Inference on Treatment Effects from a Randomized Clinical Trial in the Presence of Premature Treatment Discontinuation: The SYNERGY Trial

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1 Inference on Treatment Effects from a Randomized Clinical Trial in the Presence of Premature Treatment Discontinuation: The SYNERGY Trial Marie Davidian Department of Statistics North Carolina State University Duke Clinical Research Institute davidian (Joint work with M. Zhang, A.A. Tsiatis, K. Pieper, and K. Mahaffey) Treatment Effects/Premature Discontinuation 1

2 Outline 1. Motivation: The SYNERGY trial 2. Conceptualization 3. A statistical framework 4. Inference 5. Implementation 6. Application to SYNERGY 7. Simulation studies 8. Discussion Treatment Effects/Premature Discontinuation 2

3 Motivation: The SYNERGY trial Duke Clinical Research Institute (DCRI): Part of Duke University Medical Center World s largest academic clinical research organization World leader in cardiovascular disease (CVD) research Has conducted/coordinated some of the pioneering, high-profile, international CVD clinical trials Studies for government, pharmaceutical/biotech/device companies Maintains large clinical registries, including the Duke Databank for Cardiovascular Disease Outcomes research, medical economics,... Treatment Effects/Premature Discontinuation 3

4 Motivation: The SYNERGY trial SYNERGY: The Superior Yield of the New strategy of Enoxaparin, Revascularization, and GlYcoprotein IIb/IIIa inhibitors trial Sponsored by Sanofi-Aventis, conducted by DCRI Randomized, open-label, multi-center trial with almost 10,000 high-risk patients with non-st segment elevation acute coronary syndromes likely to undergo PCI (angioplasty) or CABG (bypass) Compare the anticoagulants enoxaparin (Lovenox, ENOX, by injection every 12 hours) and unfractionated heparin (UFH, by IV bolus/continuous infusion) Primary endpoint: All-cause death or MI (myocardial infarction) within 30 days Secondary outcomes: All-cause death within 1 year, TIMI severe bleeding within 30 days Treatment Effects/Premature Discontinuation 4

5 Motivation: The SYNERGY trial SYNERGY protocol: Study drug to be continued until treating physician deemed no further anticoagulation required treatment completion Study drug to be mandatorily discontinued if bleeding, other adverse events, thrombocytopenia, need for CABG,... Optional discontinuation: In the trial Some subjects never received assigned study drug Some subjects stopped assigned study drug for reasons not sanctioned by protocol (e.g., MD or patient preference, etc) Some subjects switched (crossed over ) to the other drug; not sanctioned by protocol Fortunately: Times of completion and discontinuation with reasons were recorded on CRFs Treatment Effects/Premature Discontinuation 5

6 Motivation: The SYNERGY trial Results: Intent-to-treat analyses Primary analysis of 30 day death/mi: hazard ratio 0.95 ( ) Secondary analysis of 1 year death: hazard ratio 1.06 ( ) Contradicts previous findings showing ENOX superior to UFH Secondary analysis of TIMI bleeding: odds ratio 1.21 ( ) Higher risk, more aggressively managed patient population? Discontinuation? 24.4% (12.2% optional, 11.3% mandatory) of ENOX subjects vs. 14.4% (7.5% optional, 6.9% mandatory) of UFH subjects Question: What would have been the difference in UFH and ENOX survival distributions had no subject discontinued his/her assigned treatment? Treatment Effects/Premature Discontinuation 6

7 Motivation: The SYNERGY trial Proposed analyses: Delete all subjects discontinuing assigned study drug for any reason from the data set, do standard analysis Artificially censor outcomes for all subjects discontinuing assigned study drug for any reason at the times of discontinuation, do standard analysis Fit a proportional hazards (PH) model with binary time-dependent on/off indicators for each treatment Question: What would have been the difference in UFH and ENOX survival distributions had no subject discontinued his/her assigned treatment? What is really meant by this? Do any of these analyses address it? Treatment Effects/Premature Discontinuation 7

8 Motivation: The SYNERGY trial Our objective: An instructive demonstration of how to conceptualize this problem Systematic evolution of consulting problem to satisfactory solution More precise statement of the question Statistical framework = Inverse probability risk set weighting (Robins and Rotnitzky, 1992; Robins, 1993; Hernán et al., 2006) Treatment Effects/Premature Discontinuation 8

9 Conceptualization Ideal goal: Clinical trial with (possibly censored) time-to-event endpoint Difference in survival distributions were all subjects in the population to follow each of the treatment regimens studied Noninformative censoring, compliance with regimens = standard analyses (PH model, logrank) yield valid inferences on this effect Noncompliance = Intent-to-treat perspective Intent-to-treat does not address the ideal goal Treatment Effects/Premature Discontinuation 9

