A Multistate Model for Cure and Death ois Timsit 2 and Martin - - PowerPoint PPT Presentation

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

A Multistate Model for Cure and Death

Harriet Sommer1, Martin Wolkewitz1, Jean-Franc ¸ois Timsit2 and Martin Schumacher1

• n behalf of COMBACTE consortium

1 Institute for Medical Biometry and Statistics –

University Medical Center Freiburg (Germany)

2 Bichat Hospital – Paris Diderot University (France)

March 17, 2015 (Dortmund)

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 1

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Introduction

◮ antimicrobial resistance is a growing problem worldwide ◮ evaluated to the top three threats identified by the WHO – estimated 25.000

deaths and e1,5 Billion per year in Europe

◮ urgent need for new medicines ◮ to tackle antimicrobial resistance, the Innovative Medicines Initiative (IMI)

set up the New Drugs for Bad Bugs Programme (ND4BB) with several calls for different (sub-)topics including Combatting Bacterial Resistance in Europe (COMBACTE)

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 2

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

ND4BB – COMBACTE

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 3

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

ND4BB – COMBACTE – STAT-Net

◮ COMBACTE includes several networks, e.g. STAT-Net (research platform) ◮ motivation of STAT-Net: evaluate novel clinical trial design strategies

based on modern biostatistical and epidemiological concepts to increase efficiency and success rates of clinical trials

◮ clinical trials with patients that suffer from severe diseases and an

additional resistant infection

◮ in this population, a mortality rate of about 10% up to 30% can be

assumed within 30 days

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 4

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

ND4BB – COMBACTE – STAT-Net

◮ the new treatment should improve the cure rates (clinical cure or

microbiological cure – difficult to define)

◮ we have to understand the etiological process how the new treatment

influences the cure process ⇒ multistate model

◮ following step: two-armed clinical trial design

→ new treatment should be superior regarding cure and non-inferior regarding death → develop a test technique for the combination of non-inferiority and superiority

◮ aim: provide an analysis strategy that is preconditioned for planning such a

trial

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 5

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Mathematical Background

0: alive 1: dead λ(t)

◮ simplest multistate model: transition from initial state 0 (e.g. alive) to

absorbing state 1 (e.g. dead) at some random failure time T (survival time)

◮ hazard rate λ(t) = lim

h→0 P(t<T≤t+h|T>t) h

instantaneous probability per time unit of going from state 0 to state 1 (transition intensity)

◮ survival function

S(t) = P(T > t) = 1 − P(T ≤ t) = 1 − F(t) = exp

• −

t

0 λ(u)du

• S(t) = probability of being in state 0 at time t

F(t) = probability of being in state 1 at time t F(t) = or transition probability from state 0 to state 1 for [0, t]

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 6

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Competing Risks

1 2 λ01(t) λ02(t) 1 2 λ01(t) λ02(t) λ12(t)

competing risks model (multiple absorbing endpoints) ◮ event-specific hazard rate λ0i(t) = limh→0

P(t<T≤t+h; cause i|T>t) h

◮ P00(0, t) = S(t) = exp

• −

t 2

i=1 λ0i(u)du

• ◮ cumulative incidence function

P0i(0, t) = t

0 P00(0, u)λ0i(u)du

depends on all event specific hazards! illness-death-model without recovery illness-death-model without recovery ◮ transition probability P01(0, t) = t

0 P00(0, u)λ01(u)

P11(u, t)

• =exp
• −

t

u λ12(v)dv

• du

P02(0, t) = 1 − (P00(0, t) + P01(0, t))

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 7

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

The Cure-Death-Model

randomisation 30 days

Infection Cure Death

λ01(t) λ02(t) λ12(t)

“Although many experts believe that mortality is the ultimate patient-centered

• utcome for critically ill patients, others have called for greater use of nonmortal

clinical endpoints [. . . ]. Unfortunately, nonmortal endpoints face [. . . ] the limits of commonly used statistical methods for addressing the competing risks and informative dropout attributable to high ICU mortality rates.” Harhay et al., Am J Respir Crit Care Med, 2014

