Sciences grant P30-ESO9106. Address reprint requests to

Phase II Clinical Trial Design for Noncytotoxic Anticancer Agentsfor which Time to Disease Progression is the Primary EndpointRunning title: Phase II Trial Design for Time to Progression Rosemarie Mick, M.S., John J. Crowley, Ph.D. and Raymond J. Carroll, Ph.D.Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, Philadelphia (R.M.), Program in Biostatistics, Fred Hutchinson Cancer Research Center, Seattle (J.J.C.) and Department of Statistics, Texas A&M University, College Station (R.J.C.)Dr. Carroll’s research was supported by National Cancer Institute grant CA-57030 and by the Texas A&M Center for Environmental and Rural Health via National Institute of Environmental Health Sciences grant P30-ESO9106.Address reprint requests to:Rosemarie Mick, M.S.University of PennsylvaniaDepartment of Biostatistics and Epidemiology609 Blockley HallPhiladelphia, PA 19104email: rmick@ABSTRACTPhase II evaluation is a critical screening step in the development of new cancer treatments. Historically, anticancer agents have been cytotoxic; they kill existing cells. As such, the primary endpoint for phase II evaluation has been tumor response rate, the percentage of patients whose tumors shrink >50%. Biotechnology has led to promising new anticancer agents that are cytostatic. In contrast to cytotoxics, these agents modulate tumor environments and/or cellular targets and are expected to delay tumor growth. Phase II evaluation of such agents may instead focus on failure time endpoints, such as time to disease progression. We examine a phase II trial design that evaluates clinical benefit by comparing sequentially-measured paired failure times within each treated patient. Clinical efficacy is defined by a hazard ratio.Assuming patients eligible for a phase II study of a new cytostatic agent have failed previous cancer treatment, their most recent prior time to progression interval, TTP1, is uncensored. Time to progression after the cytostatic agent, TTP2, may or may not be censored at analysis. The design is motivated by a “growth modulation index” (TTP2/TTP1) and the proposition that a cytostatic agent be considered effective if the index is greater than 1.33. A χ2 test statistic is employed to evaluate the paired failure time data (TTP1, TTP2). The degree of correlation between the paired failure times is a key feature of this design. Power of the test was evaluated through simulation of trials. Assuming a null hazard ratio equal to 1.0, a trial designed to detect an alternative hazard ratio equal to 1.3, based on accrual of 25 patients/year for 2 years (50 patients total) and with an additional 2 years of follow-up, has 25%, 46%, and 83% power based on correlations of 0.3, 0.5 and 0.7, respectively. These results demonstrate efficiency of the trial design, given moderate to strong correlations between paired failure times.KEY WORDS: Phase II trial, cytostatic agent, time to progression, paired failure times.INTRODUCTIONThe primary goals of phase II clinical trials are to estimate efficacy and toxicity of a new anticancer agent or combination of agents [1,2]. Phase II evaluation is a critical screening step in the development of new cancer treatments. Evidence of clinical efficacy demonstrated in a phase II trial often determines whether the new treatment warrants further study.Historically, anticancer agents have been cytotoxic; they work by killing existing cancer cells and/or by interfering with the generation of new cancer cells. Effectiveness is determined by the ability of the cytotoxic agent or combination of agents to shrink or eradicate tumors in patients. The primary endpoint for phase II trials has been tumor response rate, defined as the proportion of treated patients whose tumors shrink by more than 50%. To demonstrate clinical efficacy, a new agent must provide evidence for a meaningful clinical benefit. As such, phase II trials are designed to identify agents that yield a population-specific response rate (e.g., a true response rate >20%), which varies by cancer site, stage of disease and prior treatment history. It follows that a key assumption of any phase II trial is the selection of a reasonable target response rate. Most often, we rely on published studies to determine historical estimates which may be augmented within the phase II trial by randomization of a modest fraction of patients to an accepted standard treatment [3,4].Standard phase II trial designs for response rates exhibit a number of favorable features. In many cases, tumor response can be evaluated reliably after several courses of treatment such that timely evaluation of the trial results can be completed within months after the final patient has been treated. A