10 Conceptualization Following a treatment regimen: In principle: Subjects adhere to a prespecified, static plan of treatment administration (e.g., van der Laan and Peterson, 2007) However: Circumstances where discontinuation of regimen is mandatory, e.g., adverse event (safety, ethical reasons), CABG = Mandatory discontinuation is consistent with how treatment is intended to or must be administered = Following should acknowledge this Dynamic treatment regimes: Take ENOX (UFH) until completion or occurrence of an event meriting mandatory discontinuation (an algorithm for giving treatment) Treatment Effects/Premature Discontinuation 10

11 Conceptualization More realistic goal: Difference in survival distributions were all subjects in the population to follow each of the dynamic treatment regimes corresponding to ENOX and UFH Optional discontinuation: Is not consistent with how treatment is intended to or must be administered Would not happen with certainty Represents noncompliance with the dynamic treatment regimes Should thus be distinguished from mandatory discontinuation Treatment Effects/Premature Discontinuation 11

12 Conceptualization Question, better stated: What would have been the difference in survival distributions corresponding to the dynamic treatment regimes for ENOX and UFH had no subject discontinued his/her assigned treatment for optional reasons? Do the analyses mentioned previously address this? Problem: All are ad hoc, none arise explicitly from addressing this goal... Better idea: Define a statistical framework in which the treatment effect of interest corresponding to this question can be defined formally = suggest valid inferential methods Treatment Effects/Premature Discontinuation 12

13 Statistical framework Situation: As in SYNERGY Time-to-event outcome up to t max (e.g., 30 days, 1 year) Outcomes administratively censored at t max All subjects can be followed to t max whether or not they discontinue assigned treatment for any reason Outcomes censored prior to t max are administratively censored First step: Characterize the ideal situation with no optional discontinuation through t max Dynamic treatment regimes z = 0 (UFH) and 1 (ENOX) Continue on z until completion or event meriting mandatory discontinuation Treatment Effects/Premature Discontinuation 13

14 Statistical framework Important: Discontinuation is an action that can be imposed on a subject, not an outcome Potential outcomes: For treatment z T (z) = potential event time if no optional discontinuation through t max C (z) = potential censoring time through t max M (z) = potential time to mandatory discontinuation or treatment completion (whichever first) S (z) = min{t (z), C (z), M (z)} = time of first thing to happen V H (z, u) = history of post-randomization covariates through time u if no optional discontinuation through t max P = [T (z), C (z), M (z), S (z), V H (z, u), 0 < u S (z), z = 0,1] Also: Baseline covariates X Treatment Effects/Premature Discontinuation 14

15 Statistical framework Effect of interest: Model for (net-specific) hazard for T (z) λ z(t) = lim h 0 h 1 Pr{t T (z) < t + h T (z) t} = λ 0(t) exp(βz) β = log hazard ratio for regime 1 to regime 0 Can also consider hazard conditional on X, i.e., λ z(t X) = lim h 0 h 1 Pr{t T (z) < t+h T (z) t, X} = λ 0(t) exp(βz+γ T X) Treatment Effects/Premature Discontinuation 15

16 Statistical framework Ideal observed data: For a trial with n subjects and no optional discontinuations W i = {Z i, X i, U i, i, S i, E i, V H i (S i )}, i = 1,...,n Z i = observed (randomized) treatment assignment U i = min{t i (Z i), C i (Z i)} i = I{T i (Z i) C i (Z i)} S i = min{m i (Z i), U i } = time of first thing to happen E i = 1 if S i = M i (Z i), E i = 0 otherwise V H i (u) = V H i (Z i, u) Treatment Effects/Premature Discontinuation 16

17 Statistical framework Inference on β: Assume T (z) C (z), z = 0,1 Standard analysis Fit the (cause-specific) hazard model λ(t Z) = lim h 0 h 1 Pr(t U < t+h, i = 1 U t, Z) = λ 0 (t) exp(βz) Solve the partial likelihood score equation n { n j=1 Z i Z j exp(βz j )Yj (u) } n j=1 exp(βz j)yj (u) dni (u) = 0 i=1 N i (u) is the counting process I(U i u, i = 1) Y i (u) is the at-risk process I(U i u) S i, E i, V H u (u) not needed Treatment Effects/Premature Discontinuation 17

18 Statistical framework Actual observed data: Some subjects optionally discontinue W i = {Z i, X i, U i, i, S i, E i, V H i (S i )} Define O i = time to optional discontinuation (if subject does); otherwise, set O i = Time to failure/censoring U i ; censoring indicator i = 1 if failure, = 0 if censoring S i = min{o i, M i (Z i), U i }, E i = 1, 2, 3 if S i = O i, M i (Z i), U i = time of first thing to happen O i = S i I(E i = 1) + I(E i > 1) Counting process N i (u) = I(U i u, i = 1) At-risk process Y i (u) = I(U i u) Treatment Effects/Premature Discontinuation 18

19 Statistical framework The problem: Assume (U i, i ) = (U i, i ) if O i min{t max, M i (Z i), U i } Otherwise, (U i, i ) not necessarily equal to (U i, i ) So, for some subjects, only partial information on hazard for T (z) = Standard analysis using (U i, i ) in place of (U i, i ) for inference on β may not apply... Treatment Effects/Premature Discontinuation 19

