Impact of censoring on the statistical methods for handling non-proportional hazards in Immuno-Oncology studies Yifan Huang, Luping Zhao, Jiabu Ye, and Pralay Mukhopadhyay Duke Industry Statistical Symposium 08 September 2017

Outline Introduction – statistical challenges in IO trials Objective – assess performance of different statistical analysis methods With various types of non proportional hazards patterns With different censoring mechanisms Methods Statistical analysis methods evaluated Simulation setup Preliminary results Summary

Delayed treatment effect CM – 141 (2L SCCHN) CM – 017 (2L Squamous NSCLC)

Crossing survival functions CM – 026 (1L NSCLC) CM- 057 (Non-squamous NSCLC)

Biomarker subgroups CM- 057 (Non-squamous NSCLC)

Example of proportional hazards (PH) HR=0.6 at all time points Constant hazard in each arm median 1 / median 2 = 0.6

Example of non-PH Increasing hazard in one arm, decreasing hazard in the other HR increases over time

Statistical analysis methods evaluated Based on the hazard function (using data up to max event time) Log-rank test Weighted log-rank test Based on the survival function (using data up to a specific time point) Difference in RMST (unweighted) Weighted KM Based on a point on the survival function Median Landmark

Restricted mean survival time (RMST) The shaded region (area under the survival curve) represents the RMST with a truncation time of 5 months The RMST calculated is 4.3 The statistical interpretation would be “at 5 months, the mean survival of a patient is 4.3 months” The clinical interpretation would be “the life expectancy of the patient over the next 5 months is 4.3 months”

Restricted mean survival time (RMST) RMST in the first year since treatment starts: 6.6  8.3 months Ref: Borghaei 2015, The new England journal o f medicine Data extracted by Wenmei Huang using R shiny tool developed by Monika Huhn RMST in the first 2 years since treatment starts: 11.1  12.8 months Difference in RMST in the first 2 years is 1.7 months Clinical interpretation: patients receiving nivolumab have a 1.7-month longer life expectancy during the first 2 years from treatment start

Simulation setup - scenarios Non-PH assumptions Delayed treatment effect Diminishing treatment effect Crossing survival functions Censoring mechanism Type 1 censoring: data cut-off (DCO) at 24m after LPI (DCO1) Type 2 censoring: data cut-off at 70% maturity (DCO2) Type 1 censoring: data cut-off at 12m after LPI (DCO3) Early censoring (interim analysis): data cut-off at 50% maturity

Simulation setup – generating non-PH survival data Piecewise exponential distribution Piecewise failure rate Different parameters of the same distribution Different distributions

Delayed treatment effect – simulation Sample size: 200 pts/arm, 1:1 randomization ratio, Median OS in control: 12 m Treatment effect: HR1=1, HR2=0.5, HR change point: 6 m, (a smaller trt effect was also evaluated) Accrual (uniform): 18 m, DCO1 (Type 1 censoring): 24m after LPI; DCO2 (Type 2 censoring): 70% maturity; DCO3 (Type 1 censoring): 12m after LPI; Interim (early censoring): 50% maturity Piecewise exponential distribution HR1: HR in the first piece HR2: HR in the second piece DCO Follow up after LPI (month) DCO1 41.6 DCO2 36.1 DCO3 29.7 More censoring

Delayed treatment effect (impact of FU on HR estimate) DCO1 Average HR=0.66 DCO3 Average HR=0.70 DCO2 Average HR=0.68 DCO_IA Average HR=0.76

Delayed treatment effect (impact on power and bias) Within each method, power decreases as censoring increases Log-rank (0,0) (1,0) and RMST are sensitive to censoring – power drops faster, whereas log-rank (1,1) (0,1) are more robust Landmark is sensitive to selection of analysis time point, but robust to amount of censoring Log-rank (0,0) and RMST had similar performance Log-rank (0,0) had similar power as Log-rank (1,1) (0,1) given sufficient follow-up; on the contrary, Log-rank (1,1) (0,1) is more powerful at interim with shorter follow up Bias is generally small, but relatively larger with more censoring DCO1 (Type 1 censoring): 24m after LPI; DCO2 (Type 2 censoring): 70% maturity; DCO3 (Type 1 censoring): 12m after LPI; Interim (early censoring): 50% maturity

