Sample size re-estimation: recent developments and practical considerations

The SWiFT trial (Study of Whole Blood in Frontline Trauma)-the clinical and cost effectiveness of pre-hospital whole blood versus standard care in patients with life-threatening traumatic haemorrhage: study protocol for a multi-centre randomised controlled trial

BACKGROUND

Early blood transfusion improves survival in patients with life-threatening bleeding, but the optimal transfusion strategy in the pre-hospital setting has yet to be established. Although there is some evidence of benefit with the use of whole blood, there have been no randomised controlled trials exploring the clinical and cost effectiveness of pre-hospital administration of whole blood versus component therapy for trauma patients with life-threatening bleeding. The aim of this trial is to determine whether pre-hospital leukocyte-depleted whole blood transfusion is better than standard care (blood component transfusion) in reducing the proportion of participants who experience death or massive transfusion at 24 h.

METHODS

This is a multi-centre, superiority, open-label, randomised controlled trial with internal pilot and within-trial cost-effectiveness analysis. Patients of any age will be eligible if they have suffered major traumatic haemorrhage and are attended by a participating air ambulance service. The primary outcome is the proportion of participants with traumatic haemorrhage who have died (all-cause mortality) or received massive transfusion in the first 24 h from randomisation. A number of secondary clinical, process, and safety endpoints will be collected and analysed. Cost (provision of whole blood, hospital, health, and wider care resource use) and outcome data will be synthesised to present incremental cost-effectiveness ratios for the trial primary outcome and cost per quality-adjusted life year at 90 days after injury. We plan to recruit 848 participants (a two-sided test with 85% power, 5% type I error, 1-1 allocation, and one interim analysis would require 602 participants-after allowing for 25% of participants in traumatic cardiac arrest and an additional 5% drop out, the sample size is 848).

DISCUSSION

The SWiFT trial will recruit 848 participants across at least ten air ambulances services in the UK. It will investigate the clinical and cost-effectiveness of whole blood transfusion versus component therapy in the management of patients with life-threatening bleeding in the pre-hospital setting.

TRIAL REGISTRATION

ISRCTN: 23657907; EudraCT: 2021-006876-18; IRAS Number: 300414; REC: 22/SC/0072, 21 Dec 2021.

Recent innovations in adaptive trial designs: A review of design opportunities in translational research

Clinical trials are constantly evolving in the context of increasingly complex research questions and potentially limited resources. In this review article, we discuss the emergence of "adaptive" clinical trials that allow for the preplanned modification of an ongoing clinical trial based on the accumulating evidence with application across translational research. These modifications may include terminating a trial before completion due to futility or efficacy, re-estimating the needed sample size to ensure adequate power, enriching the target population enrolled in the study, selecting across multiple treatment arms, revising allocation ratios used for randomization, or selecting the most appropriate endpoint. Emerging topics related to borrowing information from historic or supplemental data sources, sequential multiple assignment randomized trials (SMART), master protocol and seamless designs, and phase I dose-finding studies are also presented. Each design element includes a brief overview with an accompanying case study to illustrate the design method in practice. We close with brief discussions relating to the statistical considerations for these contemporary designs.

Acipimox in Mitochondrial Myopathy (AIMM): study protocol for a randomised, double-blinded, placebo-controlled, adaptive design trial of the efficacy of acipimox in adult patients with mitochondrial myopathy

BACKGROUND

Mitochondrial disease is a heterogenous group of rare, complex neurometabolic disorders. Despite their individual rarity, collectively mitochondrial diseases represent the most common cause of inherited metabolic disorders in the UK; they affect 1 in every 4300 individuals, up to 15,000 adults (and a similar number of children) in the UK. Mitochondrial disease manifests multisystem and isolated organ involvement, commonly affecting those tissues with high energy demands, such as skeletal muscle. Myopathy manifesting as fatigue, muscle weakness and exercise intolerance is common and debilitating in patients with mitochondrial disease. Currently, there are no effective licensed treatments and consequently, there is an urgent clinical need to find an effective drug therapy.

AIM

To investigate the efficacy of 12-week treatment with acipimox on the adenosine triphosphate (ATP) content of skeletal muscle in patients with mitochondrial disease and myopathy.

METHODS

AIMM is a single-centre, double blind, placebo-controlled, adaptive designed trial, evaluating the efficacy of 12 weeks' administration of acipimox on skeletal muscle ATP content in patients with mitochondrial myopathy. Eligible patients will receive the trial investigational medicinal product (IMP), either acipimox or matched placebo. Participants will also be prescribed low dose aspirin as a non-investigational medical product (nIMP) in order to protect the blinding of the treatment assignment. Eighty to 120 participants will be recruited as required, with an interim analysis for sample size re-estimation and futility assessment being undertaken once the primary outcome for 50 participants has been obtained. Randomisation will be on a 1:1 basis, stratified by Fatigue Impact Scale (FIS) (dichotomised as < 40, ≥ 40). Participants will take part in the trial for up to 20 weeks, from screening visits through to follow-up at 16 weeks post randomisation. The primary outcome of change in ATP content in skeletal muscle and secondary outcomes relating to quality of life, perceived fatigue, disease burden, limb function, balance and walking, skeletal muscle analysis and symptom-limited cardiopulmonary fitness (optional) will be assessed between baseline and 12 weeks.

DISCUSSION

The AIMM trial will investigate the effect of acipimox on modulating muscle ATP content and whether it can be repurposed as a new treatment for mitochondrial disease with myopathy.

TRIAL REGISTRATION

EudraCT2018-002721-29 . Registered on 24 December 2018, ISRCTN 12895613. Registered on 03 January 2019, https://www.isrctn.com/search?q=aimm.

The Determining Effective Testing in Emergency Departments and Care Coordination on Treatment Outcomes (DETECT) for Hepatitis C (Hep C) Screening Trial: rationale and design of a multi-center pragmatic randomized clinical trial of hepatitis C screening in emergency departments

Background

Early identification of HCV is a critical health priority, especially now that treatment options are available to limit further transmission and provide cure before long-term sequelae develop. Emergency departments (EDs) are important clinical settings for HCV screening given that EDs serve many at-risk patients who do not access other forms of healthcare. In this article, we describe the rationale and design of The Determining Effective Testing in Emergency Departments and Care Coordination on Treatment Outcomes (DETECT) for Hepatitis C (Hep C) Screening Trial.

