This document discusses methods for adjusting for treatment switching in randomized controlled trials. It addresses the problem that intention-to-treat analysis may not accurately estimate treatment effectiveness when patients in the control group can switch to the experimental treatment. The document outlines several adjustment methods, including rank preserving structural failure time models and two-stage estimation, and discusses the issue of informative censoring due to treatment switching. It also presents a simulation study comparing the performance of adjustment methods with and without re-censoring to artificially censor patients who switched.

1. Adjusting for treatment switching in
randomised controlled trials
Nicholas Latimer, University of Sheffield, Sheffield, UK,
Reader in Health Economics,
NIHR Post Doctoral Research Fellow
Thanks to Ian White, Keith Abrams and Uwe Siebert who I
have been working with on this

2. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
2

3. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
3

4. Health economic evaluation
Economic evaluation aims to ensure the benefits of
programmes that are implemented exceed their opportunity
costs
Aim is to compare the new treatment to all relevant
comparators
Usually this involves a comparison of the costs and effects of
the new treatment and the standard treatment
Usually information to make these comparisons is taken from
randomised controlled trials
4

5. Treatment switching
What if patients randomised to the control group in a clinical
trial are permitted to switch onto the experimental treatment at
some point during the trial?
5

6. Survival time
Control Treatment
Intervention
Control  Intervention
PFS
PFS
PFS
PPS
PPS
PPS
True OS difference
ITT OS
difference
Treatment switching: Patients randomised to the control
group are allowed to switch to the new intervention
• Common in oncology RCTs
PFS = Progression-free survival; PPS = Post-progression survival;
OS = Overall survival

7. Treatment switching: Patients randomised to the control
group are allowed to switch to the new intervention
• Common in oncology RCTs
ITT analysis likely to fail to
address the decision problem
Different analytical methods
are needed to estimate
effectiveness and cost-effectiveness
PFS = Progression-free survival; PPS = Post-progression survival;
OS = Overall survival

8. Treatment switching
 Is an issue in over 55% of oncology technology assessments
 Adjustment methods can change decisions
8
NICE TA321 Dabrafenib for melanoma
57% switched
ITT analysis: OS HR 0.76; ICER £95,225
Adjustment analysis: OS HR 0.55; ICER £49,019
 Dabrafenib was recommended for use

9. • But…
• <50% TAs include adjustments for switching
• ≈60% of adjustment analyses rejected
Poor application of methodsLow decision-maker confidence in
methods
Treatment switching
- Methods make untestable
assumptions
- May lack face-validity
- Analysts have to make
many choices when
applying methods
- Concern that favourable
application decisions are
being made
- Or that methods have just
been used “badly”

10. • Reliance on ITT, or upon poor adjustment analyses, has
severe consequences
− Inappropriate recommendations
− Sub-optimal resource allocation
− Lost lives, lost QALYs
Treatment switching

11. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
11

12. 1. Develop analytical
techniques/methods to address
barriers that restrict use of
adjustment methods
2. Establish techniques/methods in
practice
• Address barriers around
testability of methodological
assumptions
• Further examine application
choices
• Use case studies to
establish practical use of
methods/techniques
• Without this, adjustment
analyses likely to remain
under-used
Addressing the problem (my fellowship)
This is what I’m going to focus
on today

13. Application decisions
When applying adjustment methods, analysts must make
several decisions, e.g…
Which covariates to include in the analysis (which variables are
predictive of survival and influence the probability of switching?)
Duration of the treatment effect (is it likely to endure beyond
treatment discontinuation?)
Whether or not to re-censor
13

14. Motivating example
14
Trametinib vs chemotherapy for metastatic melanoma [67% of control group
patients switched onto trametinib]
From: Latimer NR et al. Cancer Medicine 2016; 5(5):806–815
Re-censoring had a
big impact on the
results of the
adjustment methods
- Why?
- Which analysis is
more reliable?

15. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
15

16. Adjustment methods
• Two of the available adjustment methods involve estimating
counterfactual survival times using a counterfactual survival model
(Rank Preserving Structural Failure Time Model (RPSFTM) and two-
stage estimation (TSE))
𝑇𝑖 = 𝑇𝑜𝑓𝑓 𝑖
+ 𝑇𝑜𝑛 𝑖
(1)
𝑈𝑖 = 𝑇𝑜𝑓𝑓 𝑖
+ 𝑒 𝜓
𝑇𝑜𝑛 𝑖
(2)
𝑇𝑖 = observed survival time for individual i
𝑈𝑖 = untreated survival time for individual i
𝑇𝑜𝑓𝑓 𝑖
= Time spent off treatment for individual i
𝑇𝑜𝑛 𝑖
= Time spent on treatment for individual i
𝑒 𝜓 is a time ratio associated with treatment (inverse of the treatment effect)
• Estimate 𝜓 and plug into (2) to calculate untreated survival times
16