number of multistage designs now exist that meet both statistical and ethical considerations [5-10]. These designs allow for sequential treatment and evaluation of modestly sized cohorts of patients. Early stopping of the trial is allowed if accumulated evidence for clinical efficacy is lacking. Randomized phase II designs allow for the simultaneous enrollment to and screening of several promising regimens [11]. These trials impose some balance in patient features and, although direct comparisons are not intended, they allow for an initial priority ranking among treatment arms.Recently, biotechnology has led to the discovery of many promising anticancer agents. Antiangiogenesis factors, growth modulators (e.g., farnesyl transferase and signal transduction inhibitors), monoclonal antibodies and adenovirus (gene therapy) vaccines are all poised for phase II evaluation. Interestingly, many of these agents are not cytotoxic but cytostatic. Instead of killing cells, they appear to modulate tumor environments and/or cellular targets. For example, antiangiogenesis factors block the growth of new blood vessels that surround and feed a tumor [12]. Without increased blood supply, a tumor cannot grow. It follows that many biologic agents, such as angiogenesis inhibitors, may not beexpected to shrink tumors, but are more likely to delay tumor progression. This mechanistic difference has become well-appreciated by those developing cytostatic agents [13-16]. Thus, the paradigm for drug development must be altered for noncytotoxic agents. In fact, several companies that develop matrix metalloproteinase inhibitors (MMPIs) have considered skipping phase II evaluation altogether, and proceeding instead directly to phase III trials. These adjuvant studies are designed to test the impact of MMPIs on disease recurrence [17-19].How do we design rational phase II trials that exploit the expected mechanisms of these novel agents? First, we must consider appropriate endpoints for clinical and biologic effects. For many agents, supporting endpoints, such as biomarkers that measure the mechanisms of biologic action, have not been discovered. Because a delay in disease progression is the expected clinical outcome, failure time endpoints are preferable to response rates. Time to progression, defined as the time from initiation of therapy to first documentation of disease progression or worsening of disease-related symptoms, is one such endpoint. Alternatively, progression-free survival may be employed in which death is included as failure. As with any phase II trial, definition of meaningful clinical benefit is a key issue. A population-specific failure-time endpoint (e.g., the median failure time or failure rate at a specific time point) is needed. Historical failure-time estimates are subject to the same sources of variability (e.g., types of patients treated or treatment intensity) and precision (e.g., study size) as historical response rate estimates. And because the precision of failure-time endpoints is also dependent on observed events, the maturity of historical studies must be considered.Trials with time to progression as the primary endpoint pose some challenges not previously encountered with phase II trials of event rates. Beyond the usual challenge of identifying trials of comparable historical controls, the definition and measurement of time to progression must be consistent with current usage. Study results may not be immediate as with standard phase II trials unless short term endpoints, such as 3- or 6-month failure-free rates, are employed. Multistage designs will not be feasible for certain patient populations, because extended follow-up for disease progression may be necessary, precluding early termination.PHASE II TRIAL DESIGNPhase II trial designs for failure-time endpoints that fall within a hypothesis testing framework and minimize accrual to inferior treatments are desirable because of statistical and ethical considerations [20]. The motivation for the proposed design stems from the “growth modulation index,” a method of evaluation suggested by Von Hoff in which each patient serves as his/her own historical control [14]. The growth modulation index is defined as the ratio of a patient’s time to progression on a phase II cytostatictreatment, TTP2, relative to the time to progression observed from the patient’s most recent prior anticancer treatment, TTP1, which serves as the patient-specific historical control value. Most recent time time to progression may be viewed as a clinical surrogate for tumor sensitivity at initiation of cytostatic treatment, an aggregate of patient- and tumor-level factors.Von Hoff suggested that a cytostatic agent be considered effective if the growth modulation