Methods

The DETECT Hep C Screening Trial is a multi-center prospective pragmatic randomized two-arm parallel-group superiority trial to test the comparative effectiveness of nontargeted and targeted HCV screening in the ED with a primary hypothesis that nontargeted screening is superior to targeted screening when identifying newly diagnosed HCV. This trial will be performed in the EDs at Denver Health Medical Center (Denver, CO), Johns Hopkins Hospital (Baltimore, MD), and the University of Mississippi Medical Center (Jackson, MS), sites representing approximately 225,000 annual adult visits, and designed using the PRECIS-2 framework for pragmatic trials. When complete, we will have enrolled a minimum of 125,000 randomized patient visits and have performed 13,965 HCV tests. In Denver, the Screening Trial will serve as a conduit for a distinct randomized comparative effectiveness trial to evaluate linkage-to-HCV care strategies. All sites will further contribute to embedded observational studies to assess cost effectiveness, disparities, and social determinants of health in screening, linkage-to-care, and treatment for HCV.

Discussion

When complete, The DETECT Hep C Screening Trial will represent the largest ED-based pragmatic clinical trial to date and all studies, in aggregate, will significantly inform how to best perform ED-based HCV screening.

Trial registration

ClinicalTrials.gov ID: NCT04003454. Registered on 1 July 2019.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13063-022-06265-1.

Repurposing Probenecid for the Treatment of Heart Failure (Re-Prosper-HF): a study protocol for a randomized placebo-controlled clinical trial

BACKGROUND

Improving contractility in heart failure with reduced ejection fraction (HFrEF) has resurfaced as a potential treatment goal. Inotropic therapy is now better understood through its underlying mechanism as opposed to the observed effect of increasing contractility. Calcitropes are a subgroup of inotropes that largely depend on the stimulation of adenylyl cyclase to transform ATP into cyclic adenosine monophosphate (cAMP). At least two clinically relevant calcitropes-istaroxime and probenecid-improve contractility through an increase in systolic intracellular calcium without activating cAMP production. Probenecid, which has been safely used clinically for decades in non-cardiac conditions, has recently been identified as an agonist of the transient receptor potential vanilloid 2 channel. Translational studies have shown that it improves calcium cycling and contractility without activating noxious pathways associated with cAMP-dependent calcitropes and can improve cardiac function in patients with HFrEF.

METHODS

The Re-Prosper-HF study (Repurposing Probenecid for the Treatment of Heart Failure with Reduced Ejection Fraction) is a three-site double-blinded randomized-controlled trial that will test the hypothesis that probenecid can improve cardiac function in patients with HFrEF. Up to 120 patients will be randomized in this double-blind, placebo-controlled study that will assess whether oral probenecid administered at 1 g orally twice per day for 180 days in patients with NYHA II-III HFrEF improves systolic function (aim 1), functional status (aim 2), and self-reported health status (aim 3).

DISCUSSION

Findings from this study will provide data informing its use for improving symptomatology in patients with HFrEF as well as exploratory data for outcomes such as hospital admission rates.

TRIAL TEGISTRATION

The Re-Prosper HF Study (Re-Prosper HF) is registered on ClinicalTrials.gov with the identifier as NCT04551222. Registered on 9 September 2020.

Leveraging external data in the design and analysis of clinical trials in neuro-oncology

Integration of external control data, with patient-level information, in clinical trials has the potential to accelerate the development of new treatments in neuro-oncology by contextualising single-arm studies and improving decision making (eg, early stopping decisions). Based on a series of presentations at the 2020 Clinical Trials Think Tank hosted by the Society of Neuro-Oncology, we provide an overview on the use of external control data representative of the standard of care in the design and analysis of clinical trials. High-quality patient-level records, rigorous methods, and validation analyses are necessary to effectively leverage external data. We review study designs, statistical methods, risks, and potential distortions in using external data from completed trials and real-world data, as well as data sources, data sharing models, ongoing work, and applications in glioblastoma.

How cutting-edge trial design can assess outcomes

PURPOSE OF REVIEW

Randomized clinical trials (RCTs) have come to be accepted as the gold standard for assessing the efficacy and effectiveness of therapeutics and interventions in medicine. In this paper, we aim to describe some evolving concepts associated with the design and conduct of RCTs and outline new approaches aiming to increase efficiency and reduce costs.

RECENT FINDINGS

A well-powered and performed RCT is usually a study involving several different centers from different geographical areas that enrolls a large number of patients in diverse clinical settings. Altogether, these features increase the generalizability of the study and make the rapid implementation of the findings more likely. However, this does not come without cost. Among several possible alternatives to conventional RCTs, the most important ones are related to the unit of randomization (individual vs. cluster), study design (conventional vs. adaptive), randomization scheme (fixed vs. response-adaptive), data collection (conventional case report forms vs. registry-embedded) and statistical approach (frequentist vs. Bayesian).

SUMMARY

While conventional RCTs remain the gold standard for generating evidence, new trial designs may be considered to reduce sample size and costs while improving trial efficiency and power. However, they raise new challenges for testing feasibility, conduct, ethical oversight and statistical analysis.

Statistical consideration when adding new arms to ongoing clinical trials: the potentials and the caveats

BACKGROUND

Platform trials improve the efficiency of the drug development process through flexible features such as adding and dropping arms as evidence emerges. The benefits and practical challenges of implementing novel trial designs have been discussed widely in the literature, yet less consideration has been given to the statistical implications of adding arms. MAIN: We explain different statistical considerations that arise from allowing new research interventions to be added in for ongoing studies. We present recent methodology development on addressing these issues and illustrate design and analysis approaches that might be enhanced to provide robust inference from platform trials. We also discuss the implication of changing the control arm, how patient eligibility for different arms may complicate the trial design and analysis, and how operational bias may arise when revealing some results of the trials. Lastly, we comment on the appropriateness and the application of platform trials in phase II and phase III settings, as well as publicly versus industry-funded trials.

CONCLUSION

Platform trials provide great opportunities for improving the efficiency of evaluating interventions. Although several statistical issues are present, there are a range of methods available that allow robust and efficient design and analysis of these trials.

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

Intraoperative xenon for prevention of delirium after on-pump cardiac surgery: a randomised, observer-blind, controlled clinical trial

BACKGROUND

Older patients undergoing cardiac surgery have a 40-60% risk of developing postoperative delirium (POD), which is associated with increased morbidity and mortality. In animals, xenon has been found to be neuroprotective. Little is known about its neuroprotective effects in humans. We evaluated whether xenon anaesthesia prevents POD in patients undergoing cardiac surgery.

METHODS

We conducted a randomised, observer-blind, controlled trial in which 190 patients 65 yr or older undergoing on-pump cardiac surgery were randomly allocated to xenon or sevoflurane anaesthesia. During cardiopulmonary bypass, propofol infusion was used for anaesthetic maintenance. Subjects were screened for POD daily during the first 5 postoperative days using the 3-Minute Diagnostic Interview for Confusion Assessment Method (CAM) or with a CAM version for patients in ICU (CAM-ICU). Other methods to detect delirium, such as chart review, were also used. Secondary outcomes included the duration and severity of POD, and postoperative cognitive function.