17. Estimating 𝝍 – RPSFTM
Use g-estimation to identify 𝝍
Two key assumptions:
a) Perfect randomisation – no treatment, equal average survival
b) Common treatment effect – no matter when treatment received
Counterfactual survival model: 𝑈𝑖 = 𝑇𝑜𝑓𝑓 𝑖
+ 𝑒 𝜓 𝑇𝑜𝑛 𝑖
We know 𝑇𝑜𝑓𝑓 𝑖
We know 𝑇𝑜𝑛 𝑖
We know (assume) that 𝑈𝑖 is equal between randomised groups
𝒆 𝝍 is the only unknown
 Test lots of values of 𝝍 until we find one that results in equal average 𝑻𝒊 𝟎
between randomised groups (g-estimation)
17

18. Estimating 𝝍 – RPSFTM
Use g-estimation to identify 𝝍
Two key assumptions:
a) Perfect randomisation – no treatment, equal average survival
b) Common treatment effect – no matter when treatment received
Counterfactual survival model: 𝑈𝑖 = 𝑇𝑜𝑓𝑓 𝑖
+ 𝑒 𝜓 𝑇𝑜𝑛 𝑖
We know 𝑇𝑜𝑓𝑓 𝑖
We know 𝑇𝑜𝑛 𝑖
We know (assume) that 𝑇𝑖 0 is equal between randomised groups
𝒆 𝝍 is the only unknown
 Test lots of values of 𝝍 until we find one that results in equal average 𝑻𝒊 𝟎
between randomised groups (g-estimation)
18
For each patient in the control and
experimental group, plug value for 𝜓
into:
𝑈𝑖 = 𝑇𝑜𝑓𝑓 𝑖
+ 𝑒 𝜓 𝑇𝑜𝑛 𝑖
Are untreated survival times equal?
… if not, try next value for 𝜓

19. 19
Estimating 𝝍 – TSE

20. Survival time
Control  Non-switchers
Control  Switchers
PFS
PFS
PPS
PPS
2. Estimate post-secondary
baseline treatment effect in
switchers compared to non-
switchers using an AFT model
1. Identify
secondary baseline
in control group
3. “Shrink” survival times in
switchers according to the
AF, deriving counterfactual
survival times
PPS
20
No unmeasured
confounding
Estimating 𝝍 – TSE

21. Censoring
RPSFTM and TSE both estimate counterfactual survival times
Assuming treatment is beneficial, survival times will be shrunken
Usually not everyone dies in cancer trials
For switchers who die, we estimate shrunken event times
For switchers who are censored, we estimate shrunken censoring times
 This is a problem
For survival analysis to be unbiased, censoring times must be
independent of any prognostic variables
But here, we are censoring switchers at an earlier time-point
Whether and when patients switch is unlikely to be random
Shrinking censoring times for switchers but not non-switchers
constitutes informative censoring
21

22. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
22

23. Re-censoring
Standard solution to this is re-censoring
Artificially censor everyone in the group(s) affected by switching
(irrespective of whether they switched) to their earliest possible
censoring time over all possible treatment strategies. This breaks the
relationship between prognosis and censoring time.
23

24. Re-censoring
Control arm (switchers)
Control arm (non-switchers)
24
𝐶𝑒𝑛𝑠𝑜𝑟𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑇 𝑠𝑐𝑎𝑙𝑒𝑅𝑒 − 𝑐𝑒𝑛𝑠𝑜𝑟 ℎ𝑒𝑟𝑒
Survival and
censoring times
shrunk to adjust for
switching
Switchers are
censored before
non-switchers
S
S
S
1
2
3
4
5
6

25. Re-censoring and health economics
25
Re-censoring has long been accepted as a requirement when
estimating counterfactual survival times (Robins1989; White 1999)
It means we have estimates of treatment effects that are not subject
to informative censoring, up to the maximum re-censored time-point
 For use in economic evaluation, is that enough? Is it useful?

26. Re-censoring and health economics
26
Economic evaluations usually need to extrapolate out to a life-time
Re-censoring involves censoring people artificially early
 Results in lost longer term information
From: Latimer NR et al. Cancer Medicine 2016; 5(5):806–815
HR=0.43 HR=0.53

27. Re-censoring and health economics
27
Economic evaluations usually need to extrapolate out to a life-time
Re-censoring involves censoring people artificially early
 Results in lost longer term information
From: Latimer NR et al. Cancer Medicine 2016; 5(5):806–815
HR=0.43 HR=0.53
• What if the treatment effect changes over
time?
• What if longer-term trends in the hazard
function haven’t become established in the
re-censored dataset?
 What is more important – lost information, or
informative censoring?

28. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
28

29. Simulation study
Simulate survival times, apply switching from control group (after
progression) that is related to prognosis
Apply adjustment methods with and without re-censoring
RPSFTM
RPSFTMnr
Compare bias (and empirical standard error, root mean squared error, coverage)
in estimation of control group restricted mean survival time (RMST)
at end of trial follow-up
Vary potentially important characteristics across scenarios
treatment effect size
complexity of survivor function
switch proportion
144 scenarios in total (only going to show you a subset of these)
29
TSE
TSEnr
common treatment effect
switcher prognosis
disease severity

30. Data generation
In the majority of scenarios used a mixture Weibull model to
simulate survival times
Allows complex survivor functions to be generated, which we
believe are likely to reflect reality better than a simple parametric
distribution
30
0.000.250.500.751.00
320 312 291 257 208 177 0Experimental group
180 169 138 106 65 17 0Control group
Number at risk
0 100 200 300 400 500 600
Analysis time (days)
Control group
Experimental group
.0005
.001
.0015
.002
.0025
Hazardrate
0 100 200 300 400 500 600
Analysis time (days)
Control group
Experimental group

31. Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
31
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

32. 32
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
RPSFTM
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

33. 33
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
RPSFTM
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
Why does RPSFTM under-estimate RMST?
2. No common treatment effect
When switchers get a reduced effect RPSFTM over-adjusts
because the treatment effect in switchers is assumed to be just
as big as it is in the experimental group – RPSFTM does even
worse in these scenarios
.0005
.001
.0015
.002
.0025
Hazardrate
0 100 200 300 400 500 600
Analysis time (days)
Control group
Experimental group
Two sources of negative bias:
1. Simulated decreasing hazards over time
 When re-censor, have to extrapolate
from re-censored dataset to estimate
RMST at the end of trial follow-up
 Decreasing hazards haven’t established
before re-censoring time-point, so
extrapolation over-estimates long-term
hazards and under-estimates RMST

34. 34
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
RPSFTM
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE
No CTE
CTE No CTE
CTE
No CTE
CTE

35. 35
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
RPSFTM
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

36. 36
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
RPSFTM
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE
No CTE
CTE No CTE
CTE
No CTE
CTE
Why does TSE under-estimate RMST?
 TSE does better than RPSFTM when there is not a common
treatment effect, and does similarly when there is a common
treatment effect
 Note, for TSE and RPSFTM, size of treatment effect is biggest
influence on bias – increase effect size = more lost information
.0005
.001
.0015
.002
.0025
Hazardrate
0 100 200 300 400 500 600
Analysis time (days)
Control group
Experimental group
Same reason as RPSFTM:
1. Loss of longer-term information means
that re-censored data-set does not
contain information on the decreasing
hazards over time
BUT, TSE does not assume a common
treatment effect, so is not prone to this
additional negative bias

37. 37
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
RPSFTM
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE
No CTE
CTE No CTE
CTE
No CTE
CTE

38. 38
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

39. 39
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE
No CTE
CTE No CTE
CTE
No CTE
CTE
Why does RPSFTM nr over-estimate RMST?
Two competing sources of bias:
1. Informative censoring
 Switchers are censored at earlier time-points
 Non-switchers are not
 Re-censoring affects the right-hand-side of the KM curve
 Non-switchers who have long-term survival are by definition
people who have done well (perhaps they haven’t even had
disease progression yet)
 Not re-censoring leaves the best performing patients with the
longest censoring times – hence inducing positive bias
2. Common treatment effect. When switchers get a reduced
effect the RPSFTM over-adjusts inducing negative bias
 To some extent, these two biases cancel out
 RPSFTMnr does better when there is not a CTE

40. 40
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE No CTE CTE
No CTE CTE
No CTE
CTE

41. 41
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
TSEnr
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

42. 42
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
TSEnr
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE
No CTE
CTE No CTE
CTE
No CTE
CTE
Why does TSEnr over-estimate RMST?
Same reason as RPSFTMnr
1. Informative censoring means that the best performing
patients have the longest censoring times – hence RMST is
over-estimated
BUT, TSEnr does not assume a common treatment effect, so
there is no competing negative bias
 Some trend towards RPSFTMnr doing slightly better than
TSEnr when there is not a CTE
 Note, for RPSFTMnr and TSEnr increased switch proportion
and (to a lesser extent) increased treatment effect were the
most important drivers of bias – both result in informative
censoring being a bigger problem (increased selection effect
and increased censoring disparity between switchers and
non-switchers)

