Simultaneous inference procedures for the comparison of multiple characteristics of two survival functions.

Survival time is the primary endpoint of many randomized controlled trials, and a treatment effect is typically quantified by the hazard ratio under the assumption of proportional hazards. Awareness is increasing that in many settings this assumption is a priori violated, for example, due to delayed onset of drug effect. In these cases, interpretation of the hazard ratio estimate is ambiguous and statistical inference for alternative parameters to quantify a treatment effect is warranted. We consider differences or ratios of milestone survival probabilities or quantiles, differences in restricted mean survival times, and an average hazard ratio to be of interest. Typically, more than one such parameter needs to be reported to assess possible treatment benefits, and in confirmatory trials, the according inferential procedures need to be adjusted for multiplicity. A simple Bonferroni adjustment may be too conservative because the different parameters of interest typically show considerable correlation. Hence simultaneous inference procedures that take into account the correlation are warranted. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we provide an estimate for their covariance matrix. We propose according to the parametric multiple testing procedures and simultaneous confidence intervals. Also, the logrank test may be included in the framework. Finite sample type I error rate and power are studied by simulation. The methods are illustrated with an example from oncology. A software implementation is provided in the R package nph.

Red blood cell transfusion-related dynamics of extracellular vesicles in intensive care patients: a prospective subanalysis.

Extracellular vesicles (EVs) accumulate during packed red blood cell (PRBC) storage. To date, the involvement of EVs in transfusion-related immunomodulation (TRIM) has not been prospectively evaluated in intensive care unit (ICU) patients. This was a prospective subanalysis of a recent observational feasibility study in postoperative ICU patients after: (1) open aortic surgery (Aorta), (2) bilateral lung transplantation (LuTx), and (3) other types of surgery (Comparison). Patient plasma was collected three times each before and after leukoreduced PRBC transfusion at 30-min intervals. The total number of EVs and EVs derived from erythrocytes (EryEVs), total platelets (total PEVs), activated platelets, granulocytes (GEVs), monocytes, and myeloid cells in PRBC samples and patient plasma were analyzed by flow cytometry. Statistical analysis was performed by Spearman's correlation test, linear mixed models and pairwise comparisons by Wilcoxon matched-pairs test. Twenty-three patients (Aorta n = 5, LuTx n = 9, Comparison n = 9) were included in the final analysis. All EV subgroups analyzed were detectable in all PRBCs samples (n = 23), but concentrations did not correlate with storage time. Moreover, all EVs analyzed were detectable in all plasma samples (n = 138), and EV counts were consistent before transfusion. Concentrations of total EVs, EryEVs, total PEVs, and GEVs increased after transfusion compared with baseline in the entire cohort but not in specific study groups. Furthermore, the change in plasma EV counts (total EVs and EryEVs) after transfusion correlated with PRBC storage time in the entire cohort. Extracellular vesicles were detectable in all PRBC and plasma samples. Individual EV subtypes increased after transfusion in the entire cohort, and in part correlated with storage duration. Future clinical studies to investigate the role of EVs in TRIM are warranted and should anticipate a larger sample size.Trial registration: Clinicaltrials.gov: NCT03782623.

Comparing maximum diameter and volume when assessing the growth of small abdominal aortic aneurysms using longitudinal CTA data: cohort study.

BACKGROUND: Monitoring of abdominal aortic aneurysms (AAAs) is currently based on serial measurements of maximum aortic diameter. Additional assessment of aneurysm volume has previously been proposed to possibly improve growth prediction and treatment decisions. To evaluate the use of supplementing volume measurements, the authors aimed to characterise the growth distribution of AAA volume and to compare the growth rates of the maximum diameter and volume at the patient level. METHODS: Maximum diameter and volume were monitored every 6 months in 84 patients with small AAAs, with a total of 331 computed tomographic angiographies (with initial maximum diameters of 30-68 mm). A previously developed statistical growth model for AAAs was applied to assess the growth distribution of volume and to compare individual growth rates for volume and for maximum diameter. RESULTS: The median (25-75% quantile) expansion in volume was 13.4 (6.5-24.7) % per year. Cube root transformed volume and maximum diameter showed a closely linear association with a within-subject correlation of 0.77. At the surgery threshold maximum diameter of 55 mm, the median (25-75% quantile) volume was 132 (103-167) ml. In 39% of subjects, growth rates for volume and maximum diameter were equivalent, in 33% growth was faster in volume and in 27% growth was faster in maximum diameter. CONCLUSION: At the population level, volume and maximum diameter show a substantial association such that the average volume is approximately proportional to the average maximum diameter raised to a power of three. At the individual level, however, in the majority of patient's AAAs grow at different pace in different dimensions. Hence, closer monitoring of aneurysms with sub-critical diameter but suspicious morphology may benefit from complementing maximum diameter by volume or related measurements.