RESULTS

The overall incidence of POD was 41% (78/190). There was no statistically significant difference in the POD incidence between the xenon and sevoflurane groups (42.7% [41/96] vs 39.4% [37/94], P=0.583). The odds ratio for POD when comparing xenon with sevoflurane was 1.18 (95% confidence interval, 0.65-2.16).

CONCLUSIONS

In older patients undergoing cardiac surgery, xenon anaesthesia did not result in a significant reduction in POD. Based on these results alone, use of xenon cannot be recommended for this purpose.

CLINICAL TRIAL REGISTRATION

EudraCT: 2014-005370-11 (May 13, 2015; https://www.clinicaltrialsregister.eu/ctr-search/search?query=2014-005370-11).

Follow up after sample size re-estimation in a breast cancer randomized trial for disease-free survival

BACKGROUND

While the clinical trials and statistical methodology literature on sample size re-estimation (SSRE) is robust, evaluation of SSRE procedures following the completion of a clinical trial has been sparsely reported. In blinded sample size re-estimation, only nuisance parameters are re-estimated, and the blinding of the current trial treatment effect is preserved. Blinded re-estimation procedures are well-accepted by regulatory agencies and funders. We review our experience of sample size re-estimation in a large international, National Institutes of Health funded clinical trial for adjuvant breast cancer treatment, and evaluate our blinded sample size re-estimation procedure for this time-to-event trial. We evaluated the SSRE procedure by examining assumptions made during the re-estimation process, estimates resulting from re-estimation, and the impact on final trial results with and without the addition of participants, following sample size re-estimation.

METHODS

We compared the control group failure probabilities estimated at the time of SSRE to estimates used in the original planning, to the final un-blinded control group failure probability estimates for those included in the SSRE procedure (SSRE cohort), and to the final total control group failure probability estimates. The impact of re-estimation on the final comparison between randomized treatment groups is evaluated for those in the originally planned cohort (n = 340) and for the combination of those recruited in the originally planned cohort and those added after re-estimation (n = 509).

RESULTS

Very little difference is observed between the originally planned cohort and all randomized patients in the control group failure probabilities over time or in the overall hazard ratio estimating treatment effect (originally planned cohort HR 1.25 (0.86, 1.79); all randomized cohort HR 1.24 95% CI (0.91, 1.68)). At the time of blinded SSRE, the estimated control group failure probabilities at 3 years (0.24) and 5 years (0.40) were similar to those for the SSRE cohort once un-blinded (3 years, 0.22 (0.16, 0.30); 5 years, 0.33 (0.26, 0.41)).

CONCLUSIONS

We found that our re-estimation procedure performed reasonably well in estimating the control group failure probabilities at the time of re-estimation. Particularly for time-to-event outcomes, pre-planned blinded SSRE procedures may be the best option to aid in maintaining power.

TRIAL REGISTRATION

ClinicalTrials.gov, NCT00201851 . Registered on 9 September 2005. Retrospectively registered.

An efficient sample size adaptation strategy with adjustment of randomization ratio

In clinical trials, sample size reestimation is a useful strategy for mitigating the risk of uncertainty in design assumptions and ensuring sufficient power for the final analysis. In particular, sample size reestimation based on unblinded interim effect size can often lead to sample size increase, and statistical adjustment is usually needed for the final analysis to ensure that type I error rate is appropriately controlled. In current literature, sample size reestimation and corresponding type I error control are discussed in the context of maintaining the original randomization ratio across treatment groups, which we refer to as "proportional increase." In practice, not all studies are designed based on an optimal randomization ratio due to practical reasons. In such cases, when sample size is to be increased, it is more efficient to allocate the additional subjects such that the randomization ratio is brought closer to an optimal ratio. In this research, we propose an adaptive randomization ratio change when sample size increase is warranted. We refer to this strategy as "nonproportional increase," as the number of subjects increased in each treatment group is no longer proportional to the original randomization ratio. The proposed method boosts power not only through the increase of the sample size, but also via efficient allocation of the additional subjects. The control of type I error rate is shown analytically. Simulations are performed to illustrate the theoretical results.

Modelling Thirty-day Mortality in the Acute Respiratory Distress Syndrome (ARDS) in an Adult ICU

Variables predicting thirty-day outcome from Acute Respiratory Distress Syndrome (ARDS) were analysed using Cox regression structured for time-varying covariates. Over a three-year period, 1996–1998, consecutive patients with ARDS (bilateral chest X-ray opacities, PaO2/FiO2 ratio of <200 and an acute precipitating event) were identified using a prospective computerized data base in a university teaching hospital ICU.

The cohort, 106 mechanically ventilated patients, was of mean (SD) age 63.5 (15.5) years and 37% were female. Primary lung injury occurred in 45% and 24% were postoperative. ICU-admission day APACHE II score was 25 (8); ARDS onset time from ICU admission was 1 day (median: range 0-16) and 30 day mortality was 41% (95% CI: 33%-51%). At ARDS onset, PaO2/FiO2 ratio was 92 (31), 81% had four-quadrant chest X-ray opacification and lung injury score was 2.75 (0.45). Average mechanical ventilator tidal volume was 10.3 ml/ predicted kg weight. Cox model mortality predictors (hazard ratio, 95% CI) were: APACHE II score, 1.15 (1.09-1.21); ARDS lag time (days), 0.72 (0.58-0.89); direct versus indirect injury, 2.89 (1.45-5.76); PaO2/FiO2 ratio, 0.98 (0.97-0.99); operative versus non-operative category, 0.24 (0.09-0.63). Time-varying effects were evident for PaO2/FiO2 ratio, operative versus non-operative category and ventilator tidal volume assessed as a categorical predictor with a cut-point of 8 ml/kg predicted weight (mean tidal volumes, 7.1 (1.9) vs 10.7 (1.6) ml/kg predicted weight). Thirty-day survival was improved for patients ventilated with lower tidal volumes.

Survival predictors in ARDS were multifactorial and related to patient-injury-time interaction and level of mechanical ventilator tidal volume.

Wearable Cardioverter-Defibrillator after Myocardial Infarction

BACKGROUND

Despite the high rate of sudden death after myocardial infarction among patients with a low ejection fraction, implantable cardioverter-defibrillators are contraindicated until 40 to 90 days after myocardial infarction. Whether a wearable cardioverter-defibrillator would reduce the incidence of sudden death during this high-risk period is unclear.

