Evaluation of methods that adjust for treatment switching in clinical trials Richard Fox a , Lucinda Billingham a b , Keith Abrams c a Cancer Research UK Clinical Trials Unit, University of Birmingham, UK b MRC Midland Hub for Trials Methodology Research, University of Birmingham, UK c Centre for Biostatistics and Genetic Epidemiology, University of Leicester, UK
I NTRODUCTION Patients in RCTs may switch treatments for reasons associated with their illness Treatment switching dilutes estimates of treatment efficacy From a review of trials featuring treatment switching we observed 84% switching in one trial Progression Control Randomised Switch to intervention Intervention We investigate this scenario (switch control to intervention) 2
M ETHODS 9 methods identified Hazard (6) and Time Ratio (3) scales Time ratios Measure of treatment effect Extent survival time is modified by treatment e.g. TR=2 implies survival time doubled on average Some methods have numerous test / assumptions 3
M ETHODS - H AZARD R ATIO SCALE Intention to treat (ITT) 1. Per-protocol 2. Delete patients that switch (PPD) i. or Censor at time of switch (PPC) ii. Time varying covariate (TVC) 3. Adjusted Cox Model (AdjCox) Law & Kaldor 1996 1 4. Causal PH estimator (CaPH) Loeys & Goetghebeur 2003 2 5. Inverse Probability Treatment Weighting (IPTW) 6. Hernan et al 2000 3 4
M ETHODS - T IME R ATIO SCALE Rank preserving structural failure time model (RPSFT) 1. Multiple tests (*4) Robins & Tsiatis 1991 4 i. Iterative parameter estimation (IPE) Branson & Whitehead 2002 5 2. Parametric randomisation based method (PRB) 3. Walker et al 2004 6 5
S IMULATING SURVIVAL DATA Survival data has Weibull distribution ( λ =1.01, γ=0.5 ) AFT property: dividing log HR by shape parameter (γ) returns acceleration parameter (TR) 7 e.g. exp(-ln(HR)/ γ ) = exp(-ln(0.7)/0.5) = 2.04 Patients randomised to control or intervention (1:1) Controlled parameters creating 24 scenarios Treatment effect % good vs bad prognosis within arm P(switching | prognosis) Survival / Switching times scaled by prognosis Censoring % Review of NICE technology appraisals informed the above 6
S WITCHING TRIGGER IPTW method requires a time dependent covariate related to treatment switching / compliance Designed biomarker level Δ ≥ 20%triggers a switch (from baseline) Beyond switching time level fluctuates around Δ = 20%level Non-switching patients Δ < 20% 25% Switching patient 20% Compliant patient 15% % Change 10% 5% 0% Months 7
A SSESSING METHODS ˆ % Bias ( ) i * 100 Standard-error of the effect-size SE ( ˆ i ) Mean Square Error (combines above) i ) 2 SE ( ˆ ( ˆ i ) 2 Coverage % estimates where 95% CI includes true effect size % successful estimates Averaged over 1000 simulated datasets for each scenario 8
R ESULTS – L OW B IAS S CENARIOS Scenario P(switch|prognosis) % Good prognosis Effect size (Switching) within treatment group Poor prognosis Good prognosis (HR / TR) 1 (Low) 75% 0.5 0.25 0.7 /2.04 2 (Low) 50% 0.5 0.25 0.7 /2.04 H AZARD R ATIO S CALE Scenario 1 (Low Switching) Scenario 2 (Low Switching) PRB -5% -11% True effect (TR 2.04) Scenario 1 (Low Switching) Scenario 2 (Low Switching) IPTW -33% -24% -3% -4% IPE True effect (HR 0.7) -6% -20% CaPH -10% -6% RPSFT - Exp 4% 11% ADJCox 41% 190% -3% TVC RPSFT - Cox -7% PP - Censor 38% 201% RPSFT - LR -7% -3% 11% 66% PP - Delete -6% -3% RPSFT - Wei 6% 14% ITT T IME R ATIO S CALE 9
R ESULTS – H IGH B IAS S CENARIOS Scenario P(switch|prognosis) % Good prognosis Effect size (Switching) within treatment group Poor prognosis Good prognosis (HR / TR) 3 (High) 50% 0.85 0.25 0.5 / 4 4 (High) 75% 0.85 0.5 0.5 / 4 H AZARD R ATIO S CALE Scenario 3 (High Switching) Scenario 4 (High Switching) PRB -7% -4% True effect (TR 4) Scenario 3 (High Switching) Scenario 4 (High Switching) IPTW -12% -7% -3% True effect (HR 0.5) -6% IPE CaPH -17% -50% -8% -12% RPSFT - Exp ADJCox 8% 20% RPSFT - Cox -8% -6% TVC 58% 217% PP - Censor 48% 201% -8% -6% RPSFT - LR PP - Delete 14% 71% -7% -5% RPSFT - Wei 15% 28% ITT T IME R ATIO S CALE 10
R ESULTS – E RRATIC R ESULTS PRB can return erratic results Sensitive to specification of frailty Erratic PRB method PRB -2% True effect (TR 2.04) IPE -3% -7% RPSFT - Exp RPSFT - Cox -3% RPSFT - LR -3% -3% RPSFT - Wei P(switch|prognosis) % Good prognosis within Effect size Scenario treatment group Poor prognosis Good prognosis (HR / TR) Morden 8 - Sc 6 30% 0.75 0.5 0.7 / 2.04 11
R ESULTS – K EY F INDINGS Switching is common in clinical trials ITT results can be heavily biased Per-protocol is not appropriate where switching occurs Adjustment not routinely applied Some of the methods available (Stata) RPSFT and IPE consistent under these conditions IPE has 100% successful estimation IPE also returns estimates of the Weibull parameters Results robust to additional censoring 12
C ONCLUSION We recommend that the IPE method of Branson & Whitehead be utilised in the analysis of clinical trials that feature treatment switching. Available from Ian White’s software page: http://www.mrc-bsu.cam.ac.uk/Software/stata.html#Software_IW My email: foxrp@bham.ac.uk 13
E XTENSIONS Simulate alternative survival distributions Additional covariates Multiple switching directions Dependent censoring Other methods Meta / Bayes analysis Structural nested mean models Statistical analysis plan – sensitivity 14
R EFERENCES Law and J Kaldor. Survival analyses of randomised clinical trials adjusted for patients who switch 1. treatment. Stat Med, 15:2069-2076, 1996. T Loeys and E Goetghebeur. A causal proportional hazards estimator for the effect of treatment 2. actually received in a randomised trial with all-or-nothing compliance. Biometrics, 59(1):100-105, 2003. M Hernan, B Brumback, and J Robins. Marginal structural models to estimate the causal effect of 3. zidovudine on the survival of hiv-positive men. Epidemiology, 11(5):561-570, September 2000. J Robins and A Tsiatis. Correcting for non-compliance in randomised trials using rank preserving 4. structural failure time models. Communication in Statistics-Theory and Methods, 20(8):2609-2631, 1991. M Branson and J Whitehead. Estimating a treatment effect in survival studies in which patients 5. switch treatment. Stat Med, 21:2449-2463, 2002. S Walker, I White, and A Babiker. Parametric randomization-based methods for correcting for 6. treatment changes in the assessment of the causal effect of treatment. Stat Med, 23:571-590, 2004. Collett, D. (2003), Modelling Survival Data in Medical Research (2nd ed.) 7. J Morden et al. Assessing methods for dealing with treatment switching in randomised controlled 8. trials: a simulation study. BMC Med Res Methodol. 2011 Jan 11;11:4. 15
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