5 year overall survival from 75% (no lymphadenectomy) to 83%, corresponding to a hazard ratio of 0.65.

TRIAL DESIGN

Open label, randomized, controlled trial. In arm A, a total hysterectomy plus bilateral salpingo-oophorectomy is performed. In arm B, in addition, a systematic pelvic and para-aortic lymphadenectomy up to the level of the left renal vein is performed. For all patients, vaginal brachytherapy and adjuvant chemotherapy (carboplatin/paclitaxel) are recommended.

MAJOR INCLUSION CRITERIA

Patients with histologically confirmed endometrial cancer stages pT1b-pT2, all histological subtypes, and pT1a endometrioid G3, serous, clear cell, or carcinosarcomas can be included when bulky nodes are absent. When hysterectomy has already been performed (eg, for presumed low risk endometrial cancer), study participation is also possible.

EXCLUSION CRITERIA

Patients with pT1a, G1 or 2 of type 1 histology or uterine sarcomas (except for carcinosarcomas), endometrial cancers of FIGO stage III or IV (except for microscopic lymph node metastases) or visual extrauterine disease.

PRIMARY ENDPOINT

Overall survival calculated from the date of randomization until death.

SAMPLE SIZE

640 patients will be enrolled in the study.

ESTIMATED DATES FOR COMPLETING ACCRUAL AND PRESENTING RESULTS

At present, 252 patients have been recruited. Based on this, accrual should be completed in 2025. Results should be presented in 2031.

TRIAL REGISTRATION

NCT03438474.

Sample size re-estimation for pivotal clinical trials

It is well known that if the hypothesis test is left unchanged, the Type I error rate may be inflated for sample size re-estimation (SSR) designs. To address this issue, three main approaches have been proposed in the literature: combination test, conditional error and conventional test with sample size increase in the allowable region (AR) only. These three seemingly different approaches are in fact connected. For each combination test, there is a corresponding conditional error function and AR. Designing adaptation rules in this AR with conventional test guarantees the Type I error rate control but at the same time always leads to smaller power comparing to the corresponding combination test (or conditional error) approach. In cases where conventional test is still preferable, step-wise type adaptation rules that do not fully reside in the AR can be alternatively considered. We believe controversies in the statistical community on the efficiency comparisons between group sequential (GS) and SSR design stem partially from the misalignment of performance metrics and conditional versus unconditional evaluations. We advocate summary metrics, such as median, variance or tail probabilities of the sample size in addition to expectation and personalizing efficiency definition for each trial sponsor. Conditional metrics by favorable, promising and unfavorable zones of the interim results provide additional insights and should always be incorporated into the decision-making process.

Adaptive design implementation in confirmatory trials: methods, practical considerations and case studies

The rapidly changing drug development landscapes have brought unique challenges to sponsors in designing clinical trials in a faster and more efficient way. With the ability to accelerate development timeline, reduce redundant sample size, and select the right dose and patient population during the clinical trial, adaptive designs help to increase the probability of success of clinical trials and eventually contribute to bringing the promising drugs to patients earlier and fulfilling their unmet medical needs. Although extensive adaptive design methods have been proposed in recent years, a comprehensive review of how to implement adaptive design in the practical confirmatory trials is still lacking. In this paper, we will review the evolving history of adaptive designs, updates of newly released regulatory guidance and emerging practical adaptive designs, including but not limited to sample size re-estimation, seamless design and surrogate endpoint used in the interim analysis. Furthermore, we will discuss the current practice of adaptive design implementation by demonstrating a complex oncology seamless phase 2/3 adaptive design case study. Through this example, we will introduce the critical roles of each cross disciplinary function, communication process and important documents when adaptive designs are implemented in real-world setting.