Red blood cell transfusion-related eicosanoid profiles in intensive care patients-A prospective, observational feasibility study.

Introduction: Eicosanoids are bioactive lipids present in packed red blood cells (PRBCs), and might play a role in transfusion-related immunomodulation (TRIM). We tested the feasibility of analyzing eicosanoid profiles in PRBC supernatant and in plasma samples of postoperative intensive care unit (ICU) patients transfused with one unit of PRBCs. Methods: We conducted a prospective, observational feasibility study enrolling postoperative ICU patients: 1) patients treated with acetylsalicylic acid following abdominal aortic surgery (Aorta); 2) patients on immunosuppressants after bilateral lung transplantation (LuTx); and 3) patients undergoing other types of major surgery (Comparison). Abundances of arachidonic acid (AA) and seven pre-defined eicosanoids were assessed by liquid chromatography and tandem mass spectrometry. PRBC supernatant was sampled directly from the unit immediately prior to transfusion. Spearman's correlations between eicosanoid abundance in PRBCs and storage duration were assessed. Patient plasma was collected at 30-min intervals: Three times each before and after transfusion. To investigate temporal changes in eicosanoid abundances, we fitted linear mixed models. Results: Of 128 patients screened, 21 were included in the final analysis (Aorta n = 4, LuTx n = 8, Comparison n = 9). In total, 21 PRBC and 125 plasma samples were analyzed. Except for 20-hydroxyeicosatetraenoic acid (HETE), all analyzed eicosanoids were detectable in PRBCs, and their abundance positively correlated with storage duration of PRBCs. While 5-HETE, 12-HETE/8-HETE, 15-HETE, 20-HETE, and AA were detectable in virtually all plasma samples, 9-HETE and 11-HETE were detectable in only 57% and 23% of plasma samples, respectively. Conclusions: Recruitment of ICU patients into this transfusion study was challenging but feasible. Eicosanoid abundances increased in PRBC supernatants during storage. In plasma of ICU patients, eicosanoid abundances were ubiquitously detectable and showed limited fluctuations over time prior to transfusion. Taken together, larger clinical studies seem warranted and feasible to further investigate the role of PRBC-derived eicosanoids in TRIM.

Association of immediate versus delayed extubation of patients admitted to intensive care units postoperatively and outcomes: A retrospective study.

AIM OF THIS STUDY: This study seeks to investigate, whether extubation of tracheally intubated patients admitted to intensive care units (ICU) postoperatively either immediately at the day of admission (day 1) or delayed at the first postoperative day (day 2) is associated with differences in outcomes. MATERIALS AND METHODS: We performed a retrospective analysis of data from an Austrian ICU registry. Adult patients admitted between January 1st, 2012 and December 31st, 2019 following elective and emergency surgery, who were intubated at the day 1 and were extubated at day 1 or day 2, were included. We performed logistic regression analyses for in-hospital mortality and over-sedation or agitation following extubation. RESULTS: 52 982 patients constituted the main study population. 1 231 (3.3%) patients extubated at day 1 and 958 (5.9%) at day 2 died in hospital, 464 (1.3%) patients extubated at day 1 and 613 (3.8%) at day 2 demonstrated agitation or over-sedation after extubation during ICU stay; OR (95% CI) for in-hospital mortality were OR 1.17 (1.01-1.35, p = 0.031) and OR 2.15 (1.75-2.65, p<0.001) for agitation or over-sedation. CONCLUSIONS: We conclude that immediate extubation as soon as deemed feasible by clinicians is associated with favourable outcomes and may thus be considered preferable in tracheally intubated patients admitted to ICU postoperatively.

