1. Design and Analysis of Survival Trials with Treatment Crossover, delayed treatment effect and treatment dilution
Presenter: Xiaodong Luo– R&D-SANOFI US
JSM – Vancouver – July 29th, 2018

2. Acknowledgment Sanofi: Drs. Xuezhou Mao, Xun Chen, Hui Quan
FDA: Drs. Junshan Qiu, Steven Bai
Pfizer: Dr. Bo Huang
CrossPharma NPH working group

3. Outline Some NPH examples Modelling non-proportional hazards Analysis
Testing
Estimation
Discussions

4. Field study

5. CheckMate057 study

6. Potential reasons for NPH
There are many cases that the HR is not a constant, in particular, we consider
Delayed treatment effect: treatment effect won’t appear immediately post-treatment due to mechanism of drug action.
Diluted treatment effect: patients may prematurely terminate treatment but will be continued follow-up as per ITT analysis.
Treatment crossover: patients may progress/respond poorly to TX, by protocol or ethical reason, clinicians may provide rescue therapy, which could be the investigational treatment, non-trial treatment or combined treatments, etc.

7. Treatment crossover (Quick summary)
1. Crossover is a common phenomenon in survival trials due to study conduct, ethical consideration, sometimes by design. It is a better practice to consider how and when a crossover can take place in protocol than to render this as a protocol deviation/violation.
2. Crossover often leads to a reduced treatment effect. Based on some assumptions, the “true” treatment effect can be estimated (literature) . With re-randomization, the effect can be estimated with reduced accuracy.
3. Crossover often leads to non-constant hazard ratios, making it more difficult for study design and monitoring.

8. Modelling delayed treatment effect
Let 𝜆 𝑇 𝑡 and 𝜆 𝐶 (𝑡) be the hazard functions for the treatment and control.
Set
log 𝜆 𝑇 𝑡 𝜆 𝐶 𝑡 = 𝑗=1 𝐾 𝜂 𝑗 𝐼( 𝑡 𝑗−1 ≤𝑡< 𝑡 𝑗 )
where 0= 𝑡 0 < 𝑡 1 <…< 𝑡 𝐾−1 < 𝑡 𝐾 =∞ are the changing points of hazard ratios.
3. 𝜆 𝐶 (𝑡) is also a piecewise constant function with the SAME changing points 0= 𝑡 0 < 𝑡 1 <…< 𝑡 𝐾−1 < 𝑡 𝐾 =∞

9. A three-state model for treatment crossover
Markov
Semi-Markov
Hybrid
Others
1.The joint distribution of time-to-event 𝑇 and time-to-crossover 𝑇 𝑋 is uniquely determined by 𝜆 1 𝑡 , 𝜆 3 (𝑢) and 𝜆 2 𝑋 𝑡 𝑢 . 2. The control and treatment could have different sets of 𝜆 1 𝑡 , 𝜆 3 (𝑢) and 𝜆 2 𝑋 𝑡 𝑢 , corresponding to different three-state models.

10. Markov crossover 𝝀 𝟐 𝑿 𝒕|𝒖 = 𝝀 𝟐 𝒕 , 𝒕>𝒖.
𝝀 𝟐 𝑿 𝒕|𝒖 = 𝝀 𝟐 𝒕 , 𝒕>𝒖.
i.e. the new hazard after crossover does not depend on the crossover time.
The three-state model is a Markov model.
This type of crossover is useful in modelling treatment discontinuation.
The hazard rate in the treatment group will go to that of the control group if patients stop the treatment.
This may also apply to the scenario when combined treatments are used and one of which is stopped and the other is kept.

11. Semi-Markov crossover
𝝀 𝟐 𝑿 𝒕|𝒖 = 𝝀 𝟐 𝒕−𝒖 , 𝒕>𝒖.
i.e. the new hazard after crossover depends on the sojourn time from the crossover. Patients will have a renewed hazard function starting from the crossover time.
The three-state model is a Semi-Markov model.
This type of crossover is useful in modeling treatment crossover due to disease progression.
When patients in the control group progress to a more advanced stage, for ethical reason, clinicians may give the investigational treatment or other non-trial treatment to the patients. Because these patients may only expose to this treatment after crossover, the hazard function should start anew from the crossover.

12. Hybrid crossover 𝝀 𝟐 𝑿 𝒕|𝒖 =𝝅 𝝀 𝟐 𝒕−𝒖 + 𝟏−𝝅 𝝀 𝟏 𝒕 , 𝒕>𝒖.
𝝀 𝟐 𝑿 𝒕|𝒖 =𝝅 𝝀 𝟐 𝒕−𝒖 + 𝟏−𝝅 𝝀 𝟏 𝒕 , 𝒕>𝒖.
When patients in the control group progress, clinicians may do a re-randomization so these patients have a probability of π being assigned to the investigational treatment (hazard: 𝝀 𝟐 𝒕−𝒖 ) and a probability of 1−π being kept in the control (hazard: 𝝀 𝟏 𝒕 ).
This type of re-randomization often has a large 𝝅 so that patients will have a higher chance to receive the promising treatment while keeping a small but not nominal portion of patients in control to obtain a “fair” estimate of the “true” effect size.
If instead of keeping the patients in the control group, the patients may be assigned another treatment, in this case 𝝀 𝟐 𝑿 𝒕|𝒖 =𝝅 𝝀 𝟐 𝒕−𝒖 + 𝟏−𝝅 𝝀 𝟐 # 𝒕−𝒖 , where 𝝀 𝟐 # is the hazard of the progressed patients on that treatment.
This type of design may be used to compare different treatment regimens where dosing and treatment choices depend on the disease stage.