Treatment of Middle East respiratory syndrome with a combination of lopinavir/ritonavir and interferon-β1b (MIRACLE trial): statistical analysis plan for a recursive two-stage group sequential randomized controlled trial

The MIRACLE trial (MERS-CoV Infection tReated with A Combination of Lopinavir/ritonavir and intErferon-β1b) investigates the efficacy of a combination therapy of lopinavir/ritonavir and recombinant interferon-β1b provided with standard supportive care, compared to placebo provided with standard supportive care, in hospitalized patients with laboratory-confirmed MERS. The MIRACLE trial is designed as a recursive, two-stage, group sequential, multicenter, placebo-controlled, double-blind randomized controlled trial. The aim of this article is to describe the statistical analysis plan for the MIRACLE trial. The primary outcome is 90-day mortality. The primary analysis will follow the intention-to-treat principle. The MIRACLE trial is the first randomized controlled trial for MERS treatment. TRIAL REGISTRATION: ClinicalTrials.gov, NCT02845843. Registered on 27 July 2016.

Group sequential adaptive designs in series of time-to-event randomised trials in rare diseases: A simulation study

In rare diseases, fully powered large trials may not be doable in a reasonable time frame even with international collaborations. In a previous work, we proposed an approach based on a series of smaller parallel group two-arm randomised controlled trials (RCT) performed over a long research horizon. Within the series of trials, the treatment selected after each trial becomes the control treatment of the next one. We concluded that running more trials with smaller sample sizes and relaxed α-levels leads in the long term and under reasonable assumptions to larger survival benefits with a moderate increase of risk as compared to traditional designs based on larger but fewer trials designed to meet stringent evidence criteria. We now extend this quantitative framework with more 'flexible' designs including interim analyses for futility and/or efficacy, and three-arm adaptive designs with treatment selection at interim. In the simulation study, we considered different disease severities, accrual rates, and hypotheses of how treatments improve over time. For each design, we estimated the long-term survival benefit as the relative difference in hazard rates between the end and the start of the research horizon, and the risk defined as the probability of selecting at the end of the research horizon a treatment inferior to the initial control. We assessed the impact of the α-level and the choice of the stopping rule on the operating characteristics. We also compared the performance of series based on two- vs. three-arm trials. We show that relaxing α-levels within the limit of 0.1 is associated with larger survival gains and moderate increase of risk which remains within acceptable ranges. Including an interim analysis with a futility rule is associated with an additional survival gain and a better risk control as compared to series with no interim analysis, when the α-level is below or equal to 0.1, whereas the benefit of including an interim analysis is rather small for higher α-levels. Including an interim analysis for efficacy yields almost no additional gain. Series based on three-arm trials are associated with a systematic improvement in terms of survival gain and risk control as compared to series of two-arm trials.

Nested combination tests with a time-to-event endpoint using a short-term endpoint for design adaptations

Adaptive trial methodology for multiarmed trials and enrichment designs has been extensively discussed in the past. A general principle to construct test procedures that control the family-wise Type I error rate in the strong sense is based on combination tests within a closed test. Using survival data, a problem arises when using information of patients for adaptive decision making, which are under risk at interim. With the currently available testing procedures, either no testing of hypotheses in interim analyses is possible or there are restrictions on the interim data that can be used in the adaptation decisions as, essentially, only the interim test statistics of the primary endpoint may be used. We propose a general adaptive testing procedure, covering multiarmed and enrichment designs, which does not have these restrictions. An important application are clinical trials, where short-term surrogate endpoints are used as basis for trial adaptations, and we illustrate how such trials can be designed. We propose statistical models to assess the impact of effect sizes, the correlation structure between the short-term and the primary endpoint, the sample size, the timing of interim analyses, and the selection rule on the operating characteristics.