METHODS

We randomly assigned (in a 2:1 ratio) patients with acute myocardial infarction and an ejection fraction of 35% or less to receive a wearable cardioverter-defibrillator plus guideline-directed therapy (the device group) or to receive only guideline-directed therapy (the control group). The primary outcome was the composite of sudden death or death from ventricular tachyarrhythmia at 90 days (arrhythmic death). Secondary outcomes included death from any cause and nonarrhythmic death.

RESULTS

Of 2302 participants, 1524 were randomly assigned to the device group and 778 to the control group. Participants in the device group wore the device for a median of 18.0 hours per day (interquartile range, 3.8 to 22.7). Arrhythmic death occurred in 1.6% of the participants in the device group and in 2.4% of those in the control group (relative risk, 0.67; 95% confidence interval [CI], 0.37 to 1.21; P=0.18). Death from any cause occurred in 3.1% of the participants in the device group and in 4.9% of those in the control group (relative risk, 0.64; 95% CI, 0.43 to 0.98; uncorrected P=0.04), and nonarrhythmic death in 1.4% and 2.2%, respectively (relative risk, 0.63; 95% CI, 0.33 to 1.19; uncorrected P=0.15). Of the 48 participants in the device group who died, 12 were wearing the device at the time of death. A total of 20 participants in the device group (1.3%) received an appropriate shock, and 9 (0.6%) received an inappropriate shock.

CONCLUSIONS

Among patients with a recent myocardial infarction and an ejection fraction of 35% or less, the wearable cardioverter-defibrillator did not lead to a significantly lower rate of the primary outcome of arrhythmic death than control. (Funded by the National Institutes of Health and Zoll Medical; VEST ClinicalTrials.gov number, NCT01446965 .).

The inclusion of real world evidence in clinical development planning

BACKGROUND

When designing studies it is common to search the literature to investigate variability estimates to use in sample size calculations. Proprietary data of previously designed trials in a particular indication are also used to obtain estimates of variability. Estimates of treatment effects are typically obtained from randomised controlled clinical trials (RCTs). Based on the observed estimates of treatment effect, variability and the minimum clinical relevant difference to detect, the sample size for a subsequent trial is estimated. However, data from real world evidence (RWE) studies, such as observational studies and other interventional studies in patients in routine clinical practice, are not widely used in a systematic manner when designing studies. In this paper, we propose a framework for inclusion of RWE in planning of a clinical development programme.

METHODS

In our proposed approach, all evidence, from both RCTs and RWE (i.e. from studies in routine clinical practice), available at the time of designing of a new clinical trial is combined in a Bayesian network meta-analysis (NMA). The results can be used to inform the design of the next clinical trial in the programme. The NMA was performed at key milestones, such as at the end of the phase II trial and prior to the design of key phase III studies. To illustrate the methods, we designed an alternative clinical development programme in multiple sclerosis using RWE through clinical trial simulations.

RESULTS

Inclusion of RWE in the NMA and the resulting trial simulations demonstrated that 284 patients per arm were needed to achieve 90% power to detect effects of predetermined size in the TRANSFORMS study. For the FREEDOMS and FREEDOMS II clinical trials, 189 patients per arm were required. Overall there was a reduction in sample size of at least 40% across the three phase III studies, which translated to a time savings of at least 6 months for the undertaking of the fingolimod phase III programme.

CONCLUSION

The use of RWE resulted in a reduced sample size of the pivotal phase III studies, which led to substantial time savings compared to the approach of sample size calculations without RWE.

Bayesian sample size re-estimation using power priors

The sample size of a randomized controlled trial is typically chosen in order for frequentist operational characteristics to be retained. For normally distributed outcomes, an assumption for the variance needs to be made which is usually based on limited prior information. Especially in the case of small populations, the prior information might consist of only one small pilot study. A Bayesian approach formalizes the aggregation of prior information on the variance with newly collected data. The uncertainty surrounding prior estimates can be appropriately modelled by means of prior distributions. Furthermore, within the Bayesian paradigm, quantities such as the probability of a conclusive trial are directly calculated. However, if the postulated prior is not in accordance with the true variance, such calculations are not trustworthy. In this work we adapt previously suggested methodology to facilitate sample size re-estimation. In addition, we suggest the employment of power priors in order for operational characteristics to be controlled.

Sample size re-estimation in paired comparative diagnostic accuracy studies with a binary response

BACKGROUND

The sample size required to power a study to a nominal level in a paired comparative diagnostic accuracy study, i.e. studies in which the diagnostic accuracy of two testing procedures is compared relative to a gold standard, depends on the conditional dependence between the two tests - the lower the dependence the greater the sample size required. A priori, we usually do not know the dependence between the two tests and thus cannot determine the exact sample size required. One option is to use the implied sample size for the maximal negative dependence, giving the largest possible sample size. However, this is potentially wasteful of resources and unnecessarily burdensome on study participants as the study is likely to be overpowered. A more accurate estimate of the sample size can be determined at a planned interim analysis point where the sample size is re-estimated.

METHODS

This paper discusses a sample size estimation and re-estimation method based on the maximum likelihood estimates, under an implied multinomial model, of the observed values of conditional dependence between the two tests and, if required, prevalence, at a planned interim. The method is illustrated by comparing the accuracy of two procedures for the detection of pancreatic cancer, one procedure using the standard battery of tests, and the other using the standard battery with the addition of a PET/CT scan all relative to the gold standard of a cell biopsy. Simulation of the proposed method illustrates its robustness under various conditions.

RESULTS

The results show that the type I error rate of the overall experiment is stable using our suggested method and that the type II error rate is close to or above nominal. Furthermore, the instances in which the type II error rate is above nominal are in the situations where the lowest sample size is required, meaning a lower impact on the actual number of participants recruited.

CONCLUSION

We recommend multinomial model maximum likelihood estimation of the conditional dependence between paired diagnostic accuracy tests at an interim to reduce the number of participants required to power the study to at least the nominal level.

TRIAL REGISTRATION

ISRCTN ISRCTN73852054 . Registered 9th of January 2015. Retrospectively registered.

Imaging biomarker roadmap for cancer studies

Imaging biomarkers (IBs) are integral to the routine management of patients with cancer. IBs used daily in oncology include clinical TNM stage, objective response and left ventricular ejection fraction. Other CT, MRI, PET and ultrasonography biomarkers are used extensively in cancer research and drug development. New IBs need to be established either as useful tools for testing research hypotheses in clinical trials and research studies, or as clinical decision-making tools for use in healthcare, by crossing 'translational gaps' through validation and qualification. Important differences exist between IBs and biospecimen-derived biomarkers and, therefore, the development of IBs requires a tailored 'roadmap'. Recognizing this need, Cancer Research UK (CRUK) and the European Organisation for Research and Treatment of Cancer (EORTC) assembled experts to review, debate and summarize the challenges of IB validation and qualification. This consensus group has produced 14 key recommendations for accelerating the clinical translation of IBs, which highlight the role of parallel (rather than sequential) tracks of technical (assay) validation, biological/clinical validation and assessment of cost-effectiveness; the need for IB standardization and accreditation systems; the need to continually revisit IB precision; an alternative framework for biological/clinical validation of IBs; and the essential requirements for multicentre studies to qualify IBs for clinical use.