Estimands and Complex Innovative Designs.

Since the release of the ICH E9(R1) (International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use Addendum on Estimands and Sensitivity Analysis in Clinical Trials to the Guideline on Statistical Principles for Clinical Trials) document in 2019, the estimand framework has become a fundamental part of clinical trial protocols. In parallel, complex innovative designs have gained increased popularity in drug development, in particular in early development phases or in difficult experimental situations. While the estimand framework is relevant to any study in which a treatment effect is estimated, experience is lacking as regards its application to these designs. In a basket trial for example, should a different estimand be specified for each subpopulation of interest, defined, for example, by cancer site? Or can a single estimand focusing on the general population (defined, for example, by the positivity to a certain biomarker) be used? In the case of platform trials, should a different estimand be proposed for each drug investigated? In this work we discuss possible ways of implementing the estimand framework for different types of complex innovative designs. We consider trials that allow adding or selecting experimental treatment arms, modifying the control arm or the standard of care, and selecting or pooling populations. We also address the potentially data-driven, adaptive selection of estimands in an ongoing trial and disentangle certain statistical issues that pertain to estimation rather than to estimands, such as the borrowing of nonconcurrent information. We hope this discussion will facilitate the implementation of the estimand framework and its description in the study protocol when the objectives of the trial require complex innovative designs.

Growth prediction model for abdominal aortic aneurysms.

BACKGROUND: The most relevant determinant in scheduling monitoring intervals for abdominal aortic aneurysms (AAAs) is maximum diameter. The aim of the study was to develop a statistical model that takes into account specific characteristics of AAA growth distributions such as between-patient variability as well as within-patient variability across time, and allows probabilistic statements to be made regarding expected AAA growth. METHODS: CT angiography (CTA) data from patients monitored at 6-month intervals with maximum AAA diameters at baseline between 30 and 66 mm were used to develop the model. By extending the model of geometric Brownian motion with a log-normal random effect, a stochastic growth model was developed. An additional set of ultrasound-based growth data was used for external validation. RESULTS: The study data included 363 CTAs from 87 patients, and the external validation set comprised 390 patients. Internal and external cross-validation showed that the stochastic growth model allowed accurate description of the distribution of aneurysm growth. Median relative growth within 1 year was 4.1 (5-95 per cent quantile 0.5-13.3) per cent. Model calculations further resulted in relative 1-year growth of 7.0 (1.0-16.4) per cent for patients with previously observed rapid 1-year growth of 10 per cent, and 2.6 (0.3-8.3) per cent for those with previously observed slow growth of 1 per cent. The probability of exceeding a threshold of 55 mm was calculated to be 1.78 per cent at most when adhering to the current RESCAN guidelines for rescreening intervals. An online calculator based on the fitted model was made available. CONCLUSION: The stochastic growth model was found to provide a reliable tool for predicting AAA growth.

Robust group sequential designs for trials with survival endpoints and delayed response.

Randomized clinical trials in oncology typically utilize time-to-event endpoints such as progression-free survival or overall survival as their primary efficacy endpoints, and the most commonly used statistical test to analyze these endpoints is the log-rank test. The power of the log-rank test depends on the behavior of the hazard ratio of the treatment arm to the control arm. Under the assumption of proportional hazards, the log-rank test is asymptotically fully efficient. However, this proportionality assumption does not hold true if there is a delayed treatment effect. Cancer immunology has evolved over time and several cancer vaccines are available in the market for treating existing cancers. This includes sipuleucel-T for metastatic hormone-refractory prostate cancer, nivolumab for metastatic melanoma, and pembrolizumab for advanced nonsmall-cell lung cancer. As cancer vaccines require some time to elicit an immune response, a delayed treatment effect is observed, resulting in a violation of the proportional hazards assumption. Thus, the traditional log-rank test may not be optimal for testing immuno-oncology drugs in randomized clinical trials. Moreover, the new immuno-oncology compounds have been shown to be very effective in prolonging overall survival. Therefore, it is desirable to implement a group sequential design with the possibility of early stopping for overwhelming efficacy. In this paper, we investigate the max-combo test, which utilizes the maximum of two weighted log-rank statistics, as a robust alternative to the log-rank test. The new test is implemented for two-stage designs with possible early stopping at the interim analysis time point. Two classes of weights are investigated for the max-combo test: the Fleming and Harrington (1981) Gρ,γ$G^{\rho , \gamma }$ weights and the Magirr and Burman (2019) modest (τ∗)$ (\tau ^{*})$  weights.