index, the ratio TTP2/TTP1, is greater than 1.33, implying a null value of 1.0. Alternatively, one could hypothesize that by the natural history of the disease, one would expect TTP2 to be shorter than TTP1,which implies null values less than 1.0. If a biologic agent demonstrates an impact on this natural history then one may argue that meaningful clinical efficacy has been demonstrated. Thus, a range of index values, posed as null and alternative hypotheses, are discussed in the simulation sections that follow. The natural pairing of these failure times is the basis for the proposed trial design.Extensions of standard analytic methods such as proportional hazards or log-linear models have been explored for paired failure-time data [21]. Such data may arise from a single failure-time endpoint from two matched individuals or from two concurrently-measured endpoints (e.g., survival and progression-free survival) within an individual. In the proposed design, sequentially-measured paired failure times, TTP1 and TTP2, within an individual are the basis for the statistical framework. An important feature of this design is the inherent correlation between the paired observations. The assumed positive correlation stems from the widely-held premise that patients who experience relatively shorter (or longer) progression-free intervals under an initial treatment regimen, would also experience relatively shorter (or longer) intervals under a subsequent treatment regimen. The likelihood of settings supporting negative correlation is low, due to the fact that opposing paired outcomes, such as patients who experience relatively shorter progression-free intervals under an initial treatment regimen and relatively longer intervals under a subsequent treatment regimen, are much less frequent. As one would expect, if the positive correlation is strong, then the trial design may be highly efficient and require fewer patients.A sound statistical design that exploits such correlation and is efficient would satisfy both statistical and ethical considerations.ANALYSIS OF PAIRED FAILURE-TIME DATAA requirement of the design is that patients eligible for the trial of a new cytostatic agent must have failed at least one previous treatment for their cancer, thus TTP1is uncensored. This requirement may be achieved through study eligibility criteria. Time to progression on the cytostatic treatment, TTP2, may or may not be censored at the time of analysis. The statistical framework is defined by paired failure times (TTP1, TTP2), censoring status at TTP2 and null and alternative hypotheses about the effect of the cytostatic agent.Failure times are assumed to follow an exponential distribution which decays at some arbitrary hazard rate. Under the assumption of proportional hazards, a test about the efficacy of a treatment is determined by the value of the hazard ratio (HR). In this setting, a cytostatic agent may be considered effective if, on average, TTP2 > TTP1. Von Hoff’s proposed index suggests a null hazard ratio HR0 equal to 1.0 (no benefit) compared to an alternative hazard ratio HR A equal to 1.33 (meaningful benefit). Alternatively, if one expects increasingly shorter progression-free intervals with successive treatment, then a cytostatic agent may be considered effective if, on average, TTP2= TTP1. This setting suggests HR0 is less than 1.0 compared to HR A equal to 1.0. For example, testing HR0 equal to 0.7 compared to HR A equal to 1.0 translates into an effective hazard ratio of 1.43. It should be emphasized that in this latter setting, a hazard ratio equal to 1.0 would be evidence of clinical efficacy.Hypothesis tests about the hazard ratio from paired data may be conducted under alog-linear model [21]. A test of null HR0equal to 1.0 is equivalent to a test of ln[HR0] equal to 0 (similarly HR0 equal to 0.7 is equivalent to ln[HR0] equal to -0.3567). Under a log-linear model in which β0 denotes the null natural log hazard ratio, the values of natural log-transformed paired failure times are compared. Briefly, failure time pairs in which ln[TTP2] > ln[TTP1] + β0 or in which ln[TTP2] < ln[TTP1] + β0and for which TTP2is uncensored are scored as 1 or -1, respectively. Pairs in which ln[TTP2] < ln[TTP1] + β0 and for which TTP2 is censored, do not contribute to the test. Under β0, the score r s takes on the values –1 or 1, each with probability 0.5. Excluding pairs for which r s cannot be specified does not bias the test. The test statistic is a function of sums of squares of the scores for contributing failure-time pairs and has an approximate χ2distribution. Further details on the hypothesis testing framework for correlated failure times are described in the appendix.SIMULATION METHODSThe basis for the