Nonparametric adaptive enrichment designs using categorical surrogate data

Adaptive survival trials are particularly important for enrichment designs in oncology and other life-threatening diseases. Current statistical methodology for adaptive survival trials provide type I error rate control only under restrictions. For instance, if we use stage-wise P values based on increments of the log-rank test, then the information used for the interim decisions need to be restricted to the primary survival endpoint. However, it is often desirable to base interim decisions also on correlated short-term endpoints like tumor response. Alternative statistical approaches based on a patient-wise splitting of the data require unnatural restrictions on the follow-up times and do not permit to efficiently account for an early rejection of the primary null hypothesis. We therefore suggest new approaches that enable us to use discrete surrogate endpoints (like tumor response status) and also to incorporate interim rejection boundaries. The new approaches are based on weighted Kaplan-Meier estimates and thereby have additional advantages. They permit us to account for nonproportional hazards and are robust against informative censoring based on the surrogate endpoint. We will show that nonproportionality is an intrinsic and relevant issue in enrichment designs. Moreover, informative censoring based on the surrogate endpoint is likely because of withdrawals and treatment switches after insufficient treatment response. It is shown and illustrated how nonparametric tests based on weighted Kaplan-Meier estimates can be used in closed combination tests for adaptive enrichment designs, such that type I error rate control is achieved and justified asymptotically.

Treatment of Middle East Respiratory Syndrome with a combination of lopinavir-ritonavir and interferon-β1b (MIRACLE trial): study protocol for a randomized controlled trial

Background

It had been more than 5 years since the first case of Middle East Respiratory Syndrome coronavirus infection (MERS-CoV) was recorded, but no specific treatment has been investigated in randomized clinical trials. Results from in vitro and animal studies suggest that a combination of lopinavir/ritonavir and interferon-β1b (IFN-β1b) may be effective against MERS-CoV. The aim of this study is to investigate the efficacy of treatment with a combination of lopinavir/ritonavir and recombinant IFN-β1b provided with standard supportive care, compared to treatment with placebo provided with standard supportive care in patients with laboratory-confirmed MERS requiring hospital admission.

Methods

The protocol is prepared in accordance with the SPIRIT (Standard Protocol Items: Recommendations for Interventional Trials) guidelines. Hospitalized adult patients with laboratory-confirmed MERS will be enrolled in this recursive, two-stage, group sequential, multicenter, placebo-controlled, double-blind randomized controlled trial. The trial is initially designed to include 2 two-stage components. The first two-stage component is designed to adjust sample size and determine futility stopping, but not efficacy stopping. The second two-stage component is designed to determine efficacy stopping and possibly readjustment of sample size. The primary outcome is 90-day mortality.

Discussion

This will be the first randomized controlled trial of a potential treatment for MERS. The study is sponsored by King Abdullah International Medical Research Center, Riyadh, Saudi Arabia. Enrollment for this study began in November 2016, and has enrolled thirteen patients as of Jan 24-2018.

Trial registration

ClinicalTrials.gov, ID: NCT02845843. Registered on 27 July 2016.

Electronic supplementary material

The online version of this article (doi:10.1186/s13063-017-2427-0) contains supplementary material, which is available to authorized users.

Biomarker-Stratified Phase III Clinical Trials: Enhancement with a Subgroup-Focused Sequential Design

Among various design approaches to phase III clinical trials with a predictive biomarker, the marker-stratified all-comers design is advantageous because it allows for establishing the utility of both treatment and biomarker, but it is often criticized for requiring large sample sizes, as the design includes both marker-positive and marker-negative patients. In this article, we propose a simple but flexible subgroup-focused design for marker-stratified trials that allow both sequential assessment across marker-defined subgroups and adaptive subgroup selection while retaining an assessment using the entire patient cohort at the final analysis stage, possibly using established marker-based multiple testing procedures. Numerical evaluations indicate that the proposed marker-stratified design has a robustness property in preserving statistical power for detecting various profiles of treatment effects across the subgroups while effectively reducing the number of randomized patients in the marker-negative subgroup with presumably limited treatment efficacy. In contrast, the traditional all-comers and sequential enrichment designs could suffer from low statistical power for some possible profiles of treatment effects. The latter also needs long study durations and a large number of marker-screened patients. We also provide an application to SWOG S0819, a trial to assess the role of cetuximab in treating non-small cell lung cancers. These evaluations indicate that the proposed subgroup-focused approach can enhance the efficiency of the marker-stratified design for definitive evaluation of treatment and biomarker in phase III clinical trials. Clin Cancer Res; 24(5); 994-1001. ©2017 AACR.