Association of Acute Kidney Injury Receiving Kidney Replacement Therapy With Prognosis of Critically Ill Patients With and Without Cancer: A Retrospective Study.

OBJECTIVES: To assess outcomes of cancer patients receiving kidney replacement therapy due to acute kidney injury in ICUs and compare these with other patient groups receiving kidney replacement therapy in ICUs. DESIGN: Retrospective registry analysis. SETTING: Prospectively collected database of 296,424 ICU patients. PATIENTS: Patients with and without solid cancer with acute kidney injury necessitating kidney replacement therapy were identified and compared with those without acute kidney injury necessitating kidney replacement therapy. INTERVENTIONS: Descriptive statistics were used to ascertain prevalence of acute kidney injury necessitating kidney replacement therapy and solid cancer in ICU patients. Association of acute kidney injury necessitating kidney replacement therapy and cancer with prognosis was assessed using logistic regression analysis. To compare the attributable mortality of acute kidney injury necessitating kidney replacement therapy, 20,154 noncancer patients and 2,411 cancer patients without acute kidney injury necessitating kidney replacement therapy were matched with 12,827 noncancer patients and 1,079 cancer patients with acute kidney injury necessitating kidney replacement therapy. MEASUREMENTS AND MAIN RESULTS: Thirty-five thousand three hundred fifty-six ICU patients (11.9%) had solid cancer. Acute kidney injury necessitating kidney replacement therapy was present in 1,408 (4.0%) cancer patients and 13,637 (5.2%) noncancer patients. Crude ICU and hospital mortality was higher in the cancer group (646 [45.9%] vs 4,674 [34.3%], p < 0.001, and 787 [55.9%] vs 5,935 [43.5%], p < 0.001). In multivariable logistic regression analyses, odds ratio (95% CI) for hospital mortality was 1.73 (1.62-1.85) for cancer compared with no cancer 3.57 (3.32-3.83) for acute kidney injury necessitating kidney replacement therapy and 1.07 (0.86-1.33) for their interaction. In the matched subcohort, attributable hospital mortality of acute kidney injury necessitating kidney replacement therapy was 56.7% in noncancer patients and 48.0% in cancer patients. CONCLUSIONS: Occurrence rate of acute kidney injury necessitating kidney replacement therapy and prognosis in ICU patients with solid cancer are comparable with other ICU patient groups. In cancer, acute kidney injury necessitating kidney replacement therapy is associated with higher crude hospital mortality. However, the specific attributable mortality conveyed by acute kidney injury necessitating kidney replacement therapy is actually lower in cancer patients than in noncancer patients. Diagnosis of cancer per se does not justify withholding kidney replacement therapy.

Factors associated with physician decision making on withholding cardiopulmonary resuscitation in prehospital medicine.

This study seeks to identify factors that are associated with decisions of prehospital physicians to start (continue, if ongoing) or withhold (terminate, if ongoing) CPR in patients with OHCA. We conducted a retrospective study using anonymised data from a prehospital physician response system. Data on patients attended for cardiac arrest between January 1st, 2010 and December 31st, 2018 except babies at birth were included. Logistic regression analysis with start of CPR by physicians as the dependent variable and possible associated factors as independent variables adjusted for anonymised physician identifiers was conducted. 1525 patient data sets were analysed. Obvious signs of death were present in 278 cases; in the remaining 1247, resuscitation was attempted in 920 (74%) and were withheld in 327 (26%). Factors significantly associated with higher likelihood of CPR by physicians (OR 95% CI) were resuscitation efforts by EMS before physician arrival (60.45, 19.89-184.29), first monitored heart rhythm (3.07, 1.21-7.79 for PEA; 29.25, 1.93-442. 51 for VF / pVT compared to asystole); advanced patient age (modelled using cubic splines), physician response time (0.92, 0.87-0.97 per minute) and malignancy (0.22, 0.05-0.92) were significantly associated with lower odds of CPR. We thus conclude that prehospital physicians make decisions to start or withhold resuscitation routinely and base those mostly on situational information and immediately available patient information known to impact outcomes.