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Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Analogies in Oncology

Tumour Response to treatment Death/Progression

◮ originally, these kind of models are used in cancer studies ◮ death or progression are competing events for the tumour response

(e.g. tumour shrinking by 50 per cent)

◮ naive analysis of time to response would ignore competing risks ◮ caution: So-called “cure-models” in oncology are different! They consider

cure not as outcome but as a state that prevents an observation of the

• utcome (e.g. recurrence or death).

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 9

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

OUTCOMEREA Data

◮ French multicenter study – includes 32 hospitals with a total of 6238 patients

ICU Infection Death Discharge Death Discharge

◮ use observational data to examine the underlying death hazard rate of

patients with infection, here: pneumonia, (0.0212) and without infection (0.0186)

◮ death rate after being cured in cure-death model should be similar to the

mortality rate for non-infected patients, at least for early deaths

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Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Simulation

With these rates, several simulation scenarios are examined: Infection Cure Death λ01(t)

0.0212 0.0186

scenario 1: λ01(t) = 0.02 scenario 2: λ01(t) = 0.04 scenario 3: λ01(t) = 0.06 scenario 4: λ01(t) = 0.08 scenario 5: λ01(t) = 0.1 scenario 6: λ01(t) = 0.12

10 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0 Time Transition Probability Probability to be Cured and stay Cured Probability for Death

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 11

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Simulation

Let us now set the rate from cure to death to 0.005: Infection Cure Death λ01(t)

0.0212 0.005

scenario 1: λ01(t) = 0.02 scenario 2: λ01(t) = 0.04 scenario 3: λ01(t) = 0.06 scenario 4: λ01(t) = 0.08 scenario 5: λ01(t) = 0.1 scenario 6: λ01(t) = 0.12

10 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0 Time Transition Probability Probability to be Cured and stay Cured Probability for Death

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Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Limitations

◮ estimation of baseline hazard functions shows that hazards are not constant

• ver time

◮ OUTCOMEREA data contains ICU mortality, in the cure-death-model

all-cause mortality will be considered

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Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Discussion and Future Work I

◮ Harhay et al. point out that nonmortal endpoints (here: cure) as well as

mortality are important for studies including critically ill patients → cure-death-model provides suitable conditions, handles competing risks

◮ simulation:

French OUTCOMEREA data provided a possibility to examine realistic death rates for first simulations (→ hazards are not constant over time) → simulate time-dependent hazards

◮ application:

up to now, application was not possible because of unsuitable data examples (too old, incomplete follow-up) → a suitable study to test this model, which provides a complete follow-up (up to 30 days), is the recent published ceftobiprole trial by Basilea → currently, the data transfer with Freiburg team is prepared

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 14

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Discussion and Future Work II

◮ still, an agreement for the cure definition has to be made

→ a delphi technique with a panel of intensivists is planned

◮ following step: two-armed clinical trial design

→ new treatment should be superior regarding cure and non-inferior regarding death → develop a test technique for the combination of non-inferiority and superiority and for the difference of two transition probabilities

◮ include frailty term to adjust for heterogeneity between different intensive

care units

◮ aim: provide an analysis strategy that is preconditioned for a trial design

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Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