simulation was generation of correlated exponential failure times, assumed to arise in an individual patient. Hypothesis tests about the natural log hazard ratio (β) were then conducted on simulated patient data for trials of various sizes.The first step was to generate correlated exponential failure times to represent the uncensored failure time TTP1 and censored or uncensored failure time, TTP2. The distribution of TTP1 was defined to have a median value, m, equal to 1 year. The distribution of TTP2 was defined to have a median value equal to m[exp(β)], resulting in a hazard ratio equal to exp(β).We generated correlated exponential failure times as follows. Let X0, X1 and X2 be independent standard gamma random variables with shapes θ0, (1 - θ0) and (1 - θ0), respectively. Then, from properties of the gamma distribution, X0 + X1 and X0 + X2 are marginally exponential random variables with mean 1 and their covariance is var(X0) = θ0 and hence, their correlation = θ0 [22]. We defined TTP1 and TTP2 to beTTP1 = (X0 + X1)m and TTP2 = (X0 + X2)m[exp(β)] .ln[2] ln[2]These distributions have medians m and m[exp(β)], respectively, and correlation θ0.The next step of the simulation addressed censoring of TTP2. Two years of patient accrual and 2 additional years of follow-up (total duration 4 years) were assumed, as these were felt to reflect the conduct of most phase II investigations. Uniform censoring of TTP2 was assumed with minimum and maximum follow-up of 2 and 4 years, respectively (~U[2,4]). A patient’s TTP2 observation was generated and if it was greater than or equal to the censoring time, then TTP2 was set equal to the censoring time and the patient was considered censored.Trials with varied sample and effect sizes were simulated so that trends in power could be evaluated. We investigated trial sizes that ranged from 20 to 100 patients in increments of 10 patients. A number of null and alternative hazard ratios were investigated. A null hazard ratio equal to 1.0 was tested (employing log hazard ratio of zero) against alternative hazard ratios that ranged from 1.1 to 2.0 in increments of 0.1, while a null hazard ratio equal to 0.7 (log hazard ratio of -0.3567) was tested against alternative hazard ratios that ranged from 0.8 to 1.7.For each study, a significance test was performed on the paired observations using the method described in the appendix. One thousand trials were simulated for each sample size and effect size combination. Power was defined as the percentage of simulated trials that exhibited a significant result at the 0.05 level (χ2 > 3.84). Based on the normal approximation to the binomial and 1000 trials, the width of the 95% confidence interval for power can be no greater than 3%. All simulations were performed in S-PLUS Version 4.5 (MathSoft, Inc.)Since the magnitude of correlation and its impact on power were of particular interest, correlation between paired failure times was allowed to vary over a wide range (0.1 to 0.9). Weak, moderate and strong correlation among paired failure times, represented by Pearson correlation values of 0.3, 0.5, and 0.7, respectively, were selected for presentation. Three dimensional (X axis = study size, Y axis = alternative hazard ratio and Z axis = power) response surfaces were constructed for each level ofcorrelation. Nonparametric surfaces were fit with bivariate splines without smoothing using SAS (Version 6.12, SAS Institute, Inc) PROC G3GRID and plotted with SAS PROC G3D. Contour plots were then constructed based on the fitted response surfaces by SAS PROC GCONTOUR. Contours, also known as isoboles, of varying combinations of study size and effect size, represent constant values of power (e.g., 80%).SIMULATION RESULTSA total of 1620 unique combinations of study size, effect size and correlation among failure times was studied. Power properties were evaluated by 1000 simulated clinical trials for each combination of factors. Table 1 displays the results for a subset of simulations representing combinations of study and effect size and degree of correlation. Assuming a null hazard ratio equal to 1.0, a trial designed to detect an alternative hazard ratio equal to 1.3 (Von Hoff’s suggested definition of clinical efficacy), based on accrual of 50 patients over 2 years and with an additional 2 years of follow-up, has 25%, 46%, and 83% power based on correlations of 0.3, 0.5 and 0.7, respectively.In Figures 1a to 1f, a null hazard ratio equal to 1.0 was assumed. As noted in Figures 1a to 1c, the response surfaces crest in the upper left background, indicating expected increases in power for increasing effect size and study size. Power increased sharply with increasing correlation between paired failure times. In Figures 1d to 1f, 