Xenon for the prevention of postoperative delirium in cardiac surgery: study protocol for a randomized controlled clinical trial

Background

Postoperative delirium (POD) is a manifestation of acute postoperative brain dysfunction that is frequently observed after cardiac surgery. POD is associated with short-term complications such as an increase in mortality, morbidity, costs and length of stay, but can also have long-term sequelae, including persistent cognitive deficits, loss of independence, and increased mortality for up to 2 years. The noble gas xenon has been demonstrated in various models of neuronal injury to exhibit remarkable neuroprotective properties. We therefore hypothesize that xenon anesthesia reduces the incidence of POD in elderly patients undergoing cardiac surgery with the use of cardiopulmonary bypass.

Methods/Design

One hundred and ninety patients, older than 65 years, and scheduled for elective cardiac surgery, will be enrolled in this prospective, randomized, controlled trial. Patients will be randomized to receive general anesthesia with either xenon or sevoflurane. Primary outcome parameter will be the incidence of POD in the first 5 postoperative days. The occurrence of POD will be assessed by trained research personnel, blinded to study group, with the validated 3-minute Diagnostic Confusion Assessment Method (3D-CAM) (on the intensive care unit in its version specifically adapted for the ICU), in addition to chart review and the results of delirium screening tools that will be performed by the bedside nurses). Secondary outcome parameters include duration and severity of POD, and postoperative cognitive function as assessed with the Mini-Mental State Examination.

Discussion

Older patients undergoing cardiac surgery are at particular risk to develop POD. Xenon provides remarkable hemodynamic stability and has been suggested in preclinical studies to exhibit neuroprotective properties. The present trial will assess whether the promising profile of xenon can be translated into a better outcome in the geriatric population.

Trial registration

EudraCT Identifier: 2014-005370-11 (13 May 2015).

Sample Size Calculation: Inaccurate A Priori Assumptions for Nuisance Parameters Can Greatly Affect the Power of a Randomized Controlled Trial

We aimed to examine the extent to which inaccurate assumptions for nuisance parameters used to calculate sample size can affect the power of a randomized controlled trial (RCT). In a simulation study, we separately considered an RCT with continuous, dichotomous or time-to-event outcomes, with associated nuisance parameters of standard deviation, success rate in the control group and survival rate in the control group at some time point, respectively. For each type of outcome, we calculated a required sample size N for a hypothesized treatment effect, an assumed nuisance parameter and a nominal power of 80%. We then assumed a nuisance parameter associated with a relative error at the design stage. For each type of outcome, we randomly drew 10,000 relative errors of the associated nuisance parameter (from empirical distributions derived from a previously published review). Then, retro-fitting the sample size formula, we derived, for the pre-calculated sample size N, the real power of the RCT, taking into account the relative error for the nuisance parameter. In total, 23%, 0% and 18% of RCTs with continuous, binary and time-to-event outcomes, respectively, were underpowered (i.e., the real power was < 60%, as compared with the 80% nominal power); 41%, 16% and 6%, respectively, were overpowered (i.e., with real power > 90%). Even with proper calculation of sample size, a substantial number of trials are underpowered or overpowered because of imprecise knowledge of nuisance parameters. Such findings raise questions about how sample size for RCTs should be determined.

Design of telehealth trials--introducing adaptive approaches

BACKGROUND

The field of telehealth and telemedicine is expanding as the need to improve efficiency of health care becomes more pressing. The decision to implement a telehealth system is generally an expensive undertaking that impacts a large number of patients and other stakeholders. It is therefore extremely important that the decision is fully supported by accurate evaluation of telehealth interventions.

OBJECTIVE

Numerous reviews of telehealth have described the evidence base as inconsistent. In response they call for larger, more rigorously controlled trials, and trials which go beyond evaluation of clinical effectiveness alone. The aim of this paper is to discuss various ways in which evaluation of telehealth could be improved by the use of adaptive trial designs.

RESULTS

We discuss various adaptive design options, such as sample size reviews and changing the study hypothesis to address uncertain parameters, group sequential trials and multi-arm multi-stage trials to improve efficiency, and enrichment designs to maximise the chances of obtaining clear evidence about the telehealth intervention.

CONCLUSION

There is potential to address the flaws discussed in the telehealth literature through the adoption of adaptive approaches to trial design. Such designs could lead to improvements in efficiency, allow the evaluation of multiple telehealth interventions in a cost-effective way, or accurately assess a range of endpoints that are important in the overall success of a telehealth programme.

A two-stage Bayesian design with sample size reestimation and subgroup analysis for phase II binary response trials

Frequentist sample size determination for binary outcome data in a two-arm clinical trial requires initial guesses of the event probabilities for the two treatments. Misspecification of these event rates may lead to a poor estimate of the necessary sample size. In contrast, the Bayesian approach that considers the treatment effect to be random variable having some distribution may offer a better, more flexible approach. The Bayesian sample size proposed by (Whitehead et al., 2008) for exploratory studies on efficacy justifies the acceptable minimum sample size by a "conclusiveness" condition. In this work, we introduce a new two-stage Bayesian design with sample size reestimation at the interim stage. Our design inherits the properties of good interpretation and easy implementation from Whitehead et al. (2008), generalizes their method to a two-sample setting, and uses a fully Bayesian predictive approach to reduce an overly large initial sample size when necessary. Moreover, our design can be extended to allow patient level covariates via logistic regression, now adjusting sample size within each subgroup based on interim analyses. We illustrate the benefits of our approach with a design in non-Hodgkin lymphoma with a simple binary covariate (patient gender), offering an initial step toward within-trial personalized medicine.

Understanding the FDA guidance on adaptive designs: historical, legal, and statistical perspectives

The recent Food and Drug Administration (FDA) guidance for industry on adaptive designs is perhaps one of the important undertakings by CDER/CBER Office of Biostatistics. Undoubtedly, adaptive designs may affect almost all phases of clinical development and impact nearly all aspects of clinical trial planning, execution and statistical inference. Thus, it is a significant accomplishment for the Office of Biostatistics to develop this well-thought-out and all-encompassing guidance document. In this paper, we discuss some critical topical issues of adaptive designs with supporting methodological work from either existing literature, additional technical notes, or accompanying papers. In particular, we provide numerous sources of design, conduct, analysis, and interpretation bias that arise from statistical procedures. We illustrate, as a result, and caution that substantial research is necessary for many adaptive designs to meet required scientific standards prior to their applications in clinical trials.

