1. 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

2. 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

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

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

5. Biomarker subgroups
CM- 057 (Non-squamous NSCLC)

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

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

8. 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

9. 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”

10. 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

11. 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

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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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