80%, 85% and 90% power contours are presented. A trial designed to accrue 50 patients over 2 years has 80% power to detect hazard ratios approximately equal to 1.90, 1.60 and 1.30 based on correlations of 0.3, 0.5 and 0.7, respectively.In Figures 2a to 2f, a null hazard ratio equal to 0.70 was assumed. As mentioned previously, a trial designed to detect an alternative hazard ratio equal to 1.0, as evidence of clinical efficacy, translates into an “effective” hazard ratio of 1.43. Figures 2a to 2c, again display increases in power with increasing effect and study size. Power increased with increasing correlation. A trial designed to detect an alternative hazard ratio equal to 1.0 with 50 patients accrued over 2 years has 46%, 69% and 99% power based on correlations of 0.3, 0.5 and 0.7, respectively. Figures 2d to 2f display 80%, 85% and 90% power contours.A trial designed to accrue 50 patients over 2 years has 80% power to detect hazard ratios approximately equal to 1.30, 1.10 and 0.90 based on correlations of 0.3, 0.5 and 0.7, respectively. These results clearly demonstrate the efficiency of the study design, in the presence of moderate to strong correlation.OBSERVED PAIRED FAILURE-TIME DATAIt is obvious that the implementation of the proposed phase II design relies on a reasonable estimate of the correlation between sequentially-measured paired failure times. There are no publishedreports that describe this correlation, although clinicians and biostatisticians have opinions on the range of relevant values. Table 2 displays correlations between sequentially-measured paired failure times obtained from three cancer cooperative group trials [23-25]. These studies are not drawn from a well-defined sampling strategy and therefore may not be representative. The Pearson correlations ranged from 0.19 to 0.56. Heterogeneity of correlations is expected among differing study populations due to variations in disease site and stage, degree of previous treatments and tumor sensitivity to second line treatments. Exclusion of a single outlier pair in CALGB 8751 resulted in Pearson and Spearman values of 0.25 and 0.43, respectively. For each patient, the ratio TTP2/ TTP1was calculated. Interestingly, the median of the distribution for the ratio was less than 1.0 for all three studies. When analyzed by the paired failure time method, none of these studies yielded a significant result in favor of the second failure time, relative to a null hazard ratio of 0.7.DISCUSSIONIt is evident that novel phase II trial designs are needed to evaluate new anticancer treatments that are expected to delay tumor growth but not shrink tumors, like standard cytotoxic agents. Clinicians involved in early development of such agents clearly understand this challenge and are seeking statistically sound solutions. Eckhardt et al. recently report on their completed phase I trial of SU101, an agent that interferes with signal transduction by inhibition of platelet-derived growth factor receptor-mediated cellular processes [26]. In contemplating the upcoming phase II evaluation of SU101, the authors acknowledge that cytostasis is an effect that will not be addressed adequately by standard phase II trials. They suggest that efficacy may best be measured by time to progression, quality of life, symptomatic improvement or overall survival. Eisenhauer has proposed an alternative measure of clinical benefit, the progression rate, defined by the percentage of patients who progress in the first 8 weeks of treatment [27]. Based on her review of the National Cancer Institute of Canada Clinical Trials Group experience, several recently evaluated cytotoxic agents that demonstrated acceptable response rates during phase II evaluation also yielded low rates of on-treatment progression.Currently, phase II trials of failure-time endpoints are designed as single arm comparisons to historical control estimates. These trials have been sized by simple modification of a standard formula for censored failure-time endpoints employed for randomized controlled trials [28]. Employing this method, a single arm study that employs a historical control estimate and is designed to detect a hazard ratio = 1.3 at one-sided significance of 5% with 50 patients accrued over 2 years and with 2 additional years of follow-up would have 53% power. Interestingly, similar power (46%) was obtained by the paired failure-time design assuming moderate correlation of 0.5 and exploiting patient-specific historical data. Some clinicians find it difficult to interpret the relative merit of time to progression estimates from single armtrials, for which there is no active control group. Historically-based designs may also be augmented with concurrent controls, by randomizing