Impact of immortal time

and selection bias on

exposure-response

modelling

Mats O Karlsson

Uppsala University, Uppsala, Sweden

Immortal time is a span of cohort follow-up during which,

because of exposure definition, the outcome under

study could not occur.

Suissa, Am J Epidemiology, 2008

Immortal time bias

Subjects are classified according to a variable

occuring after baseline, for example

- Receiving tea and crumpets (Ho et al., 2013)

- Having a drug-related side-effect

- Having a cancer recurrence

- Having a measureable drug exposure

Immortal time bias, cont’d

A continuous variable, assessed post-baseline, is

used in survival analysis as if it was available at

baseline, for example

- Chemotherapy dose-intensity

- Adherence to therapy

- Total cumulative exposure (AUC)

- Maximal in reduction in tumor size

Depth of tumor response

McCoach et al. Ann Oncol 2017 28(11):2707-2714

Response by Weber et al., Ann Oncol 2018 29(1):282-3

How handle post-baseline

information?

Do not assume that post-baseline information is

available already at baseline

Do not use information from the future to predict

the present survival

Alternatives for using post-baseline information:

Time-varying covariates

Landmark analysis (with dynamic prediction)

Joint models (events/time-varying covariates)

Dynamic prediction using

landmark analysis

Landmarking: covariate regression coefficients

Note, graph is from a different example

Hein Putter. The landmark approach, Dynamic prediction workshop, Bordeaux 2013

Multi-State Markov model

Parameter estimates of the multi-

state model

Modelling alternatives

Markov model for ACR20 responder,

non-responder and dropout

Lacroix et al., Clin Pharmacol Ther, 2009

1Responder

0Non-

Responder

2Dropped

out

Pr00 of remaining

non-responder

Pr11 of remaining

responderPr10 of becoming

responder

Pr01 of becoming

non-responder

Pr12 of

dropping out

Pr02 of

dropping out

Sleep state model

Karlsson et al., Clin Pharmacol Ther 2000

Time in stageP

robabili

ty o

f

falli

ng a

sle

ep

Concentration

Pro

babili

ty o

f

falli

ng a

sle

ep

Time of night

Pro

babili

ty o

f

falli

ng a

sle

ep

Stomach

F = proximal stomach

A = distal stomach

Small intestine

SI:1-4 transit

Colon

AC = Ascending colon

TC = Transverse colon

DC = Descending colon

KSI

FA

SI:1 SI:2 SI:3 SI:4

AC

KFA

KAF

KAS

KSI KSI KSI

TCDC

KTC KAC

SCR

KDC

Sigmoid colon /

Rectum

Bergstrand et al., CPT 2009

Gastro-intestinal tablet transit model

Competing risks analysis of the Finnish

diabetes prevention study

Ibrahim et al., PAGE 2019

Parametric models for analysis

of time-to-event data

+ Flexible in model definition

+ Can handle many complexities

Competing risks

Interval censoring

Multiple absorbing states

Time-varying covariates in multi-state models

Joint models (PK/PD/TTE/RTTE)

Predicted outcomes driving hazard

Continuous time integration

- Complex model building

- Parametric model assumptions

Tumor growth inhibition model (TGI)

𝑑𝑆𝐿𝐷

𝑑𝑡= 𝑘𝐺𝑅𝑂𝑊 ∙ 𝑆𝐿𝐷 𝑡 − 𝑘𝐷𝑅𝑈𝐺 ∙ 𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝑡 ∙ 𝑒−𝜆∙𝑡 ∙ 𝑆𝐿𝐷 𝑡

𝑑𝐷𝑜𝑐𝑒𝑡𝑎𝑥𝑒𝑙

𝑑𝑡= −𝑘𝐾𝑃𝐷 ∙ 𝐷𝑜𝑐𝑒𝑡𝑎𝑥𝑒𝑙 𝑡

𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝑡 = 𝐷𝑜𝑐𝑒𝑡𝑎𝑥𝑒𝑙 𝑡

Claret et al., J Clin Oncol 2009.

Bender et al., PAGE 2017

Mixture multi-state model (MMSM)

Progression

107

Stable

0

Decrease

14

Death

340

Second line

88

225

314

10

180

155

31

144

Sreenath Krishnan, Lena Friberg, Mats Karlsson, for illustration

Covariate effects

Progression

Stable

Decrease

Death

Second line SLD0

SLD0

dSLD

TTP

AGE

SLD0 TTP

AGE

Increases the HZ of transition

Decreases the HZ of transition

SLD0 = baseline SLD

dSLD = SLDt-1-SLDt-2

TTP = time to progression

Sreenath Krishnan, Lena Friberg, Mats Karlsson, for illustration

ID=1

ID=1

ID=1

ID=1

ID=1

ID=1

Selection bias

Dose ranging without exposure information quantifies relation in Fig 2

Exposure measure after single dose level can’t distinguish between Fig 1 and 2

Dose ranging with exposure information may allow quantitation of both dose and

exposure effect and to what extent the latter is correlated to outcome

Hernan et al., Epidemiology 2004

Trastuzemab – clinical development

Shah et al., J Clin Oncol 2017Bang et al., Lancet 2010

Cosson et al., Cancar Clin Pharmacol 2014

Lyuak et al., Clin Transl Sci (2019) 12, 481-489

Analyzed 69 Pfizer dose-ranging studies

68 of these studies were well described by an Emax model

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20

Effe

ct

Dose

Emax model properties:

D90/D10 = 81

Comparison of aspects

for exposure-response

Non-oncology

Small molecule

Oncology

mAb

Dose-range for efficacy wide / moderate none / narrow

Drug PK correlated with

disease

seldom often

Elimination routes renal / hepatic target-mediated / FcRn

receptor levels / cachexia

/ hypermetabolism / ADAs

/…

Time-varying PK seldom / well understood often / poorly understood

Variability in exposure

2-arm dose-ranging versus CL

Drug %CV CL

Nivolumab 43%

Ipilimumab 40%

Tremelimumab 38%

Docetaxel 41%

0%

20%

40%

60%

80%

100%

120%

0 2 4 6 8

Exp

osu

re v

aria

bili

ty (

%C

V)

[High dose - Low dose]/[low dose]

Summary

To addressing immortality bias, use

time-varying covariates

dynamic predictions using landmarking

parametric models

Selection bias in exposure response analysis

If only one dose level, don’t trust exposure

response analyses

Clinical trial simulations may be effective to

learn about (modest) dose-ranging studies

Thank you!

Milligan et al. Clin Pharmacol Ther 93:502-14 (2014)

Root causes for the inability of the emerging

study efficacy data to correspond to the

study’s a priori efficacy hypothesis

Milligan et al. Clin Pharmacol Ther 93:502-14 (2014)

Implementation dose-finding trials

Milligan et al. Clin Pharmacol Ther 93:502-14 (2014)

Causes of Compound Failure: 2007 -

2010 and 2013 - 2015

Phase 2 Phase 3

Arrowsmith J. Nat Rev Drug Discov 2011;10: Feb; Arrowsmith J. Nat Rev Drug Discov 2011;10: May; Harrison RK. Nat Rev Drug Discov 2016;15:817-8

Phase 2 Phase 3

(Lack of) Efficacy

continues to be the

major cause of failure