Sample size adjustment designs with time-to-event outcomes: A caution

BACKGROUND

Sample size adjustment designs, which allow increasing the study sample size based on interim analysis of outcome data from a randomized clinical trial, have been increasingly promoted in the biostatistical literature. Although it is recognized that group sequential designs can be at least as efficient as sample size adjustment designs, many authors argue that a key advantage of these designs is their flexibility; interim sample size adjustment decisions can incorporate information and business interests external to the trial. Recently, Chen et al. (Clinical Trials 2015) considered sample size adjustment applications in the time-to-event setting using a design (CDL) that limits adjustments to situations where the interim results are promising. The authors demonstrated that while CDL provides little gain in unconditional power (versus fixed-sample-size designs), there is a considerable increase in conditional power for trials in which the sample size is adjusted.

METHODS

In time-to-event settings, sample size adjustment allows an increase in the number of events required for the final analysis. This can be achieved by either (a) following the original study population until the additional events are observed thus focusing on the tail of the survival curves or (b) enrolling a potentially large number of additional patients thus focusing on the early differences in survival curves. We use the CDL approach to investigate performance of sample size adjustment designs in time-to-event trials.

RESULTS

Through simulations, we demonstrate that when the magnitude of the true treatment effect changes over time, interim information on the shape of the survival curves can be used to enrich the final analysis with events from the time period with the strongest treatment effect. In particular, interested parties have the ability to make the end-of-trial treatment effect larger (on average) based on decisions using interim outcome data. Furthermore, in "clinical null" cases where there is no benefit due to crossing survival curves, the sample size adjustment design is shown to increase the probability of recommending an ineffective therapy.

CONCLUSION

Access to interim information on the shape of the survival curves may jeopardize the perceived integrity of trials using sample size adjustment designs. Therefore, given the lack of efficiency advantage over group sequential designs, sample size adjustment designs in time-to-event settings remain unjustified.

Sample Size Reassessment and Hypothesis Testing in Adaptive Survival Trials

Mid-study design modifications are becoming increasingly accepted in confirmatory clinical trials, so long as appropriate methods are applied such that error rates are controlled. It is therefore unfortunate that the important case of time-to-event endpoints is not easily handled by the standard theory. We analyze current methods that allow design modifications to be based on the full interim data, i.e., not only the observed event times but also secondary endpoint and safety data from patients who are yet to have an event. We show that the final test statistic may ignore a substantial subset of the observed event times. An alternative test incorporating all event times is found, where a conservative assumption must be made in order to guarantee type I error control. We examine the power of this approach using the example of a clinical trial comparing two cancer therapies.

Twenty-five years of confirmatory adaptive designs: opportunities and pitfalls

'Multistage testing with adaptive designs' was the title of an article by Peter Bauer that appeared 1989 in the German journal Biometrie und Informatik in Medizin und Biologie. The journal does not exist anymore but the methodology found widespread interest in the scientific community over the past 25 years. The use of such multistage adaptive designs raised many controversial discussions from the beginning on, especially after the publication by Bauer and Köhne 1994 in Biometrics: Broad enthusiasm about potential applications of such designs faced critical positions regarding their statistical efficiency. Despite, or possibly because of, this controversy, the methodology and its areas of applications grew steadily over the years, with significant contributions from statisticians working in academia, industry and agencies around the world. In the meantime, such type of adaptive designs have become the subject of two major regulatory guidance documents in the US and Europe and the field is still evolving. Developments are particularly noteworthy in the most important applications of adaptive designs, including sample size reassessment, treatment selection procedures, and population enrichment designs. In this article, we summarize the developments over the past 25 years from different perspectives. We provide a historical overview of the early days, review the key methodological concepts and summarize regulatory and industry perspectives on such designs. Then, we illustrate the application of adaptive designs with three case studies, including unblinded sample size reassessment, adaptive treatment selection, and adaptive endpoint selection. We also discuss the availability of software for evaluating and performing such designs. We conclude with a critical review of how expectations from the beginning were fulfilled, and - if not - discuss potential reasons why this did not happen.