Delayed treatment effects, treatment switching and heterogeneous patient populations: How to design and analyze RCTs in oncology.

In the analysis of survival times, the logrank test and the Cox model have been established as key tools, which do not require specific distributional assumptions. Under the assumption of proportional hazards, they are efficient and their results can be interpreted unambiguously. However, delayed treatment effects, disease progression, treatment switchers or the presence of subgroups with differential treatment effects may challenge the assumption of proportional hazards. In practice, weighted logrank tests emphasizing either early, intermediate or late event times via an appropriate weighting function may be used to accommodate for an expected pattern of non-proportionality. We model these sources of non-proportional hazards via a mixture of survival functions with piecewise constant hazard. The model is then applied to study the power of unweighted and weighted log-rank tests, as well as maximum tests allowing different time dependent weights. Simulation results suggest a robust performance of maximum tests across different scenarios, with little loss in power compared to the most powerful among the considered weighting schemes and huge power gain compared to unfavorable weights. The actual sources of non-proportional hazards are not obvious from resulting populationwise survival functions, highlighting the importance of detailed simulations in the planning phase of a trial when assuming non-proportional hazards.We provide the required tools in a software package, allowing to model data generating processes under complex non-proportional hazard scenarios, to simulate data from these models and to perform the weighted logrank tests.

The Evolution of Master Protocol Clinical Trial Designs: A Systematic Literature Review.

PURPOSE: Recent years have seen a change in the way that clinical trials are being conducted. There has been a rise of designs more flexible than traditional adaptive and group sequential trials which allow the investigation of multiple substudies with possibly different objectives, interventions, and subgroups conducted within an overall trial structure, summarized by the term master protocol. This review aims to identify existing master protocol studies and summarize their characteristics. The review also identifies articles relevant to the design of master protocol trials, such as proposed trial designs and related methods. METHODS: We conducted a comprehensive systematic search to review current literature on master protocol trials from a design and analysis perspective, focusing on platform trials and considering basket and umbrella trials. Articles were included regardless of statistical complexity and classified as reviews related to planned or conducted trials, trial designs, or statistical methods. The results of the literature search are reported, and some features of the identified articles are summarized. FINDINGS: Most of the trials using master protocols were designed as single-arm (n = 29/50), Phase II trials (n = 32/50) in oncology (n = 42/50) using a binary endpoint (n = 26/50) and frequentist decision rules (n = 37/50). We observed an exponential increase in publications in this domain during the last few years in both planned and conducted trials, as well as relevant methods, which we assume has not yet reached its peak. Although many operational and statistical challenges associated with such trials remain, the general consensus seems to be that master protocols provide potentially enormous advantages in efficiency and flexibility of clinical drug development. IMPLICATIONS: Master protocol trials and especially platform trials have the potential to revolutionize clinical drug development if the methodologic and operational challenges can be overcome.

A critical review of graphics for subgroup analyses in clinical trials.

Subgroup analyses are a routine part of clinical trials to investigate whether treatment effects are homogeneous across the study population. Graphical approaches play a key role in subgroup analyses to visualise effect sizes of subgroups, to aid the identification of groups that respond differentially, and to communicate the results to a wider audience. Many existing approaches do not capture the core information and are prone to lead to a misinterpretation of the subgroup effects. In this work, we critically appraise existing visualisation techniques, propose useful extensions to increase their utility and attempt to develop an effective visualisation approach. We focus on forest plots, UpSet plots, Galbraith plots, subpopulation treatment effect pattern plot, and contour plots, and comment on other approaches whose utility is more limited. We illustrate the methods using data from a prostate cancer study.

Subgroup identification in clinical trials via the predicted individual treatment effect.

