The Cure-Death Model A new approach for a randomised clinical trial - - PowerPoint PPT Presentation

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

The Cure-Death Model

A new approach for a randomised clinical trial design to increase efficiency of clinical endpoint evaluations

ISCB 2015 (Utrecht)

Harriet Sommer1, Martin Wolkewitz1, Jan Beyersmann2, and Martin Schumacher1

1 Institute for Medical Biometry and Statistics, Medical Center – University of Freiburg (Germany) 2 Institute of Statistics, Ulm University (Germany)

Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 1

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Introduction – ND4BB

◮ 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), started Jan 2013

Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 2

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

ND4BB – COMBACTE

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

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

◮ recommendations given by the existing guidelines (see e.g. FDA or EMA)

are not consistent nor is their practical application

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

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, compare treatments

◮ develop a statistical test technique for the difference of two

treatments

◮ extend test technique for a combination of non-inferiority and

superiority

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

trial and improve existing guidelines

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Mathematical Background

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))

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

The Cure-Death Model

randomization 30 days

randomization 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 Mathematical Background The Cure-Death Model Application Discussion and Future Work

Simulation

◮ we simulated different scenarios, compared the simple competing risks

model with the cure-death model and thus showed that mortality after being cured cannot be ignored either

◮ French OUTCOMEREA data provided a possibility to examine real death

rates for more realistic simulations

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

• ver time, so we also simulated transition probabilities with time-dependent

hazards

Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 8

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Ceftobiprole Trial by Basilea

Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 9

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Ceftobiprole Trial by Basilea

Awad et al., Clinical Infectious Diseases, 2014

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Ceftobiprole (ITT)

10 20 30 40 50 100 200 300 400

Ceftobiprole

time from randomization individuals

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• during treatment
• cure

death death after cure censored

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Adapted Cure-Death Model

◮ primary endpoint: clinical cure at test of cure (TOC) visit ◮ special feature of the given data: patients after TOC are no longer

under risk for transition 0 − >1

⇒ adapt model to obtain appropriate risk set!

randomization (0) TOC: cure (1) death (2) TOC: failure (3)

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Comparison ITT: (HAP excluding VAP)

10 20 30 40 0.0 0.2 0.4 0.6 0.8

ITT: Cure (HAP excluding VAP)

time from randomization probability to be cured and stay cured Ceftobiprole Linezolid/Ceftazidime 10 20 30 40 0.0 0.2 0.4 0.6 0.8

ITT: all Death (HAP excluding VAP)

time from randomization probability to die Ceftobiprole Linezolid/Ceftazidime Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 13

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Comparison ITT: (only VAP)

10 20 30 40 0.0 0.2 0.4 0.6 0.8

ITT: Cure (only VAP)

time from randomization probability to be cured and stay cured Ceftobiprole Linezolid/Ceftazidime 10 20 30 40 0.0 0.2 0.4 0.6 0.8

ITT: all Death (only VAP)

time from randomization probability to die Ceftobiprole Linezolid/Ceftazidime Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 14

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Conclusion

◮ the recent published Ceftobiprole trial by Basilea is a suitable study to

test this model, with a complete follow-up (up to 30 days)

◮ model has to be adapted if cure can only be recorded at one time point ◮ Ceftobiprole is non-inferior to Ceftazidime/Linezolid for patients with HAP

(N=781) and HAP excluding VAP (N=571); non-inferiority was not demonstrated in VAP patients (N=210)

◮ temporal dynamic of the probability to be cured and stay cured and the

probability to die was not considered in the paper but displayed by the cure-death model

◮ analysis using only clinically evaluable patients (per protocol and

considered relevant in non-inferiority studies) might be overoptimistic: probability to be cured and stay cured too high, probability to die too low

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Discussion and Future Work I

◮ recommendations given by the existing guidelines (see e.g. FDA or EMA)

regarding the selection of primary endpoints in anti-infectives studies are not consistent nor is their practical application

◮ Harhay et al. (2014) 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 ◮ still, an agreement for the cure definition has to be made for future trials

→ a delphi technique with a panel of intensivists is planned

◮ include frailty term to adjust for heterogeneity between different ICUs

(see e.g. Ceftobiprole trial: conducted at 157 sites in Europe, North and South America, and the Asia-Pacific region)

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Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Discussion and Future Work II

◮ following step: two-armed clinical trial design, compare treatments

◮ develop a logrank-type or Gray-type statistical test technique for

the difference of two transition probabilities [or two (cumulative) hazards]

◮ alternative: test based on simultaneous confidence bands for the

difference of two transition probabilities [or two cumulative hazards] → use the wild bootstrap according to Lin (1997); see talk of Tobias Bluhmki in session C09

◮ extend test technique for a combination of non-inferiority and superiority ◮ aim: provide an analysis strategy that is preconditioned for a trial design

and improve existing guidelines

Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 17

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Some References

Andersen PK, Keiding N. Multi-state models for event history analysis. Statistical Methods in Medical Research. 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 Microbiology. 2014 Beyersmann J, Di Termini S, Pauly M. Weak convergence of the wild bootstrap for the Aalen–Johansen estimator of the cumulative incidence function of a competing risk. Scandinavian Journal of Statistics. 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. American Journal of Respiratory and Critical Care
• Medicine. 2014

Lin DY. Non-parametric inference for cumulative incidence functions in competing risks studies. Statistics in Medicine. 1997 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 Medicine. 2014 Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 18

Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work

Backup

Nosocomial Pneumonia Study BAP248/307 Analysis of HAP versus VAP

Ceftobiprole Linezolid/Ceftazidi me N n (%) N n (%)

• Difg. (%)a

95% CI # Intent-to-treat Nosocomial Pneumonia (all) 391 195 (49.9) 390 206 (52.8) −2.9 (−10.0 ; 4.1) HAP (excluding VAP) 287 171 (59.6) 284 167 (58.8) 0.8 (−7.3 ; 8.8) VAP 104 24 (23.1) 106 39 (36.8) −13.7 (−26.0; −1.5) Clinically evaluable Nosocomial Pneumonia (all) 251 174 (69.3) 244 174 (71.3) −2.0 (−10.0 ; 6.1) HAP (excluding VAP) 198 154 (77.8) 185 141 (76.2) 1.6 (−6.9 ; 10.0) VAP 53 20 (37.7) 59 33 (55.9) −18.2 (−36.4; −0.0)

n is the number of subjects with clinical cure at TOC.

a Difgerence ceftobiprole minus linezolid/ceftazidime. # T

wo‑sided 95% CI is based on the Normal approximation to the difgerence of the two proportions.

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