Testing multiple primary endpoints in clinical trials with sample size adaptation

In this paper, we propose a design that uses a short-term endpoint for accelerated approval at interim analysis and a long-term endpoint for full approval at final analysis with sample size adaptation based on the long-term endpoint. Two sample size adaptation rules are compared: an adaptation rule to maintain the conditional power at a prespecified level and a step function type adaptation rule to better address the bias issue. Three testing procedures are proposed: alpha splitting between the two endpoints; alpha exhaustive between the endpoints; and alpha exhaustive with improved critical value based on correlation. Family-wise error rate is proved to be strongly controlled for the two endpoints, sample size adaptation, and two analysis time points with the proposed designs. We show that using alpha exhaustive designs greatly improve the power when both endpoints are effective, and the power difference between the two adaptation rules is minimal. The proposed design can be extended to more general settings.

[Modern study designs and analysis methods in clinical research]

BACKGROUND

Progress in the field of medical research requires further development of clinical trial methodology to overcome the challenges resulting from small patient populations and restricted resources.

METHODS

Classical single-stage designs with fixed sample sizes do not allow for interim analyses or design modifications. In contrast, adaptive designs adhere to established quality criteria while providing flexibility when conducting a clinical trial. In the face of new discoveries or information collected in the course of a trial, sample size adjustment, the selection of the target population and further design modifications can be performed. This enhances the chance of success of a clinical trial. Besides adaptive designs, classical approaches may be replaced or complemented by Bayesian methods. In a Bayesian approach prior knowledge can be efficiently included and hence the amount of information utilized in statistical analyses is increased. Furthermore, Bayes procedures allow the results of a statistical evaluation to be displayed very clearly.

CONCLUSION

Modern approaches, such as adaptive designs and Bayesian designs overcome the challenges in clinical research due to enhanced flexibility and efficiency. In addition, both approaches can be combined.

Adaptive seamless designs with interim treatment selection: a case study in oncology

The planning of an oncology clinical trial with a seamless phase II/III adaptive design is discussed. Two regimens of an experimental treatment are compared to a control at an interim analysis, and the most-promising regimen is selected to continue, together with control, until the end of the study. Because the primary endpoint is expected to be immature at the interim regimen selection analysis, designs that incorporate primary as well as surrogate endpoints in the regimen selection process are considered. The final testing of efficacy at the end of the study comparing the selected regimen to the control with respect to the primary endpoint uses all relevant data collected both before and after the regimen selection analysis. Several approaches for testing the primary hypothesis are assessed with regard to power and type I error rate. Because the operating characteristics of these designs depend on the specific regimen selection rules considered, benchmark scenarios are proposed in which a perfect surrogate and no surrogate is used at the regimen selection analysis. The operating characteristics of these benchmark scenarios provide a range where those of the actual study design are expected to lie. A discussion on family-wise error rate control for testing primary and key secondary endpoints as well as an assessment of bias in the final treatment effect estimate for the selected regimen are also presented.

Blinded versus unblinded covariate selection in confirmatory survival trials

Adjustment for covariates and specification of the correct covariate set are important issues in the analysis of clinical trials. Edwards (1999) proposes a model selection approach where the model is chosen on the final data set, which remains blinded for treatment group allocation. We investigate this method for time-to-event endpoints and compare its performance to variable selection within an adaptive design. This adaptive design integrates the methods of Schäfer and Müller (2001) and Keiding et al. (1987) and allows variable selection on the unblinded data during an interim analysis. Monte Carlo simulation shows that Edwards' method-though blinded-outperforms the adaptive method in terms of ability to select the survival relevant covariates and power. The application of the methods is illustrated by a clinical trial example.

