Planning and analyzing clinical trials with competing risks: Recommendations for choosing appropriate statistical methodology Presented by Misun Yu Lee1 JSM 2019 Co-authors: J. C. Poythress2 and James Young1 1Astellas Pharma Inc. 2 Department of Statistics, University of Georgia, Athens

DISCLAIMER: The speaker is a paid employee of Astellas.  This presentation is intended for informational purposes only and does not replace independent professional judgment. This presentation is not intended to be legal advice.  Statements of fact, positions taken and opinions expressed are those of the speaker individually and, unless expressly stated to the contrary, do not necessarily reflect the opinion or position of the speaker’s employer, Astellas, or any of its subsidiaries and/or related entities. JSM 2019

What is a competing risk? In time-to-event analysis, more than one type of event may be possible. If multiple, mutually exclusive events occur, it is known as a competing risks situation. Example from cardiovascular study: Event of interest 1: Death from cardiac arrest Event of interest 2: Death from stroke Event of interest 3: Death from other cardiovascular cause Competing risk: Death from non-cardiovascular cause Example from oncology: Event of interest: Death from lung cancer Competing risk: Death from any other cause (including other types of cancer) JSM 2019 of 12

Estimands for Competing Risks Cumulative Incidence Function (CIF):   Non-parametric estimator of the CIF : Appropriate: Aalen-Johansen estimator Estimand: the CIF itself Inappropriate: 1-KM, where KM is the Kaplan-Meier estimator of the survival function obtained by treating competing risks as censored. Semi-parametric models for the CIF: Fine-Gray subdistribution hazards model Estimands: subhazard ratio & CIF Cause-specific hazards model Estimands: cause-specific hazard ratios & CIF JSM 2019 of 12

Models for Competing Risks Fine-Gray (F-G) Model Proportional hazards model for the subhazard function: the instantaneous rate of the event of interest, given that no event has occurred up to time t, or a competing event occurred before time t. One-to-one relationship with the cumulative incidence function (CIF). Recommended when the research question is one of clinical prognosis. Advantages Can tell how a covariate affects the CIF by looking at the subhazard ratio (SHR). Disadvantages SHR has an awkward direct interpretation. Not suitable when more than one type of event is of interest. JSM 2019 of 12

Models for Competing Risks Cause-Specific Hazards (CSH) Model Proportional hazards model for the cause-specific hazards function: the instantaneous rate of each event type, given that no event has occurred up to time t. No one-to-one relationship with the cumulative incidence function (CIF). Recommended when the research question is one of disease etiology. Advantages Cause-specific hazards ratio (csHR) has a natural direct interpretation. Suitable when more than one type of event is of interest. Disadvantages Can’t tell how a covariate affects the CIF by looking at the csHR. Estimation of the CIF is complicated. JSM 2019 of 12

Model choice should not be based on the research question alone. Take-home Message Model choice should not be based on the research question alone. Adequacy of model fit is an equally important concern. JSM 2019 of 12

Model fit is less of a concern when the effect size is small to moderate Non-parametric (black lines) and model-based estimators (blue lines: F-G model, green lines: CSH model) of the CIFs for two treatment groups (simulated data): True F-G model, HR=1.5 True CSH model, HR=1.5 JSM 2019 of 12

Model fit is important when the effect size is large Non-parametric (black lines) and model-based estimators (blue lines: F-G model, green lines: CSH model) of the CIFs for two treatment groups (simulated data): True F-G model, HR=3 True CSH model, HR=3 JSM 2019 of 12

Model fit matters in real data analysis Non-parametric (black lines) and model-based estimators (blue lines: F-G model, green lines: CSH model) of the CIFs for autologous vs. allogeneic transplants (OKISS data): End of neutropenia Blood stream infection Death JSM 2019 of 12

Recommendations for Planning Clinical Trials Don’ts: Don’t ignore competing risks! Don’t base model choice solely on the research question. Do’s: Do report the results from both the F-G model and CSH model. The models provide complementary information: F-G model: covariate effects on the probabilities of events. CSH model: covariate effects on the rates of events. Do check that the model provides adequate fit to the data. Do incorporate a contingency plan into the SAP. If there is evidence for severe lack-of-fit for one model, base the trial conclusions on a model that fits the data adequately. JSM 2019 of 12

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References & Acknowledgements OKISS data: Nadine Grambauer and Andreas Neudecker. 2011. compeir: Event-specific incidence rates for competing risks data. R package version 1.0. Accepted: Pharmaceutical Statistics, Ref PST-18-0108.R1 Complete list of references are in the paper. JSM 2019 of 12