Diminishing treatment effect – simulation Sample size: 200 pts/arm, 1:1 randomization ratio, Median OS in control: 12 m Treatment effect: HR1=0.5, HR2=1.1, HR change point: 12 m, (a smaller trt effect was also evaluated) Accrual (uniform): 18 m, DCO1 (Type 1 censoring): 24m after LPI; DCO2(Type 2 censoring): 70% maturity; DCO3 (Type 1 censoring): 12m after LPI; Interim (early censoring): 50% maturity Piecewise exponential distribution HR1: HR in the first piece HR2: HR in the second piece DCO Follow up after LPI (month) DCO1 41.2 DCO2 32.8 DCO3 29.6 More censoring

Diminishing treatment effect (impact of FU on HR estimate) DCO1 Average HR=0.76 DCO3 Average HR=0.68 DCO2 Average HR=0.71 DCO_IA Average HR=0.62

Diminishing treatment effect (impact on power and bias) Within each method, power increases as censoring increases Log-rank (1,1) (0,1) are sensitive to censoring – power drops faster, whereas log-rank (0,0) (1,0) and RMST are more robust Landmark is sensitive to selection of analysis time point, but robust to amount of censoring Log-rank (0,0) and RMST had similar performance Bias is generally small, but relatively larger with more censoring DCO1 (Type 1 censoring): 24m after LPI; DCO2 (Type 2 censoring): 70% maturity; DCO3 (Type 1 censoring): 12m after LPI; Interim (early censoring): 50% maturity

Crossing survival functions – simulation Sample size: 200 pts/arm, 1:1 randomization ratio, Median OS in control: 15 m Treatment effect: HR1=1.8, HR2=0.5, HR change point: 6 m, (a different trt effect was also evaluated) Accrual (uniform): 18 m, DCO1 (Type 1 censoring): 24m after LPI; DCO2(Type 2 censoring): 70% maturity; DCO3 (Type 1 censoring): 12m after LPI; Interim (early censoring): 50% maturity Piecewise exponential distribution HR1: HR in the first piece HR2: HR in the second piece DCO Follow up after LPI (month) DCO1 41.6 DCO2 39.2 DCO3 29.7 More censoring

Crossing survival functions (impact of FU on HR estimate) – simulation DCO1 Average HR=0.90 DCO3 Average HR=1.02 DCO2 Average HR=0.91 DCO_IA Average HR=1.16

Crossing survival functions – simulation Power is generally low Log-rank (1,1) (0,1) is more power than RMST because there is (late) difference in the hazard function, not in survival function (AUC) Bias is generally small, but relatively larger with more censoring DCO1 (Type 1 censoring): 24m after LPI; DCO2 (Type 2 censoring): 70% maturity; DCO3 (Type 1 censoring): 12m after LPI; Interim (early censoring): 50% maturity

Summary Non-PH creates challenges in designing and analyzing IO trials Performance of various statistical methods for non-PH time-to-event data was assessed using simulation with different censoring mechanisms Log-rank test (un-weighted) performs well with sufficient FU Weighted log-rank test can be more powerful and robust to censoring, if the correct non-PH pattern is known RMST had similar power as log-rank test (un-weighted), if the truncation time is similar to the max event time used by log-rank test RMST could be less powerful than log-rank test (un-weighted), if the difference in survival (AUC) is small while there is still difference in hazard; however, RMST may reflect the survival benefit more directly Bias is generally small, but relatively larger with more censoring Ongoing and future work More simulation scenarios for better generalisability  More methods such as weighted RMST Models beyond one-number summary, e.g., change point model