A practical simulation method to calculate sample size of group sequential trials for time-to-event data under exponential and Weibull distribution

Group sequential design has been widely applied in clinical trials in the past few decades. The sample size estimation is a vital concern of sponsors and investigators. Especially in the survival group sequential trials, it is a thorny question because of its ambiguous distributional form, censored data and different definition of information time. A practical and easy-to-use simulation-based method is proposed for multi-stage two-arm survival group sequential design in the article and its SAS program is available. Besides the exponential distribution, which is usually assumed for survival data, the Weibull distribution is considered here. The incorporation of the probability of discontinuation in the simulation leads to the more accurate estimate. The assessment indexes calculated in the simulation are helpful to the determination of number and timing of the interim analysis. The use of the method in the survival group sequential trials is illustrated and the effects of the varied shape parameter on the sample size under the Weibull distribution are explored by employing an example. According to the simulation results, a method to estimate the shape parameter of the Weibull distribution is proposed based on the median survival time of the test drug and the hazard ratio, which are prespecified by the investigators and other participants. 10+ simulations are recommended to achieve the robust estimate of the sample size. Furthermore, the method is still applicable in adaptive design if the strategy of sample size scheme determination is adopted when designing or the minor modifications on the program are made.

A practical comparison of blinded methods for sample size reviews in survival data clinical trials

This paper presents practical approaches to the problem of sample size re-estimation in the case of clinical trials with survival data when proportional hazards can be assumed. When data are readily available at the time of the review, on a full range of survival experiences across the recruited patients, it is shown that, as expected, performing a blinded re-estimation procedure is straightforward and can help to maintain the trial's pre-specified error rates. Two alternative methods for dealing with the situation where limited survival experiences are available at the time of the sample size review are then presented and compared. In this instance, extrapolation is required in order to undertake the sample size re-estimation. Worked examples, together with results from a simulation study are described. It is concluded that, as in the standard case, use of either extrapolation approach successfully protects the trial error rates.

An adaptive group sequential phase II design to compare treatments for survival endpoints in rare patient entities

For rare diseases, standard treatments are often not available and essential study parameters are difficult or impossible to obtain. Therefore, designs of clinical trials for these diseases are often based on little information. Adaptive designs allow such trials to be started and to gain information during the study. Motivated by a trial for a rare subtype of renal-cell carcinoma, we present a two-stage adaptive design for right-censored time-to-event data and a two-sided test. After the first stage, one can stop for futility or continue with reestimated sample size. The properties of such designs are analyzed by simulation studies.

Sample size re-estimation for survival data in clinical trials with an adaptive design

In clinical trials with survival data, investigators may wish to re-estimate the sample size based on the observed effect size while the trial is ongoing. Besides the inflation of the type-I error rate due to sample size re-estimation, the method for calculating the sample size in an interim analysis should be carefully considered because the data in each stage are mutually dependent in trials with survival data. Although the interim hazard estimate is commonly used to re-estimate the sample size, the estimate can sometimes be considerably higher or lower than the hypothesized hazard by chance. We propose an interim hazard ratio estimate that can be used to re-estimate the sample size under those circumstances. The proposed method was demonstrated through a simulation study and an actual clinical trial as an example. The effect of the shape parameter for the Weibull survival distribution on the sample size re-estimation is presented.

Placebo-controlled, double-blind, prospective, randomized study on the effect of octreotide LAR in the control of tumor growth in patients with metastatic neuroendocrine midgut tumors: a report from the PROMID Study Group

PURPOSE

Somatostatin analogs are indicated for symptom control in patients with gastroenteropancreatic neuroendocrine tumors (NETs). The ability of somatostatin analogs to control the growth of well-differentiated metastatic NETs is a matter of debate. We performed a placebo-controlled, double-blind, phase IIIB study in patients with well-differentiated metastatic midgut NETs. The hypothesis was that octreotide LAR prolongs time to tumor progression and survival.

PATIENTS AND METHODS

Treatment-naive patients were randomly assigned to either placebo or octreotide LAR 30 mg intramuscularly in monthly intervals until tumor progression or death. The primary efficacy end point was time to tumor progression. Secondary end points were survival time and tumor response. This report is based on 67 tumor progressions and 16 observed deaths in 85 patients at the time of the planned interim analysis.

