time dependent and landmarking analysis - skion · pdf file-5pt time-dependent covariates...

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Time-dependent covariates Landmarking analysis

Time Dependent and Landmarkinganalysis

Marta Fiocco

Department of Medical Statistics and BioinformaticsLeiden University Medical Center

Dutch Children Oncology Group (DCOG)

Utrecht, April 3, 2014

Time Dependent variables and Landmarking analysis Marta Fiocco

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Outline

Time-dependent covariates

Landmarking analysis...in action...


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I Typical question: what is the effect of response tochemotherapy on survival?

I Common way of analysis: make two groups, a ’responder’group and a ’non-responder’ group and compare survivalbetween these two groups

I Problem with this approach: a potential responder will onlybelong to the ’responder’ group if he/she survives until timeof response

I Individuals in the responder group are immortal for sometime, this gives them an unfair survival advantage:’immortal time bias’


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A nice example

Do Oscar-winners liver longer?

I In a paper by Redelmeier and Singh (Ann Intern Med2001), the authors showed that Oscar-winning actors andactresses lived longer than their peers (almost 4 yearslonger then their less successful peers)

I Does this mean that an actor/actress will live longer whenhe/she receives an Oscar?

I In the 2001 paper the authors combined all winners intoone group and all losers into another group and comparedwinners’ and non-winners’ survival from birth.


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Kaplan-Meier winners versus non-winners; log-rank testgives as p-value: 0.005


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I Does the analysis suggests that an actor/actress will livelonger when he/she receives an Oscar?

I With this approach winning the prize gets credit for howlong the winner lived before winning the prize

I An actor/actress has to be alive to receive an Oscar, soOscar-winning actors are older, not get older

I Well known "immortal time"


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Two correct approaches:

time-dependent covariates

Landmark analysis

I Define Z (t) as response by time tI Z (t) = 0, for all t before the time of responseI Z (t) = 1, for all t after time of response (if ever)

I Extend the Cox model to

h(t | Z (t)) = h0(t)exp(βZ (t))

I So

h(t | Z (t)) ={

h0(t), before response;h0(t)exp(β), after response.


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Oscar data

I Perform the analysis by using a time-dependent approachto reflect the fact that all started out as non-winners butthat some changed status over time

I p-value: 0.674

p-value: 0.674


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I Leukemia: patients might experience GVHD after trasplantI code the time-dependent covariate which is the indicator

that a patient has developed GVHD prior to time tI The GVHD covariate is initially zero and changes to a

value of one at the time GVHD is diagnosed for the patient


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I Effect of GVHD on outcome when coded incorrectly as ifknown at transplant


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I These results tell us that a patient’s risk of treatment failureincreases by 1.975 when they develop acute GVHD

I There is no effect on outcome due to chronic GVHDI If we incorrectly coded acute and chronic GVHD as if the

occurrence were known at the time of transplant (as fixedcovariates) then it appears that chronic GVHD has a highlysignificant benefit to the patient (HR=0.29, p<0.0001)

I This apparent benefit is entirely due to the fact thatpatients need to live to at least 100 days or more todevelop chronic GVHD

I When modelled correctly this ’benefit’ is not observed(HR=0.943, p=0.505)


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I The length of survival itself will influence the chance of apatient being classified into one group or the other

I Patients who eventually become responders must survivelong enough to be evaluated as responders

I This so-called guarantee time is at least as long as thetime to the first response evaluation

I This requirement of a longer survival time also provides agreater opportunity for the therapy to produce a response

I No such guarantee time is required for the non-respondergroup since patients who die during the period before thefirst response evaluation are automatically included in thenon-response group

I Patients with poor survival prognosis who die early in thestudy will not have an opportunity to enter the respondergroup and will guarantee poorer survival for thenon-response group.


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Outline

Time-dependent covariates

Landmarking analysis...in action...


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Origin of landmarking

I Origin: debate on the effect of response to chemotherapyon survival (Anderson JR, Cain KC, Gelber RD, 1983, JClin Oncol 1, 710-719)

I Common way of analysis: make two groups, a ’responder’group and a ’non-responder’ group and compare survivalbetween these two groups

I Problem with this approach: a potential responder will onlybelong to the ’responder’ group if he/she survives until timeof response

I Individuals in the responder group are immortal for sometime, this gives them an unfair survival advantage:immortal time bias


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I Crucial issue: ’responder’ versus ’non-responder’ issomething that is not known at baseline

I When studying survival, it is not allowed to make groupsbased on something that will happen in the future


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...in action...

Simulated data loosely based on response tochemotherapy

I n = 100I Time to response Tresp uniform on (0, 1) with probability

0.5, no response Tresp = ∞with probability 0.5I Time to deathTdeath exponential with mean 1, alert

independent of Tresp

I Could happen before response, in which case response isnot observed

I Censoring at 2 (years)


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...in action...


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...in action...

Groups made based on response status


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...in action...

AnalysesWrong

I Use response status at end of follow-up as if that wasknown at baseline

I Cox regression gives estimated coefficient of -0.890 withSE of 0.235 (p=0.00015)

I Response to chemotherapy significantly improves survival

Correct I

I Use response status as time-dependent covariateI Cox regression gives estimated coefficient of -0.176 with

SE of 0.258 (p=0.50)I Response to chemotherapy does not affect survival


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...in action...

Analyses

Correct II

I Fix landmark time point tLM

I Create a "landmark data set" byI Removing everyone with event or censored before tLMI Creating response groups based on response status at tLM

I Perform Cox regression with these response groups astime-fixed covariate

I Illustrated for series of landmark time pointstLM = 0.25,0.5, . . .1.5,1,75


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...in action...


time dependent and landmarking analysis - skion · pdf file-5pt time-dependent covariates...

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