Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Deviation from the Proportional Hazards Assumption in Randomized Phase 3 Clinical Trials in Oncology: Prevalence, Associated Factors and Implications Rifaquat Rahman1,2, Geoffrey Fell2,3, Steffen Ventz2,3,4, Andrea Arfé5, Alyssa M. Vanderbeek6, Lorenzo Trippa2,3,4*, Brian M. Alexander1,2* *Brian M. Alexander and Lorenzo Trippa contributed equally to this article as co-senior authors. Affiliations: 1. Department of Radiation Oncology, Center for Neuro-Oncology, Dana-Farber Cancer Institute, Harvard Medical School, Boston, MA, USA. 2. Program in Regulatory Science Research, Dana-Farber Cancer Institute, Boston, MA, USA. 3. Department of Data Sciences, Dana-Farber Cancer Institute, Boston, MA, USA. 4. Department of Biostatistics, Harvard School of Public Health, Boston, MA, USA. 5. Department of Decision Sciences, Bocconi University, Milano, Italy. 6. Department of Biostatistics, Columbia University Mailman School of Public Health, New York, NY, USA. Corresponding Author: Brian M. Alexander, MD, MPH Harvard Medical School, Armenise 109D 1 Downloaded from clincancerres.aacrjournals.org on September 24, 2021. © 2019 American Association for Cancer Research. Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. 210 Longwood Ave Boston, MA 02115 Phone: 617-732-6313 Fax: 617-975-0932 [email protected] Running title: Deviations from proportional hazards in phase 3 trials Funding: This work was supported by the Burroughs Wellcome Innovations in Regulatory Science Award. Potential Conflicts of interest: Brian Alexander reports personal fees from AbbVie, Bristol- Myers Squibb, Precision Health Economics, and Schlesinger Associates. Brian Alexander reports employment at Foundation Medicine, Inc. Abstract word count: 247 Manuscript body text word count: 3,295 Total Number of Tables & Figures: 5 Keywords: Survival analysis, trial efficiency, proportional hazards, hazard ratio, treatment effect 2 Downloaded from clincancerres.aacrjournals.org on September 24, 2021. © 2019 American Association for Cancer Research. Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Statement of Translational Relevance Deviation from proportional hazards (DPH), which occurs when a treatment exhibits variation of treatment effect over time, may be more prevalent in modern trials and can lead to under- powered clinical trials or misleading conclusions. We used reconstructed individual patient-level data from published clinical trials in recent phase III oncology clinical trials in breast, lung, colorectal and prostate cancer to investigate the prevalence of DPH, its associated factors across different clinical settings and its implications. A notable proportion of published clinical trials in oncology exhibited evidence of DPH, particularly in trials testing immunotherapy agents and analyses of non-survival endpoints. In re-analyzing immunotherapy trials, the use of alternative statistical approaches allowed for more efficient clinical trials requiring fewer patients relative to conventional trial design. Alternative statistical methods, without the proportional hazards assumptions, should be considered in the design and analysis of clinical trials in settings where DPH occurs more frequently. 3 Downloaded from clincancerres.aacrjournals.org on September 24, 2021. © 2019 American Association for Cancer Research. Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Abstract Purpose: Deviations from proportional hazards (DPH), which may be more prevalent in the era of precision medicine and immunotherapy, can lead to under-powered trials or misleading conclusions. We used a meta-analytic approach to estimate DPH across cancer trials, investigate associated factors, and evaluate data-analysis approaches for future trials. Experimental Design: We searched PubMed for phase III trials in breast, lung, prostate, and colorectal cancer published in a pre-selected list of journals between 2014-2016 and extracted individual patient-level data (IPLD) from Kaplan-Meier curves. We re-analyzed IPLD to identify DPH. Potential efficiency gains, when DPHs were present, of alternative statistical methods relative to standard log-rank based analysis were expressed as sample-size requirements for a fixed power level. Results: From 152 trials, we obtained IPLD on 129,401 patients. Among 304 Kaplan-Meier figures, 75 (24.7%) exhibited evidence of DPH, including 8 of 14 (57%) KM pairs from immunotherapy trials. Trial type (immunotherapy, odds ratio (OR) 4.29, 95%CI 1.11-16.6), metastatic patient population (OR 3.18, 95%CI 1.26-8.05), and non-OS endpoints (OR 3.23, 95%CI 1.79-5.88) were associated with DPH. In immunotherapy trials, alternative statistical approaches allowed for more efficient clinical trials with fewer patients (up to 74% reduction) relative to log-rank testing. 4 Downloaded from clincancerres.aacrjournals.org on September 24, 2021. © 2019 American Association for Cancer Research. Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Conclusions: DPH was found in a notable proportion of time-to-event outcomes in published clinical trials in oncology and was more common for immunotherapy trials and non-OS endpoints. Alternative statistical methods, without proportional hazards assumptions, should be considered in the design and analysis of clinical trials when the likelihood of DPH is high. 5 Downloaded from clincancerres.aacrjournals.org on September 24, 2021. © 2019 American Association for Cancer Research. Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Introduction Results from randomized controlled trials (RCTs) play an essential role in therapeutic development and clinical decision making. Standard clinical trial designs, summary statistics, and analytic procedures based on proportional hazards (PH) assumptions work well when the treatment effects are constant over time. Deviations from proportional hazards (DPH) occur when treatments exhibit variation of treatment effects (hazard ratio) over time. Time-varying treatment effects are increasingly recognized in modern trials (1). Understanding the characteristics and degree of time-varying treatment effects in oncology clinical trials has implications for design, analysis, and interpretability of trials, and may ultimately lead to improvements in the testing of therapies. In this context, the use of statistical models that poorly represent the true underlying time-varying treatment effect can constitute a substantial obstacle to therapeutic development. Time-varying treatment effects are one example of treatment effect heterogeneity that may be induced by several factors. Immuno-oncology (IO) trials have shown evidence of possible delayed treatment effects (1,2). Subgroups of patients with different responses to a given therapy can also manifest as a treatment effect that is not constant over time (3). Time- varying treatment effects, which define DPH, indicates that the hazard ratio (HR) varies over 6 Downloaded from clincancerres.aacrjournals.org on September 24, 2021. © 2019 American Association for Cancer Research. Author Manuscript Published OnlineFirst on July 25, 2019; DOI: 10.1158/1078-0432.CCR-18-3999 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. time after randomization. With DPH, estimates of treatment effects from PH models may not be interpretable (4). The widely used log-rank test and the Cox proportional hazards model are not optimal in terms of power when DPH is present and render sample size calculations, subsequent results and their interpretation questionable (5,6). A better understanding of the prevalence of DPH, along with factors that increase the likelihood of DPH, could substantially improve the therapeutic development process by anticipating DPH and suggesting appropriate alternative trial designs. We evaluate whether the PH model -assumed in the vast majority of oncology trials (7) – is representative of modern RCT data. We use reconstructed individual patient-level data (IPLD) (8) from published clinical trials to investigate DPH in recent phase III oncology clinical trials. We illustrate the magnitude of DPH and types of time-varying treatment effects observed across different clinical settings (IO, hormonal therapies, chemotherapies, etc.), and identify associated factors. This information can be utilized to evaluate if alternative statistical methodologies, instead of a standard PH analysis, should be considered in a given context for the design of future studies. We then evaluate alternative procedures for testing treatment effects and demonstrate how data from completed clinical trials can be used to evaluate operating characteristics