Identifying subgroups of treatment responders through the different phases of clinical trials has the potential to increase success in drug development. Recent developments in subgroup analysis consider subgroups that are defined in terms of the predicted individual treatment effect, i.e. the difference between the predicted outcome under treatment and the predicted outcome under control for each individual, which in turn may depend on multiple biomarkers. In this work, we study the properties of different modelling strategies to estimate the predicted individual treatment effect. We explore linear models and compare different estimation methods, such as maximum likelihood and the Lasso with and without randomized response. For the latter, we implement confidence intervals based on the selective inference framework to account for the model selection stage. We illustrate the methods in a dataset of a treatment for Alzheimer disease (normal response) and in a dataset of a treatment for prostate cancer (survival outcome). We also evaluate via simulations the performance of using the predicted individual treatment effect to identify subgroups where a novel treatment leads to better outcomes compared to a control treatment.

Flexible alpha allocation strategies for confirmatory adaptive enrichment clinical trials with a prespecified subgroup.

Adaptive enrichment designs have recently received considerable attention as they have the potential to make drug development process for personalized medicine more efficient. Several statistical approaches have been proposed so far in the literature and the operating characteristics of these approaches are extensively investigated using simulation studies. In this paper, we improve on existing adaptive enrichment designs by assigning unequal weights to the significance levels associated with the hypotheses of the overall population and a prespecified subgroup. More specifically, we focus on the standard combination test, a modified combination test, the marginal combination test, and the partial conditional error rate approach and explore the operating characteristics of these approaches by a simulation study. We show that these approaches can lead to power gains, compared to existing approaches, if the weights are chosen carefully.

Approaches to sample size calculation for clinical trials in rare diseases.

We discuss 3 alternative approaches to sample size calculation: traditional sample size calculation based on power to show a statistically significant effect, sample size calculation based on assurance, and sample size based on a decision-theoretic approach. These approaches are compared head-to-head for clinical trial situations in rare diseases. Specifically, we consider 3 case studies of rare diseases (Lyell disease, adult-onset Still disease, and cystic fibrosis) with the aim to plan the sample size for an upcoming clinical trial. We outline in detail the reasonable choice of parameters for these approaches for each of the 3 case studies and calculate sample sizes. We stress that the influence of the input parameters needs to be investigated in all approaches and recommend investigating different sample size approaches before deciding finally on the trial size. Highly influencing for the sample size are choice of treatment effect parameter in all approaches and the parameter for the additional cost of the new treatment in the decision-theoretic approach. These should therefore be discussed extensively.

A Randomized Trial of Bortezomib in Late Antibody-Mediated Kidney Transplant Rejection.

Late antibody-mediated rejection (ABMR) is a leading cause of kidney allograft failure. Uncontrolled studies have suggested efficacy of the proteasome inhibitor bortezomib, but no systematic trial has been undertaken to support its use in ABMR. In this randomized, placebo-controlled trial (the Bortezomib in Late Antibody-Mediated Kidney Transplant Rejection [BORTEJECT] Trial), we investigated whether two cycles of bortezomib (each cycle: 1.3 mg/m2 intravenously on days 1, 4, 8, and 11) prevent GFR decline by halting the progression of late donor-specific antibody (DSA)-positive ABMR. Forty-four DSA-positive kidney transplant recipients with characteristic ABMR morphology (median time after transplant, 5.0 years; pretransplant DSA documented in 19 recipients), who were identified on cross-sectional screening of 741 patients, were randomly assigned to receive bortezomib (n=21) or placebo (n=23). The 0.5-ml/min per 1.73 m2 per year (95% confidence interval, -4.8 to 5.8) difference detected between bortezomib and placebo in eGFR slope (primary end point) was not significant (P=0.86). We detected no significant differences between bortezomib- and placebo-treated groups in median measured GFR at 24 months (33 versus 42 ml/min per 1.73 m2; P=0.31), 2-year graft survival (81% versus 96%; P=0.12), urinary protein concentration, DSA levels, or morphologic or molecular rejection phenotypes in 24-month follow-up biopsy specimens. Bortezomib, however, associated with gastrointestinal and hematologic toxicity. In conclusion, our trial failed to show that bortezomib prevents GFR loss, improves histologic or molecular disease features, or reduces DSA, despite significant toxicity. Our results reinforce the need for systematic trials to dissect the efficiency and safety of new treatments for late ABMR.

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.