An introduction to adaptive designs and adaptation in CNS trials

Adaptive designs learn from accumulating trial data in real time and apply this knowledge to optimize subsequent study execution. A set of design rules define a priori which modifications may be incorporated into the trial design. Judicious use of adaptive designs may increase the information value per resource unit invested by avoiding allocation of patients to non-efficacious/unsafe therapies and allowing stopping decisions to be made at the earliest possible time point. Ultimately this may accelerate the development of promising therapies.

Do all patients with hematologic malignancies and severe thrombocytopenia need prophylactic platelet transfusions? Background, rationale, and design of a clinical trial (trial of platelet prophylaxis) to assess the effectiveness of prophylactic platelet transfusions

Although considerable advances have been made in many aspects of platelet transfusion therapy in the last 30 years, some areas continue to provoke debate, including the use of prophylactic platelet transfusions for the prevention of thrombocytopenic bleeding in patients with bone marrow failure. We have designed a randomized controlled trial to compare prophylactic platelet use with a threshold of a platelet count of 10 x 10(9)/L with no prophylaxis in adult thrombocytopenic patients with hematologic malignancies. The trial question is whether a no-prophylactic policy for the use of platelet transfusions in patients with hematologic malignancies is not inferior to a threshold prophylactic policy at 10 x 10(9)/L, for bleeding at World Health Organization (WHO) grade 2, 3, or 4, up to 30 days from randomization. The primary outcome measure is the proportion of patients who have a significant clinical bleed, defined as WHO grade 2 or higher up to 30 days from randomization. Subsidiary clinical outcome measures include time to first bleed and a descriptive analysis of all severe bleeds. A bleeding assessment form is completed daily for all study subjects until day 30 from randomization. Minor modifications were made to the definitions at WHO grades 1 and 2 for petechiae and duration of nose bleeds, after piloting of the bleeding assessment forms. This study has been designed as a 2-stage randomized trial with an interim analysis planned after a minimum of 100 patients had been randomized and had completed their period of observation. Patients have initially been enrolled through 3 United Kingdom hematology centers. The interim analysis has been completed, and the results have confirmed a final sample size of 600 patients. Recruitment is now being extended to other centers in United Kingdom and Australia. Local research nurses are not blinded to treatment allocation, but a number of measures to reduce risk of assessment bias include repeated education around standard operating procedures, common definitions, and duplication of assessments. The expected completion date for the 5-year study is December 2011.

The use of mid-trial reviews for design modifications in small scale clinical studies

Many clinical studies such as those in the areas of toxicology, early phase clinical trials and bioequivalence studies use small samples due to the high cost of experimentation. These studies test hypotheses based on small samples. These small samples result in low power and therefore even if the alternative hypotheses may be true the chance of it being rejected is low. The sample size is determined in an ad-hoc way and no proper scientific approach is used. Sample size calculations for clinical studies are usually conducted to determine the total number of patients needed to satisfy a specified power requirement, and their validity is dependent on pre-trial knowledge of nuisance parameters and distributional and modelling assumptions. Another short coming is that often hypotheses are tested without checking the assumptions required by the test. This paper looks at design reviews in the context of small samples. It examines several design modifications done with a small internal pilot study. In the past similar techniques have been applied to large scale studies but its performance is yet to be established in small scale clinical studies thus the contribution of this paper is in justifying the validity of these techniques for small samples too. The methodology is illustrated on an uncontrolled observational toxicology study. In this paper simulations will be presented showing that the design modifications would not influence the type-I error rate and that these would be successful in preserving the power, and the implementation of the design review procedure will be described.

Sample size re-estimation in a breast cancer trial

BACKGROUND

During the recruitment phase of a randomized breast cancer trial, investigating the time to recurrence, we found a strong suggestion that the failure probabilities used at the design stage were too high. Since most of the methodological research involving sample size re-estimation has focused on normal or binary outcomes, we developed a method which preserves blinding to re-estimate sample size in our time to event trial.

PURPOSE

A mistakenly high estimate of the failure rate at the design stage may reduce the power unacceptably for a clinically important hazard ratio. We describe an ongoing trial and an application of a sample size re-estimation method that combines current trial data with prior trial data or assumes a parametric model to re-estimate failure probabilities in a blinded fashion.

METHODS

Using our current blinded trial data and additional information from prior studies, we re-estimate the failure probabilities to be used in sample size re-calculation. We employ bootstrap re-sampling to quantify uncertainty in the re-estimated sample sizes.

RESULTS

At the time of re-estimation data from 278 patients were available, averaging 1.2 years of follow up. Using either method, we estimated a sample size increase of zero for the hazard ratio because the estimated failure probabilities at the time of re-estimation differed little from what was expected. We show that our method of blinded sample size re-estimation preserves the type I error rate. We show that when the initial guess of the failure probabilities are correct, the median increase in sample size is zero.

LIMITATIONS

Either some prior knowledge of an appropriate survival distribution shape or prior data is needed for re-estimation.

CONCLUSIONS

In trials when the accrual period is lengthy, blinded sample size re-estimation near the end of the planned accrual period should be considered. In our examples, when assumptions about failure probabilities and HRs are correct the methods usually do not increase sample size or otherwise increase it by very little. Clinical Trials 2010; 7: 219. http://ctj.sagepub.com.

Increasing the sample size at interim for a two-sample experiment without Type I error inflation

For the case of a one-sample experiment with known variance σ² =1, it has been shown that at interim analysis the sample size (SS) may be increased by any arbitrary amount provided: (1) The conditional power (CP) at interim is ≥ 50% and (2) there can be no decision to decrease the SS (stop the trial early). In this paper we verify this result for the case of a two-sample experiment with proportional SS in the treatment groups and an arbitrary common variance. Numerous authors have presented the formula for the CP at interim for a two-sample test with equal SS in the treatment groups and an arbitrary common variance, for both the one- and two-sided hypothesis tests. In this paper we derive the corresponding formula for the case of unequal, but proportional SS in the treatment groups for both one-sided superiority and two-sided hypothesis tests. Finally, we present an SAS macro for doing this calculation and provide a worked out hypothetical example. In discussion we note that this type of trial design trades the ability to stop early (for lack of efficacy) for the elimination of the Type I error penalty. The loss of early stopping requires that such a design employs a data monitoring committee, blinding of the sponsor to the interim calculations, and pre-planning of how much and under what conditions to increase the SS and that this all be formally written into an interim analysis plan before the start of the study.

