Adaptive Prediction of Event Times in Clinical Trials

Transcription

1 Adaptive Prediction of Event Times in Clinical Trials Yu Lan Southern Methodist University Advisor: Daniel F. Heitjan May 8, 2017 Yu Lan (SMU) May 8, / 19

2 Clinical Trial Prediction Event-based trials: Plan interim and final analyses around event counts, whose timing is random. Failure to adhere to protocol-defined analysis times: Potential to game stopping rules [4]. Erode confidence in trial integrity. Logistical problems in trial management. Suggests need to predict landmark event times in real time. Yu Lan (SMU) May 8, / 19

3 Real-Time Clinical Trial Prediction Bagiella and Heitjan (2001): Bayesian simulation model with Poisson accrual. Exponential event and loss times in each arm. Cook (2003): Markov-chain model yielding predicted event counts. And several others; see [3]. Yu Lan (SMU) May 8, / 19

4 Basic Framework J-arm, event-based trial that began enrollment at calendar time 0. Planned analysis at occurrence of event D. Objective: At time t 0, predict future time T at which event D will occur. Yu Lan (SMU) May 8, / 19

5 Model-based Bayesian Prediction by Simulation At time t 0, for m = 1,..., M, 1 Conditional on the accumulated data, sample from the posterior of the parameters. 2 Conditional on the sampled parameter and the data, complete the future trial data: 1 Generate hypothetical new patients. 2 Simulate event and loss times of enrolled and new patients. 3 Combine the hypothetical and enrolled patients into a single completed data set. 3 Calculate estimates of interest: Time T (m) of event D. End-of-study treatment effect. Statistical significance (predictive power). Yu Lan (SMU) May 8, / 19

6 Models to Use Parametric models: Survival and loss to follow-up: Weibull and exponential. With or without a cure fraction. Separate parameters by arm. Enrollment: Poisson with constant rate. Nonparametric model: Survival and loss to follow-up: Unrestricted. Enrollment: Unrestricted. Sample from posteriors by Bayesian Bootstrap (BB). Yu Lan (SMU) May 8, / 19

7 Adaptive clinical-trial prediction The most accurate and efficient method is to use the correct model. Often difficult to identify, especially in the early going. Develop a method that selects the model adaptively: Propose a range of parametric models M 1 M L : Compute and compare model posterior probabilities: P(M l x) = cp(m l )P(x M l ), l = 1,..., L. At each stage, create predictions from best-fitting model after BB sampling to capture uncertainty. Yu Lan (SMU) May 8, / 19

8 Simulation Design: Prediction methods: Nonparametric (NP). Adaptive. Cure model: Weibull (WC) and exponential (EC). Non-cure model: Weibull (WNC) and exponential (ENC). True-data scenarios: (Weibull, exponential) (cure, non-cure) Evaluation criteria: Coverage probability. Median interval width. Key results: Adaptive method readily identified the underlying distribution Ability to detect cure depends on cure fraction, shape parameter, and length of follow-up. Yu Lan (SMU) May 8, / 19

9 CGD study Application to the International Chronic Granulomatous Disease (ICGD) Study [8]. Randomized, double-blind, placebo-controlled trial comparing gamma interferon (γ-ifn) to placebo. Require 35 events to achieve 90% power to detect posited HR=1/3. Yu Lan (SMU) May 8, / 19

10 CGD study Infection Free Probability Placebo γ IFN Time to First Severe Infection (months) Figure: Kaplan-Meier Curves in CGD Yu Lan (SMU) May 8, / 19

11 CGD study Model selection probabilities of the adaptive method: For placebo, around 60% select ENC, 40% WNC. For γ-ifn, almost always select the ENC. Yu Lan (SMU) May 8, / 19

12 Figure: Prediction of the final (35th event) analysis date. Yu Lan (SMU) May 8, / 19 CGD study Predicted Landmark Date (Days) Adap Wei cure Wei noncure Exp cure Exp noncure Nonparametric Date of Prediction (Days)

13 RTOG 0129 Phase III trial in squamous cell carcinoma of the head and neck,comparing Accelerated-fractionation radiotherapy with concurrent cisplatin-based chemotherapy (AFX). Standard fractionation radiotherapy (SFX). Require D = 303 events to achieve 80% power to detect posited HR=0.8. Yu Lan (SMU) May 8, / 19

14 RTOG 0129 study Survival Probability SFX AFX Time to Death (months) Figure: Kaplan-Meier Curves in RTOG Yu Lan (SMU) May 8, / 19

15 RTOG 0129 study Model selection probability of the adaptive method The adaptive method first prefers ENC; after month 40, it switches to EC. At the conclusion, the adaptive method selects EC with 90% in placebo arm, and 76% in treatment arm. Yu Lan (SMU) May 8, / 19

16 Figure: Prediction of the final (303th event) analysis date. Yu Lan (SMU) May 8, / 19 RTOG 0129 study Predicted Landmark Date (Months) Adap Wei cure Wei noncure Exp cure Exp noncure Date of Prediction (Months)

17 Discussion Regarding the method: Adaptive method provides robustness with modest efficiency loss. Model survival by arm often important! BB model selection adds a further level of robustness. Yu Lan (SMU) May 8, / 19