RESULTS

Median time to tumor progression in the octreotide LAR and placebo groups was 14.3 and 6 months, respectively (hazard ratio [HR] = 0.34; 95% CI, 0.20 to 0.59; P = .000072). After 6 months of treatment, stable disease was observed in 66.7% of patients in the octreotide LAR group and 37.2% of patients in the placebo group. Functionally active and inactive tumors responded similarly. The most favorable effect was observed in patients with low hepatic tumor load and resected primary tumor. Seven and nine deaths were observed in the octreotide LAR and placebo groups, respectively. The HR for overall survival was 0.81 (95% CI, 0.30 to 2.18).

CONCLUSION

Octreotide LAR significantly lengthens time to tumor progression compared with placebo in patients with functionally active and inactive metastatic midgut NETs. Because of the low number of observed deaths, survival analysis was not confirmatory.

Adaptive trial design: a general methodology for censored time to event data

Adaptive designs allow a clinical trial design to be changed according to interim findings without inflating type I error. The Inverse Normal method can be considered as an adaptive generalization of classical group sequential designs. The use of the Inverse Normal method for censored survival data was demonstrated only for the logrank statistic. However, the logrank statistic is inefficient in the presence of nuisance covariates affecting survival. We demonstrate, how the Inverse Normal method can be applied to Cox regression analysis. The required independence between test statistics of the different stages of the trial can be obtained by two different approaches. One is using the independent increment structure of the score process. The other uses right censoring and left truncating to divide individuals follow-up into per-stage data. Simulation studies show, that performance of the adaptive design does not depend on the method used for obtaining independence. Either way, an adaptive Cox regression analyis is more efficient than an adaptive logrank analysis if nuisance covariates affect survival.

Flexible two-stage design with sample size reassessment for survival trials

Flexible trials with adaptive design modification at interim analyses have been recently proposed as an answer to cope with some limitations of traditional designs for phase III trials. Actually, the sample size and duration of fixed design trials strongly depend on the determination, prior to the study, of key parameters such as the expected treatment effect and the event rates. A misspecification of these parameters may result in an underpowered or overpowered trial. In the flexible framework, the remainder of a design can be modified at an interim analysis, while preserving the initially specified global error rates. In this work, we present a flexible design with sample size re-evaluation for survival trials and study its properties in practical settings. The results show that, if parameters are initially misspecified, the proposed method allows an improved power control with a reasonable increase in sample size, if any. Practical guidelines concerning the choice of the trial parameters are also given.

Increasing the sample size during clinical trials witht-distributed test statistics without inflating the type I error rate

In clinical trials with t-distributed test statistics the required sample size depends on the unknown variance. Taking estimates from previous studies often leads to a misspecification of the true value of the variance. Hence, re-estimation of the variance based on the collected data and re-calculation of the required sample size is attractive. We present a flexible method for extensions of fixed sample or group-sequential trials with t-distributed test statistics. The method can be applied at any time during the course of the trial and does not require the necessity to pre-specify a sample size re-calculation rule. All available information can be used to determine the new sample size. The advantage of our method when compared with other adaptive methods is maintenance of the efficient t-test design when no extensions are actually made. We show that the type I error rate is preserved.

Biventricular stimulation to prevent cardiac desynchronization: rationale, design, and endpoints of the 'Biventricular Pacing for Atrioventricular Block to Prevent Cardiac Desynchronization (BioPace)' study

