Statistics & HSCT ESH-EBMT 2014 Vienna

Myriam Labopin [email protected]

Complexity of the story…. Death 500  Acute and chronic GVHD

Competing risks

Censored data

Censored data Time-to event variables

Time-to-event variables

We are interested in T, the time elapsed between a well defined starting point (SCT) and the endpoint. T is called « survival time ».

Censored data Typical type of data

Event Lost to follow-up Study termination

Time since start of study

Time since entry in study

Censored data

Survival time = T HSCT t1

Patient 1

t2

Still alive

Patient 2

Alive at time t:

Dead

T>t1

Dies at time t: T=t2

ti : observation time for patient i

Censored observation : we only observe that survival time T is greater than observation time t. T is unknown: we do not know if the event will happen and when Censored patients are by definition only those still at risk of failure Censored data = incomplete information  missing

Censored data Censoring must be uninformative - independent of the event studied Assumption reasonable  End of study

 Loss to follow-up when unrelated to the disease Sometimes questionable  Loss to follow-up • •

Healthy participants feel less need for medical services (underestimation of survival) Subjects with advanced disease progression are more likely to leave the study (overestimation of survival)

 Another event has occurred, which prevents occurrence of the event of interest: competing risks

Censored data Question to have in mind when censoring: ‘Has a censored patient the same risk of an event as a patient still on follow-up?”

Do not censor: - Death without relapse when estimating relapse (competing risk) - Death from other causes when estimating a specific cause of death (competing risk) - Patients when they go ‘off-treatment’ for toxicity in prospective clinical trials (intent-to-treat) - Second transplant (competing or intermediate event)

Competing risks

Competing risks “Competing” : the occurrence of any event may modify or avoid the risk of the others

Dead in CR

Patients can experience only one of the events

HSCT

Relapsed

Competing risks

Relapse HSCT

Relapse at time t: T=t

T Death in CR

Competing event ≠ censoring

Alive relapse_free

Dies w/o relapse after time t: T>t

Event-free at time t: T>t

Failure from competing event is not an incomplete information Patients who relapse are no longer at risk for death in CR  censor

Patients censored : only patients alive relapse-free

Competing risks Which competing events after HSCT? When analysing: RI : death without relapse (NRM) NRM: relapse Engraftment: second transplant/death GVHD: relapse / death / (± graft failure)

Statistical methods

Description of the endpoints

Statistical methods – survival analysis Survival endpoint -> (time, status=0/1) Survival time = T HSCT

Still alive

Patient 1

Dead

Patient 2 t : observation time

Death (complete data) -> time=t, status=1

Alive (censored) -> time=t, status=0

Basic concept describing survival

Probability that an individual survives from the time origin to t

Probability that an individual dies at time t, conditional he or she have survived until that time

Statistical methods – survival analysis Non parametric estimation of the survival function  Example: survival time in 20 patients: 9, 50, 60, 114+, 153+, 272, 300, 364, 365+, 392, 400+, 450, 455, 530+, 687+, 722, 757+, 788+, 800+, 1316+ (+: censored)

 Without censoring:

Nr patients surviving beyo nd t ˆ S (t )  N 17 Sˆ (100)  20

 Problem: observation 114+

Statistical methods – survival analysis Kaplan Meier estimator : “product-limit” method  Probably well-known to all of you  Let t0 < t1 < t2 < … < tn ordered distinct event-times  For each ti:  ri : number at risk at ti  di: number of events at ti di t  1   Probability of surviving ti surviving i 1 ri

 Kaplan Meier estimate: product of the probabilities for each time  This assumes that individuals at risk at ti are representative for all patients alive at ti : independence of censoring distribution

Statistical methods – survival analysis

Probability

Kaplan Meier curve -Median survival time : time t where estimated survival is equal to 0.5 (50% ) - Nr of patients still at risk at each time:  Too few patients at risk at the end of follow-up : estimates unreliable.  a ‘plateau’ is not the probability of being ‘cured’

Median survival time (half of the patients die within the median time)

Statistical methods – Competing risks Competing risk (time, status=0/1/2) Relapse HSCT

Relapse at time t: T=t

T Death in CR

Alive relapse_free

Relapse -> (time=t: status=1) Death in CR -> (time=t; status=2) Alive relapse-free (censored) -> (time=t;status=0)

Dies w/o relapse after time t: T>t Event-free at time t: T>t

Statistical methods – Competing risks

Do not use Kaplan Meier for competing risks! Example : estimation of RI (competing risk = NRM) If we use Kaplan Meier, patients who die from NRM are censored : 1. Patient who died from NRM are not remaining at risk of relapse 2. Censoring is not independent 3. The number of patients at risk of relapse decreases and the probability of

relapse tends to 1 => Overestimation of the probability of relapse. The Kaplan-Meier estimator is biased in the presence of competing risks

Statistical methods – Competing risks

Cumulative incidence functions Crude probability of each event = probability of a specific event in the presence of all other risks acting on the population  Defined as the probability of failing from cause k before time t  Depends on the hazard of both competing events

Statistical methods – Competing risks Kaplan Meier and cumulative incidence curves KM curves - Censoring at the occurrence of a competing event - Final estimation of each event tends to 1

CI curves - Increase from 0 up to the total rate ( Wilcoxon test … • late outcome • difference at a specific point => Klein et al, Logan et al

Statistical methods – Survival endpoint Multivariate analysis – Cox model Proportional hazards Hazard rate of A: hA(t) Hazard rate of B: hB(t) Hazard ratio = Ratio of these hazards

HR(t ) 

h A (t ) hB (t )

Both hA(t) and hB(t) depend on time => in principle, HR(t) would also depend on time

Proportional hazards assumption : HR(t) is constant and does not depend on time

Statistical methods – Survival endpoints Cox model - Interpretation of the results HR=1 indicates that the risk is the same

HR>1 indicates that the risk is higher in group A HR auto selection of a bad prognostic group.

Intermediate event CANNOT be included as a fixed-time covariate

Intermediate events

How do we deal with this situation?

- Landmark analysis - Time-dependent covariates

Intermediate events Landmark analysis  Popularized by Anderson et al (1983) Fix a point in time t*: the landmark point Define covariates based on observations known before t* Study with the usual methods

Selection of landmark : Before analysis Based on some natural time of clinical significance

Intermediate events

Landmark analysis

Estimation of the OS after transplantation Survival analysis with another time origin (landmark ) = SCT Patients who die before the SCT do not contribute to the analysis Estimation of prognostic factors on patients who have received the transplant

Intermediate events Cox with intermediate event •

IE included as a time dependent variable in the model => modification of its value during time (ex SCT=“no” until SCT=“yes”)  comparison in time of patients at each time  series of landmark analysis On Study

SCT = 0

SCT = 1

Dead

SCT

-> evaluation of the effect of the IE on the estimation of survival

Intermediate events

Cox with time dependent variable : limitations Assumption : effect of the IE immediately after IE Sometimes not reasonable in practice: risk of death increase due to SCT

and then begin to decrease steadily

IE could reflect an auto selection of patients with low hazard independently on the real effect of the IE -> avoid the statement : « SCT reduces the risk of death of 20 % »

Cgvhd slide

P=0.003

Landmark at day 100

P=0.81

Statistics & HSCT – Conclusion

 Endpoints are well defined after HSCT: they are most often censored

data, some of them are competing events Analysis:

Univariate: -> Kaplan Meier & Log rank for survival-like endpoints -> Cumulative incidence and Gray test for competing events Multivariate : Cox and Fine-Gray models  Specific methods for intermediate events after transplant: landmark,

time dependent variables…