a fraction of patients to an accepted standard treatment [29]. Yet, more innovative single and multiarm phase II and III trials are being developed to evaluate these agents, such as those under consideration for the antiangiogenesis (MMPI) agents.For example, patients might be randomized to either a cytotoxic/cytostatic or cytotoxic/placebo combination regimen, after which they would be followed for disease progression and/or survival. A more novel design would allow patients to receive multiple courses of standard chemotherapy until best tumor response is achieved and then be randomized to cytostatic treatment or placebo to evaluate delay in disease relapse or progression. Recently, a randomized continuation trial design has been suggested by Ratain, that initially allows all patients to receive the new agent for a short run-in period of 2 to 4 months [30]. Patients who are compliant, tolerate the agent and have at least stable disease are then randomized to additional courses of treatment or observation. Since the randomized population is comprised of patients who are likely to derive clinical benefit, the magnitude of difference in clinical outcome between the arms is increased, thereby improving study efficiency [31]. This design may be most useful for agents expected to require chronic administration.The trial design proposed here takes an alternative approach in that each patient serves as his/her own historical control by use of a paired failure-time statistical framework. The design appears to be efficient under conditions of moderate to strong correlation between paired failure-times. Increased power would be expected by application of a nonparametric rank test [32-35]. Recently, Bonetti and colleagues applied the growth modulation index to the analysis of their completed phase II trial, originally defined by a standard design [36]. There are several obvious limitations to this design. Firstly, it requires that patients eligible for these investigational studies must have failed a previous cancer treatment, resulting in a patient-specific historical failure-time. This requirement could be imposed through study eligibility criteria, yet the procurement of accurate progression-free interval information from prior treatments may not be feasible, especially for externally-referred patients. Secondly, it is unclear whether equal consideration would be given to patients with longer and shorter first intervals for cytostatic trials. If patients with longer first intervals were systematically favored for studies of cytostatic agents, then such studies may be biased toward the null hypothesis. Thirdly, a useful rule for early termination should be considered, although such a rule may be difficult to implement. An interim analysis would probably be biased towards the null because the interim cohort would most likely be comprised of early failures that exhibit shorter second stly, correlation between successive failure times may be highly variable among study populations within any cancer site. Moreover, misspecification of the expectedcorrelation would affect the realized power, in the event that the observed correlation differs from the expected correlation employed in the sample size calculations.Novel phase II trials with failure-time endpoints are likely to become the basis for evaluations for noncytotoxic agents. These evaluations may be augmented by relevant and reliable biomarkers, as these become identified. Phase II trial designs that are feasible, efficient and offer valid methods for clinical and statistical evaluation are needed.ACKNOWLEDGEMENTSThe authors would like express appreciation to: Daniel Von Hoff, M.D. for helpful discussions concerning the growth modulation index and development of cytostatic/biologic agents, J. Jack Lee, Ph.D. and Yasuo Ohashi, Ph.D. for helpful discussions on trial design issues and Sin-Ho Jung, Ph.D. for critical input on rank tests for paired failure times. We also wish to thank an Associate Editor and a reviewer for suggestions which markedly improved an earlier draft of the manuscript.The authors are also grateful to the following cooperative group investigators and statisticians for sharing their patient-level data, which allowed us to explore magnitude of correlation between paired failure times.Pediatric Oncology Group:Sharon Murphy, M.D., Group ChairPOG 8104N. McWilliams, M.D., Study ChairJ. Shuster, Ph.D., Study StatisticianSouthwest Oncology Group:Charles Coltman, M.D., Group ChairSWOG 8312C. Russell, M.D., Study ChairS. Green, Ph.D., Study StatisticianCancer and Leukemia Group B:Richard Schilsky, M.D., Group ChairCALGB 8751G. Canellos, M.D., Study ChairD. Niedzwiecki, Ph.D., Study StatisticianG. Petroni, Ph.D., Study Statistician。