Adaptive designs for randomized trials in public health

In this article, we present a discussion of two general ways in which the traditional randomized trial can be modified or adapted in response to the data being collected. We use the term adaptive design to refer to a trial in which characteristics of the study itself, such as the proportion assigned to active intervention versus control, change during the trial in response to data being collected. The term adaptive sequence of trials refers to a decision-making process that fundamentally informs the conceptualization and conduct of each new trial with the results of previous trials. Our discussion below investigates the utility of these two types of adaptations for public health evaluations. Examples are provided to illustrate how adaptation can be used in practice. From these case studies, we discuss whether such evaluations can or should be analyzed as if they were formal randomized trials, and we discuss practical as well as ethical issues arising in the conduct of these new-generation trials.

Evaluating the adaptive performance of flexible sample size designs with treatment difference in an interval

In clinical trials, the study sample size is often chosen to provide specific power at a single point of a treatment difference. When this treatment difference is not close to the true one, the actual power of the trial can deviate from the specified power. To address this issue, we consider obtaining a flexible sample size design that provides sufficient power and has close to the 'ideal' sample size over possible values of the true treatment difference within an interval. A performance score is proposed to assess the overall performance of these flexible sample size designs. Its application to the determination of the best solution among considered candidate sample size designs is discussed and illustrated through computer simulations.

Seamless Phase II/III combination study through response adaptive randomization

In clinical trials, multiple doses of a new drug are often tested in a Phase II dose finding study. A promising dose then is chosen for further testing and confirmation of its effectiveness in a Phase III study. Although this approach is pragmatically sound, it is known to be inefficient and unreliable because of the time and resource spent on and the very limited information generated from the Phase II study. In this research, a seamless design based on adaptive patient allocation is proposed to combine the traditional Phase II and Phase III steps to achieve the objectives of dose identification and confirmation at the same time within one study. The control of type I error rate is discussed and simulations show that with the proposed method the type I error rate of the study is controlled, and its efficiency and reliability are greatly improved as compared to the traditional approach.

Release of data from an ongoing randomized clinical trial for sample size adjustment or planning

The determination of an appropriate sample size is a key issue in planning and designing randomized clinical trials. In settings with time-to-event or binary outcomes, the required sample size depends on the control-arm event (response) rate. An accurate estimate of this rate is not often available at the planning stage. Therefore, non-comparative control-arm or pooled-arm event rates from an ongoing trial are sometimes released for sample size adjustment or planning purposes. It is shown that such non-comparative data release may still contain information on the relative treatment benefit and may thus adversely affect the ongoing trial. A simple approach to minimizing the effect of the data release is suggested.

Sample size reestimation by Bayesian prediction

We review a Bayesian predictive approach for interim data monitoring and propose its application to interim sample size reestimation for clinical trials. Based on interim data, this approach predicts how the sample size of a clinical trial needs to be adjusted so as to claim a success at the conclusion of the trial with an expected probability. The method is compared with predictive power and conditional power approaches using clinical trial data. Advantages of this approach over the others are discussed.

Robustness of an odds-ratio test in a stratified group sequential trial with a binary outcome measure

Many clinical trials compare two or more treatment groups by using a binary outcome measure. For example, the goal could be to determine whether the frequency of pain episodes is significantly reduced in the treatment group (arm A) as compared to the control group (arm B). However, for ethical or regulatory reasons, group sequential designs are commonly employed. Then, based on a binomial distribution, the stopping boundaries for the interim analyses are constructed for assessing the difference in the response probabilities between the two groups. This is easily accomplished by using any of the standard procedures, e.g., those discussed by Jennison and Turnbull (2000), and using one of the most commonly used software packages, East (2000). Several factors are known to often affect the primary outcome of interest, but their true distributions are not known in advance. In addition, these factors may cause heterogeneous treatment responses among individuals in a group, and their exact effect size may be unknown. To limit the effect of such factors on the comparison of the two arms, stratified randomization is used in the actual conduct of the trial. Then, a stratified analysis based on the odds ratio proposed in Jennison and Turnbull (2000, pages 251-252) and consistent with the stratified design is undertaken. However, the stopping rules used for the interim analyses are those obtained for determining the differences in response rates in a design that was not stratified. The purpose of this paper is to assess the robustness of such an approach on the performance of the odds ratio test when the underlying distribution and effect size of the factors that influence the outcome may vary. The simulation studies indicate that, in general, the stratified approach offers consistently better results than does the unstratified approach, as long as the difference in the weighted average of the response probabilities across strata between the two groups remains closer to the hypothesized values, irrespective of the differences in the (allocation) distributions and heterogeneous response rate. However, if the response probabilities deviate significantly from the hypothesized values so that the difference in the weighted average is less than the hypothesized value, then the proposed study could be significantly underpowered.

Self-Designing Trial Combined with Classical Group Sequential Monitoring

At the interim analyses of a clinical trial, it is appealing to modify the originally planned sample size in order to achieve an adequate power to detect a meaningful treatment effect. We propose a flexible sequential monitoring scheme through combining the self-designing and classical group sequential methods. The maximum sample size does not have to be specified in advance and one efficacy interim analysis is conducted for the purpose of possible early termination after the first block of data is observed. At the interim analysis for efficacy, the usual sufficient test statistic is used and the type I error rate is adjusted to maintain the overall nominal level. At the final analysis, the test is constructed from a weighted average of the blockwise test statistics based on the sequentially collected data. The weight function at each stage is determined by the observed data prior to that stage. The futility stopping rule allows the trial to be terminated when there is no beneficial treatment effect. We conduct simulation studies to evaluate the performance of the proposed design.

Assessment of the Gould-Shih procedure for sample size re-estimation

The power of a clinical trial is partly dependent upon its sample size. With continuous data, the sample size needed to attain a desired power is a function of the within-group standard deviation. An estimate of this standard deviation can be obtained during the trial itself based upon interim data; the estimate is then used to re-estimate the sample size. Gould and Shih proposed a method, based on the EM algorithm, which they claim produces a maximum likelihood estimate of the within-group standard deviation while preserving the blind, and that the estimate is quite satisfactory. However, others have claimed that the method can produce non-unique and/or severe underestimates of the true within-group standard deviation. Here the method is thoroughly examined to resolve the conflicting claims and, via simulation, to assess its validity and the properties of its estimates. The results show that the apparent non-uniqueness of the method's estimate is due to an apparently innocuous alteration that Gould and Shih made to the EM algorithm. When this alteration is removed, the method is valid in that it produces the maximum likelihood estimate of the within-group standard deviation (and also of the within-group means). However, the estimate is negatively biased and has a large standard deviation. The simulations show that with a standardized difference of 1 or less, which is typical in most clinical trials, the standard deviation from the combined samples ignoring the groups is a better estimator, despite its obvious positive bias.