43. 43
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
-10
-8-6-4-2
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
TSEnr
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %
No CTE
CTE No CTE CTE
No CTE CTE
No CTE
CTE

44. 1. Background
2. Addressing the problem
3. Adjustment methods
4. Re-censoring (and health economics)
5. Simulation study
6. Conclusions
44

45. Conclusions (1)
Re-censoring and not re-censoring are both prone to bias when our
objectives are to estimate longer-term survival or long-term
treatment effects
 Re-censoring is likely to lead to under-estimates of control group
survival
 Not re-censoring is likely to lead to over-estimates of control group
survival
 We should do both! (provides decision-maker with useful info)
45

46. Conclusions (2)
Should also assess hazard and survivor functions to attempt to
identify the likely impact of re-censoring
 Does the hazard have a turning point or sudden change of slope? When?
And should assess the characteristics of long-term survivors to
identify the likely impact of informative censoring
 Are there any long-term survivors who did not switch?
46

47. Conclusions (3)
Should consider which method is likely to produce least bias
 Re-censoring methods are most prone to bias when the treatment
effect is high
 Non-re-censoring methods are most prone to bias when the
switching proportion is high
 Better consideration of all these issues leads to better informed
analyses, with less scope for unjustified “innocuous”
application choices
47

48. Conclusions (4)
Finally, neither method is perfect for the HTA context
Can we do better?
 Inverse probability of censoring weighting (IPCW) represents a well-
known method for dealing with informative censoring
 Perhaps we could not re-censor, and use IPCW to account for
informative censoring…?
48

49. Back-up
49

50. Results
50
Switch proportion (low, moderate)
Severity (low, high)
Complexity of survivor function (simple, moderate, high)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
Prognosis of switchers (good, poor)
Scenario9
Scenario13
Scenario57
Scenario61
-10
0
1020
1-24 25-48 49-72 73-96
Scenario
No switch
ITT
TSE
TSEnr
RPSFTM
RPSFTMnr

51. 51
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
02468
10
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
TSEnr
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

52. 52
Results holding complexity of the survivor function
(moderate), disease severity (low), prognosis of switchers
(good) constant
Switch proportion (low, moderate)
Treatment effect (low, high)
Common treatment effect (no CTE, CTE)
048
12
RMSE
1 2 3 4 5 6 7 8
Scenario
ITT
TSE
TSEnr
RPSFTM
RPSFTMnr
Low trt effect /
low switch %
Low trt effect /
high switch %High trt effect /
low switch %
High trt effect /
high switch %

53. What is a realistic hazard
function in cancer?
53
Hazardrate
Time
Trial entrants
relatively fit 
low hazard, but
increasing due
to disease
Over time patient mix
changes, long-term
survivors remain 
hazard has a turning
point, and reduces
In the long-term,
hazard increases due
to old age  hazard
has another turning
point, and increases
[May not observe this
in trial period]

54. What is a realistic hazard
function in cancer? Real case
54
All cause survival data
for 9,721 breast cancer
patients age<50,
diagnosed in England
and Wales between
1986 and end 1991
[adapted from Rutherford et al,
Journal of Statistical Computation
and Simulation, 2015;85;4:777-793]

55. • Ipilimumab plus dacarbazine compared to
dacarbazine for previously untreated metastatic
melanoma
• These data are reconstructed from the pivotal trial
publication [Robert et al, New England Journal of
Medicine. 2011; 364(26):2517-26].
Work done by Ash
Bullemont for his
MSc dissertation at
ScHARR
Issues raised by I-O therapy
Hazardrate

56. Re-censoring
Standard solution to this is re-censoring. Artificially censor everyone
(irrespective of whether they switched) to their earliest possible
censoring time over all possible treatment strategies. This breaks the
relationship between prognosis and censoring time.
Assuming the treatment is beneficial, the most favourable treatment
strategy for any patient would have been to receive treatment for the
entire duration of the study, i.e. 𝑇𝑜𝑛 𝑖
= 𝐶𝑖, where 𝐶𝑖 is the administrative
censoring time
Then, patient i’s censoring time would be shrunk to 𝑒 𝜓
𝐶𝑖
Under re-censoring,
For switchers: 𝑈𝑖 is replaced with 𝑒 𝜓
𝐶𝑖 if 𝑒 𝜓
𝐶𝑖 < 𝑈𝑖
For non-switchers: 𝑇𝑖 is replaced with 𝑒 𝜓 𝐶𝑖 if 𝑒 𝜓 𝐶𝑖 < 𝑇𝑖
If this is done for all patients in the trial, there is no longer any
relationship between switching/prognosis and censoring time 56