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 Sommer 1 , Martin Wolkewitz 1 , Jan Beyersmann 2 , and Martin Schumacher 1 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 e 1,5 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 Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 3
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 Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 4
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 Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 5
Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work Mathematical Background competing risks model (multiple absorbing endpoints) 1 λ 01 ( t ) ◮ event-specific hazard rate P ( t < T ≤ t + h ; cause i | T > t ) λ 0 i ( t ) = lim h → 0 h 0 � � t � ◮ P 00 ( 0 , t ) = S ( t ) = exp � 2 i = 1 λ 0 i ( u ) du − 0 ◮ cumulative incidence function λ 02 ( t ) 2 � t P 0 i ( 0 , t ) = 0 P 00 ( 0 , u ) λ 0 i ( u ) du depends on all event specific hazards! illness-death-model without recovery 1 λ 01 ( t ) illness-death-model without recovery λ 12 ( t ) 0 ◮ transition probability � t P 01 ( 0 , t ) = 0 P 00 ( 0 , u ) λ 01 ( u ) P 11 ( u , t ) du � ���� �� ���� � λ 02 ( t ) � t � � 2 = exp − u λ 12 ( v ) dv P 02 ( 0 , t ) = 1 − ( P 00 ( 0 , t ) + P 01 ( 0 , t )) Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 6
Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work The Cure-Death Model randomization 30 days cure λ 01 ( t ) λ 12 ( t ) randomization λ 02 ( t ) death “Although many experts believe that mortality is the ultimate patient-centered outcome 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 Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 7
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 over 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 Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 10
Introduction Mathematical Background The Cure-Death Model Application Discussion and Future Work Ceftobiprole (ITT) Ceftobiprole 400 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 300 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● individuals ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● during treatment ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● cure ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● death ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● death after cure ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● ● ● censored 0 10 20 30 40 50 time from randomization Harriet Sommer The Cure-Death Model August 25, 2015 (Utrecht) 11
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