Are Flexible Designs Sound?

Flexible designs allow large modifications of a design during an experiment. In particular, the sample size can be modified in response to interim data or external information. A standard flexible methodology combines such design modifications with a weighted test, which guarantees the type I error level. However, this inference violates basic inference principles. In an example with independent N(mu, 1) observations, the test rejects the null hypothesis of mu < or = 0 while the average of the observations is negative. We conclude that flexible design in its most general form with the corresponding weighted test is not valid. Several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests.

A general formulation for a one-sided group sequential design

BACKGROUND

A major contribution to the statistical literature on group sequential designs was provided by Pampallona and Tsiatis who developed closed form functions that can be used to iteratively calculate the boundary points of a family of popular group sequential designs. A related area of interest is the use of conditional probability calculations to make interim decisions in stochastic curtailment procedures.

PURPOSE

The purpose of the paper is to develop group sequential designs based on conditional probabilities, to compare our results to the general closed form family of designs developed by Pampallona and Tsiatis, and to relate these to commonly used stochastic curtailment procedures.

METHODS

The problem and its solution are formulated and derived mathematically. A graphical interpretation of the results provides the reader with an alternative mechanism to understand the results and their significance.

RESULTS

One-sided group sequential design boundary points, as closed form functions, are derived from conditional probability statements. These conditional probability statements can be interpreted as the probability, at the final analysis, of reversing the conclusion reached at an interim state. Under mild constraints, these boundary points are identical to the Pampallona and Tsiatis boundary points. At any interim stage when a boundary point is attained or surpassed we suggest a graphical approach to examine the conditional probability of reversing the interim decision at the final stage versus a range of possible parameter values. For stochastic curtailment procedures, we recommend relaxing (increasing) the conditional probability levels to at least 0.50 so that early stopping is at least as likely as for the O'Brien-Fleming procedure.

LIMITATIONS

The results are limited to one-sided group sequential designs.

CONCLUSIONS

Conditional probabilities of reversing interim decisions provides a useful concept to develop group sequential designs and to evaluate stochastic curtailment procedures.

Adaptive designs for pivotal trials: discussion points from the PSI Adaptive Design Expert Group

The Committee for Medicinal Products for Human Use (CHMP) is currently preparing a guideline on 'methodological issues in confirmatory clinical trials with flexible design and analysis plan'. PSI (Statisticians in the Pharmaceutical Industry) sponsored a meeting of pharmaceutical statisticians with an interest in the area to share experiences and identify potential opportunities for adaptive designs in late-phase clinical drug development. This article outlines the issues raised, resulting discussions and consensus views reached. Adaptive designs have potential utility in late-phase clinical development. Sample size re-estimation seems to be valuable and widely accepted, but should be made independent of the observed treatment effect where possible. Where unblinding is necessary, careful consideration needs to be given to preserving the integrity of the trial. An area where adaptive designs can be particularly beneficial is to allow dose selection in pivotal trials via adding/dropping treatment arms; for example, combining phase II and III of the drug development program. The more adaptations made during a late-phase clinical trial, the less likely that the clinical trial would be considered as a confirmatory trial. In all cases it would be advisable to consult with regulatory agencies at the protocol design stage. All involved should remain open to scientifically valid opportunities to improve drug development.

Operating characteristics of sample size re-estimation with futility stopping based on conditional power

Various methods have been described for re-estimating the final sample size in a clinical trial based on an interim assessment of the treatment effect. Many re-weight the observations after re-sizing so as to control the pursuant inflation in the type I error probability alpha. Lan and Trost (Estimation of parameters and sample size re-estimation. Proceedings of the American Statistical Association Biopharmaceutical Section 1997; 48-51) proposed a simple procedure based on conditional power calculated under the current trend in the data (CPT). The study is terminated for futility if CPT < or = CL, continued unchanged if CPT > or = CU, or re-sized by a factor m to yield CPT = CU if CL < CPT < CU, where CL and CU are pre-specified probability levels. The overall level alpha can be preserved since the reduction due to stopping for futility can balance the inflation due to sample size re-estimation, thus permitting any form of final analysis with no re-weighting. Herein the statistical properties of this approach are described including an evaluation of the probabilities of stopping for futility or re-sizing, the distribution of the re-sizing factor m, and the unconditional type I and II error probabilities alpha and beta. Since futility stopping does not allow a type I error but commits a type II error, then as the probability of stopping for futility increases, alpha decreases and beta increases. An iterative procedure is described for choice of the critical test value and the futility stopping boundary so as to ensure that specified alpha and beta are obtained. However, inflation in beta is controlled by reducing the probability of futility stopping, that in turn dramatically increases the possible re-sizing factor m. The procedure is also generalized to limit the maximum sample size inflation factor, such as at m max = 4. However, doing so then allows for a non-trivial fraction of studies to be re-sized at this level that still have low conditional power. These properties also apply to other methods for sample size re-estimation with a provision for stopping for futility. Sample size re-estimation procedures should be used with caution and the impact on the overall type II error probability should be assessed.

Methodological issues with adaptation of clinical trial design

Adaptation of clinical trial design generates many issues that have not been resolved for practical applications, though statistical methodology has advanced greatly. This paper focuses on some methodological issues. In one type of adaptation such as sample size re-estimation, only the postulated value of a parameter for planning the trial size may be altered. In another type, the originally intended hypothesis for testing may be modified using the internal data accumulated at an interim time of the trial, such as changing the primary endpoint and dropping a treatment arm. For sample size re-estimation, we make a contrast between an adaptive test weighting the two-stage test statistics with the statistical information given by the original design and the original sample mean test with a properly corrected critical value. We point out the difficulty in planning a confirmatory trial based on the crude information generated by exploratory trials. In regards to selecting a primary endpoint, we argue that the selection process that allows switching from one endpoint to the other with the internal data of the trial is not very likely to gain a power advantage over the simple process of selecting one from the two endpoints by testing them with an equal split of alpha (Bonferroni adjustment). For dropping a treatment arm, distributing the remaining sample size of the discontinued arm to other treatment arms can substantially improve the statistical power of identifying a superior treatment arm in the design. A common difficult methodological issue is that of how to select an adaptation rule in the trial planning stage. Pre-specification of the adaptation rule is important for the practicality consideration. Changing the originally intended hypothesis for testing with the internal data generates great concerns to clinical trial researchers.