References

Andersen PK, Keiding N. Multi-state models for event history analysis. Stat Methods Med Res. 2002 Awad SS, Rodriguez AH, Chuang YC, Marjanek Z, Pareigis AJ, Reis G, Scheeren TW, S´ anchez AS, Zhou X, Saulay M, and Engelhardt M. A phase 3 randomized double-blind comparison of Ceftobiprole Medocaril versus Ceftazidime plus Linezolid for the treatment of hospital-acquired pneumonia. Clinical Infectious Diseases. 2014 Bettiol E, Rottier WC, Del Toro MD, Harbarth S, Bonten MJ, Rodr´ ıguez-Ba˜ no J. Improved treatment of multidrug-resistant bacterial infections: utility of clinical studies. Future Microbiol. 2014 Beyersmann J, Schumacher M, Allignol A. Competing risks and multistate models with R. Springer. 2012 Binder N, Schumacher M. Missing information caused by death leads to bias in relative risk estimates. J Clin Epidemiol. 2014 Conlon ASC, Taylor JMG, Sargent DJ. Multi-state models for colon cancer recurrence and death with a cured fraction. Statistics in Medicine. 2013 Harhay MO, Wagner J, Ratcliffe SJ, Bronheim RS, Gopal A, Green S, Cooney E, Mikkelsen ME, Kerlin MP , Small DS, Halpern

• SD. Outcomes and statistical power in adult critical care randomized trial. Am J Respir Crit Care Med. 2014

Schmoor C, Schumacher M, Finke J, Beyersmann J. Competing risks and multistate models. Clin Cancer Res. 2013 Rondeau V, Mazroui Y, Gonzalez JR. Frailtypack: An R package for the analysis of correlated survival data with frailty models using penalized likelihood estimation or parametrical estimation. Journal of Statistical Software. 2012 OUTCOMEREA group. Noninvasive mechanical ventilation in acute respiratory failure: trends in use and outcomes. Intensive Care Med. 2014 Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 16

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Back-Up: Hazard Rate and Survival Function

λ(t) = lim

h→0

P(t < T ≤ t + h | T > t) h = lim

h→0

P(t < T ≤ t + h) h 1 P(T > t) = lim

h→0

P(T ≤ t + h) − P(T ≤ t) h 1 P(T > t) = lim

h→0

F(t + h) − F(t) h 1 S(t) = F′(t) S(t) = −S′(t) S(t) = − ∂ ∂t log S(t) ⇒ S(t) = exp

• −

t λ(u)du

• Sommer et al. (Freiburg)

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Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Back-Up: Competing Risks

P01(0, t) = t P00(0, u)λ01(u)du = t exp

• −

u (λ01(v) + λ02(v))dv

• λ01(u)du

= λ01 t exp (−(λ01 + λ02)u) du = λ01

• −

1 λ01 + λ02 exp (−(λ01 + λ02)u) t = λ01 λ01 + λ02 (1 − exp(−(λ01 + λ02)t)) P02(0, t) = λ02 λ01 + λ02 (1 − exp(−(λ01 + λ02)t))

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 18

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Back-Up: Meropenem Trial

◮ Sep 1991 – Jan 1993 by AstraZeneca ◮ for the treatment of patients with febrile neutropenia compare

Meropenem (carbapenem antibiotic by AZ) with Ceftazidime (third-generation cephalosporin β-lactam antibiotic)

◮ prospective, randomized and double-blind ◮ multi-centre (North-America and Netherlands) ◮ N = 411 cancer patients with 471 episodes of fever ◮ event of interest: successful clinical cure at the end of treatment

source: Feld R, DePauw B, Berman Sm Keating A, Ho W. Meropenem versus Ceftazidime in the treatment of cancer patients with febrile neutropenia: A randomized, double-blind trial. Journal of Clinical Oncology. 2000 Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 19

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Back-Up: Meropenem Trial

◮ “Patient deaths were recorded for the treatment period and the 7-day follow-up

period.”

◮ too short observation time ⇒ deaths not reported

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 20

Introduction COMBACTE Mathematical Background The Cure-Death-Model Simulation Discussion References

Back-Up: Meropenem Trial

◮ “Patient deaths were recorded for the treatment period and the 7-day follow-up

period.”

◮ too short observation time ⇒ deaths not reported

Sommer et al. (Freiburg) A Multistate Model for Cure and Death March 17, 2015 (Dortmund) 21