18 Discussion Regarding the trials: Month-to-month volatility in mortality experience can dramatically affect prediction intervals. Require more flexible enrollment models. Future research: Model how new centers join the study. Incorporate time-varying enrollment rates within centers. Yu Lan (SMU) May 8, / 19

19 References I Bagiella E, Heitjan DF (2001). Predicting analysis times in randomized clinical trials. Statistics in Medicine 20: Cook TD (2003). Methods for mid-course corrections for clinical trials with survival outcomes. Statistics in Medicine 22: Heitjan DF, Ge Z, Ying GS (2015). Real-time prediction of clinical trial enrollment and event counts: A review. Contemporary Clinical Trials 45: Proschan MA, Follmann DA, Waclawiw MA. Effects of assumption violations on type I error rate in group sequential monitoring. Biometrics 48: Ying GS, Heitjan DF, Chen TT (2004). Nonparametric prediction of event times in randomized clinical trials. Clinical Trials 1: Ying GS, Heitjan DF (2013). Prediction of event times in the REMATCH Trial. Clinical Trials 10: Yu Lan (SMU) May 8, / 19

20 References II Chen T-T (2016). Predicting analysis times in randomized clinical trials with cancer immunotherapy. BMC Biomedical Research Methodology 16. International Chronic Granulomatous Disease Cooperative Study Group (1991). A controlled trial of interferon gamma to prevent infection in Chronic Granulomatous Disease. New England Journal of Medicine 324: Yu Lan (SMU) May 8, / 19

21 Survival Probability Ambiguous non cure Cure Unambiguous non cure Time to Death (Months) Figure: KM plots under different scenarios. Yu Lan (SMU) May 8, / 13

22 Future research Number of patients enrolled Month Figure: Number of enrolled patients by month of REMATCH. Yu Lan (SMU) May 8, / 13

23 Simulation Parameter Scenario α β ρ Weibull cure Weibull Ambiguous Non-cure Exponential cure Exponential Ambiguous Non-cure Weibull Unambiguous Non-cure Exponential Unambiguous Non-cure Table: Parameters for generating data in the simulations. Yu Lan (SMU) May 8, / 13

24 Simulation (α, β, ρ) = (0.5, 1.6, 0.45) (α, β, ρ) = (2, 2.8, 0.45) Coverage rate (%) Median length Coverage rate (%) Median length Method Event ADAP WC WNC EC ENC NP Table: Prediction performance under the Weibull cure-mixture scenario. Yu Lan (SMU) May 8, / 13

25 Simulation (α, β, ρ) = (0.5, 11, 0) (α, β, ρ) = (2, 4.85, 0) Coverage rate Median length Coverage rate Median length Method Event ADAP WC WNC EC ENC NP Table: Prediction performance under the Weibull ambiguous non-cure scenario. Yu Lan (SMU) May 8, / 13

26 Simulation (α, β, ρ) = (1, 2.3, 0.45) (α, β, ρ) = (1, 7, 0) Coverage rate Median length Coverage rate Median length Method Event ADAP WC WNC EC ENC NP Table: Prediction performance under the exponential cure-mixture and exponential ambiguous non-cure scenarios. Yu Lan (SMU) May 8, / 13

27 Simulation (α, β, ρ) = (0.5, 1.6, 0) (α, β, ρ) = (2, 2.8, 0) Coverage rate Median length Coverage rate Median length Method Event ADAP WC WNC EC ENC NP Table: Prediction performance under the Weibull unambiguous non-cure scenario. Yu Lan (SMU) May 8, / 13

28 Simulation (α, β, ρ) = (1, 2.3, 0) Coverage rate Median length Method Event ADAP WC WNC EC ENC NP Table: Prediction performance under the exponential unambiguous non-cure scenario. Yu Lan (SMU) May 8, / 13

29 Simulation (α, β, ρ) = (0.5, 1.6, 0.45) (α, β, ρ) = (2, 2.8, 0.45) Method Event WC WNC EC ENC (α, β, ρ) = (0.5, 11, 0) (α, β, ρ) = (2, 4.85, 0) Method Event WC WNC EC ENC Table: Probability (%) of each model being selected by the adaptive method under scenarios of Weibull cure and Weibull ambiguous non-cure. Yu Lan (SMU) May 8, / 13

30 Simulation (α, β, ρ) = (1, 2.3, 0.45) (α, β, ρ) = (1, 7, 0) Method Event WC WNC EC ENC Table: Probability (%) of each model being selected by the adaptive method under scenarios of Exponential cure and Exponential ambiguous non-cure. Yu Lan (SMU) May 8, / 13

31 Simulation (α, β, ρ) = (0.5, 1.6, 0) (α, β, ρ) = (2, 2.8, 0) (α, β, ρ) = (1, 2.3, 0) Method Event WC WNC EC ENC Table: Probability (%) of each model being selected by the adaptive method under two scenarios of Weibull unambiguous non-cure and Exponential unambiguous non-cure. Yu Lan (SMU) May 8, / 13

32 CGD study Placebo Prob of being selected (%) γ-ifn Time (t 0 ) ENC EC WNC WC ENC EC WNC WC Table: Evolution of the model selection. Yu Lan (SMU) May 8, / 13

33 Figure: Prediction of the interim (18th event) analysis date. Yu Lan (SMU) May 8, / 13 CGD study Predicted Landmark Date (Days) _ Adap Wei cure Wei noncure Exp cure Exp noncure Nonparametric Date of Prediction (Days)