Despite the deleterious effects of cardiac dyssynchrony and the positive effects of cardiac resynchronization therapy, patients with high-degree atrioventricular block continue to receive desynchronizing right ventricular (RV) pacing systems. Although it is unclear whether the negative effects of RV pacing and left bundle branch block (LBBB) are comparable, and whether they depend on the presence and the degree of structural heart disease, one may hypothesize that RV pacing may have similar effects to LBBB. In the BioPace trial, the long-term effects of RV pacing vs. biventricular pacing will be prospectively compared in 1200 pacemaker patients with high likelihood of mostly paced ventricular events, regardless of whether in sinus rhythm or in atrial fibrillation (AF). After echocardiographic examination of left ventricular (LV) function, patients will be randomly assigned to the implantation of an RV vs. a biventricular pacing system and followed for up to 5 years. Primary study endpoints are survival, quality of life (QoL), and the distance covered in a 6-min hall walk (6-MHW) at 24 months after implantation. Secondary endpoints are QoL and the 6-MHW result at 12 months after implantation, hospitalization rate, LV dimensions, LV ejection fraction, and the development of chronic AF and other adverse events.

An overview of statistical approaches for adaptive designs and design modifications

With adaptive design methods for clinical trials, design elements such as sample size or further interim sample sizes may be changed during the course of the trial depending on all previously collected data. The focus of the overview is on group sequential approaches where the types of adaptations need not be specified in advance. An overview of the different statistical approaches for adaptive design methods proposed in the literature is given, relations between these methods are described and some perspectives of application and for future research are discussed.

Planning and analyzing adaptive group sequential survival trials

The use of adaptive methods has experienced increasing interest in the current literature on group sequential designs. Group sequential analysis in survival trials usually apply the error spending function approach due to the unpredictable amount of information available in an interim analysis. An alternative way is to apply adaptive methods where additionally the maximum amount of information and other designing parameters can be changed based on the information available at the interim stage. In this paper, it is shown how the inverse normal method can be used within a survival design using the log-rank test for comparing two survival functions. This method allows for many kinds of design modifications. In case of no modifications, the inverse normal method coincides with the commonly used analysis strategy. It is straightforward to specify effect estimates. Confidence intervals for the hazard ratio that can be calculated at each stage of the trial and intervals that can only be computed by the end of the trial are proposed. The latter also enables the calculation of median unbiased estimates. Overall p-values can be defined analogously. Properties of the analyses techniques are investigated and compared with alternative approaches. It is shown that the proposed analysis technique might help to rescue an underpowered study and opens the way to other types of changes in design. The proposed technique is implemented in the software ADDPLAN Adaptive Design, Plans and Analyses (http://www.addplan.com).

Adaptive design: estimation and inference with censored data in a semiparametric model

In this article, we provide a method of estimation for the treatment effect in the adaptive design for censored survival data with or without adjusting for risk factors other than the treatment indicator. Within the semiparametric Cox proportional hazards model, we propose a bias-adjusted parameter estimator for the treatment coefficient and its asymptotic confidence interval at the end of the trial. The method for obtaining an asymptotic confidence interval and point estimator is based on a general distribution property of the final test statistic from the weighted linear rank statistics at the interims with or without considering the nuisance covariates. The computation of the estimates is straightforward. Extensive simulation studies show that the asymptotic confidence intervals have reasonable nominal probability of coverage, and the proposed point estimators are nearly unbiased with practical sample sizes.

The advantages and disadvantages of adaptive designs for clinical trials

Flexible designs for clinical trials permit mid-trial design modifications, which are based on interim information from inside or outside the trial while meeting (regulatory) requirements for the control of the type I error rate. The basic principle is to combine stage standardized test statistics such as p-values or z-scores in a pre-specified way. The flexibility covers changes of sample sizes, treatment allocation ratios and the number of interim analyses, as well as the selection of treatments, doses and end points. The price to be paid is that non-standard test statistics must be used after an adaptation.

Strategies for changing the test statistic during a clinical trial

This article discusses the design of a clinical trial where a new treatment will be compared to a control. For a specific type of endpoint, there are a wide variety of test statistics that can be used. Also, the investigator must decide how many patients to accrue in each arm as well as the duration of the study. After an interim look at the data, the investigator may decide that a different test statistic would be more powerful or that more patients or longer follow-up is needed. In this article, we discuss a strategy for making these types of changes. This strategy controls the probability of making a type I error and can result in a procedure that has higher power than the test without adaptation.