13. Other crossovers Other crossover can be investigated.
We think the two basic types (Markov and Semi-Markov) are most common.
We then allow each of the hazard functions to be piece-wise constant functions with arbitrary number of pieces, so that the model can have maximum flexibility.

14. Analysis methods: Testing
1. Log-rank or weighted log-rank
constant HR: log-rank
early separation: Gehan, Tarone-Ware, Wilcoxon, FH(k,0), k>0
late separation: FH(0,k), k>0
2. Restricted mean survival times (RMST) or weighted Kaplan-Meier
3. Median/Quantiles
4. Survival at certain time-points (landmark analysis)
5. Combination tests (linear combination, max combination)

15. Analysis methods: Estimation
1. (Average!) hazard ratio
2. Restricted mean survival times (RMST)
3. Median/Quantiles
4. Survival at certain time-points (landmark analysis)

16. The R package: PWEALL

17. Example 1(Delayed effect)
Annual event rates for control: 0.09, 0.07, 0.05 for yr 1, 2 and 2+;
Hazard ratio: HR=0.8 and HR=0.75 with 1-yr delayed;
n=4600 using 14-month accrual : c(100, 200, 300*2, 400*8, 300, 200)
Rates for loss-to-FU: 0% 1st yr and 1.5% afterwards (same for both groups)
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

18. Example 1(Delayed effect)
Two-sided 𝜶=𝟎.𝟎𝟓, power=0.85 and equal allocation using LR
HR=0.8, D=722, ~39 months;
HR=0.75 with 12-m delay, D=795, ~44 months.
Not considering delayed treatment effect leads to reduced power
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

19. Example 1(Delayed effect)
Solid: LR
Dotted: RMST
Solid: LR
Dotted: RMST
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

20. Example 2(Mimics CheckMate057)
Solid: TX
Dashed: Ctrl
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

21. Example 2(Mimics CheckMate057)
12-month recruitment period with uniform accrual rate.
10% yearly drop-out rate that is the same in both groups.
Equally assign 500 patients per group.
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

22. Example 2(Mimics CheckMate057)
Solid: RMST diff
Dashed: LR
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

23. Example 2(Mimics CheckMate057)
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.
RMSTs were calculated at t-0.5

24. Example 3(Control crosses to treatment)
Annual event rates for control: 0.3 for 1st 6m, 0.25 for 2nd 6m and 0.2 for the rest;
Hazard ratio: HR=0.65 and HR=0.6 with 3-m delayed;
n=800 using 6-month accrual : c(100*2, 200*2, 100*2)
Rates for loss-to-FU: 5% 1st yr and 8% afterwards (same for both groups)
Annual rate for progression: 40% for control and 20% for treatment
Crossover: at progression, control patients will cross to the treatment arm
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

25. Example 3(Control crosses to treatment)
Two-sided 𝜶=𝟎.𝟎𝟓, power=0.85 and equal allocation, log-rank is used
HR=0.65 w/o crossover, D=194, ~20 months;
HR=0.65 w crossover, cannot reach 85% power;
HR=0.6 with 3-m delay w/o crossover, D=242, ~26 months;
HR=0.6 with 3-m delay w crossover, cannot reach 85% power.
Treatment crossover significantly reduces power.
A balance between treating patients and conducting trials needs to be considered.
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

26. Example 3(Control crosses to treatment)
Insert plot here.
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

27. Discussion Tx delay, dilution and crossover are not rarely seen.
The effects often lead to reduced/contaminated Tx effect, making it difficult to power a study.
Different types of crossover may exist in different therapeutic areas. Too much crossover allowed may impact the outcome/validity of the trial, but not considering it may reduce power as well.
We recommend to at least look into these effects as a conservative way for study design.
In the presence of crossover, various analyses (ITT, on-treatment, per-protocol etc.) may be needed to examine the treatment effect.
Interim analyses need to be carefully planned.
Timeline prediction(at design and during study) can be conducted using PWEALL.
With delayed treatment effect and w/o treatment dilution, we will accumulate 809 evetns in 55 m (439 C and 370 T), overall HR=0.8361, power=74.6%
In order to get 85% power, tt=64 m with 894 events (488 C and 406 T), overall HR=
The overall HR will reach 0.81 at 74 m.

28. Q & A
Thank you!