20 Inference Standard analysis: Solve in β n { n j=1 Z i Z j exp(βz j )Yj (u) } n j=1 exp(βz j)yj (u) dni (u) = 0 i=1 Modification: Weight contributions of subjects in each risk set who have not yet optionally discontinued assigned treatment Hazard rate for O at u 0 given Q i = (P i, X i): Allow optional discontinuation at time 0 For u > 0 q(u, Z, Q ) = lim h 0 h 1 Pr(u O < u + h O u, Z, Q ) At u = 0, function with mass p 0 (Z, Q ) = Pr(O = 0 O 0, Z, Q ) = Pr(O = 0 Z, Q ) Treatment Effects/Premature Discontinuation 20

21 Inference Key: When u > S, q(u, Z, Q ) = 0 because no possibility of being observed to optionally discontinue once mandatory discontinuation/completion, censoring or failure has occurred Thus, for all realizations of Z and Q for which S u, for u > 0, q(u, Z, Q ) = lim h 0 h 1 Pr(u S < u + h, E = 1 S u, Z, Q ) (cause-specific hazard) Treatment Effects/Premature Discontinuation 21

22 Inference Critical assumption: For consistent estimation of β Similar to missing at random For Q(u) = {V H (u), X}, assume q(u, Z, Q ) = q{u, Z, Q(u)} for u S and p 0 (Z, Q ) = p 0 (Z, X) I.e., the hazard at time u depends on (Z, Q ) when S > u only through the data Q(u) observed to time u...and p 0 (Z, Q ) depends on Q only through X Plausible decision to optionally discontinue likely based on subject characteristics and experience up to time u Issue Was all relevant information captured in the trial and hence available in Q(u)? Treatment Effects/Premature Discontinuation 22

23 Inference Write: q{u, Z i, Q i (u)} and p 0 (Z i, X i ) Connection between ideal and actual observed data: Observed data counting process N i (u) = I(U i u, i = 1) and at risk process Y i (u) = I(U i u) Observe dn i (u) and Y i (u) on i only if O i u, i.e., I(O i u) dn i (u) = I(O i u) dn i (u) I(O i u)y i (u) = I(O i u)y i (u) = information on ideal comes only from individuals at risk who have not yet optionally discontinued Re-weight their contributions to mimic those had there been no optional discontinuation Treatment Effects/Premature Discontinuation 23

24 Inference Define: [ K{u, Z, Q( ), S} = {1 p 0 (Z, X)} exp u S 0 q{s, Z, Q(s)} ds ] means minimum of p 0 (Z, X) replaced by 0 if no optional discontinuations at time 0 Weighting: Replace dn i I(O i u)dn i (u) K{u, Z i, Q i ( ), S i } (u) and Yi (u) in ideal estimating equations by and I(O i u)y i (u) K{u, Z i, Q i ( ), S i } Expectations given Q are equal to dn i (u) and Y i (u) Treatment Effects/Premature Discontinuation 24

25 Inference Result: Solve in β n { n j=1 Z i Z } j exp(βz j )Y j (u)κ(u, W j ) n j=1 exp(βz κ(u, W i )dn i (u) = 0 j)y j (u)κ(u, W j ) i=1 κ(u, W) = w(u, Z) stabilizes the weights w(u, Z)I(O u) K{u, Z, Q( ), S} w(u, Z) 1 unstabilized inverse weights w(u, Z) = {1 p 0 (Z)} exp { u 0 r(s, Z) ds}, where r(u, Z) = lim h 0 h 1 Pr(u S i u + h, E i = 1 S i u, Z) Must assume K{u, Z, Q( ), S)} ǫ > 0 for all u 0 Can be shown: Leads to unbiased estimating equation Treatment Effects/Premature Discontinuation 25

26 Implementation 1. Categorize treatment discontinuations as mandatory or optional 2. Form K{u, Z, Q( ), S} (and w(u, Z) if needed) via models for q{u, Z, Q(u)}, p 0 (Z, X) (and r(u, Z) if needed) q{u, Z, Q(u)}: Fit a PH model to data S i = min{o i, M i (Z i), U i }, Λ i = I(i optionally discontinued before t max ) with covariates Z i, X i, V H i (u) (or separately by treatment) p 0 (Z, X): Define H i = I(O i = 0), fit binary regression model Pr(H i = 1 Z i, X i ) w(u, Z): Fit a PH model to data S i = min{o i, M i (Z i), U i }, Λ i = I(i optionally discontinued before t max ) with covariate Z i (or separate Kaplan-Meier estimates by treatment) Treatment Effects/Premature Discontinuation 26

27 Implementation 3. For each i and u equal to every distinct event time, estimate K{u, Z, Q( ), S} (and w(u, Z) if needed); e.g., using Breslow s estimator 4. For each i, create weights at each distinct event time u equal to 0 if i optionally discontinued by u or using the estimates from step 3 if not 5. Substitute weights in the modified score equations and solve Step 5: May be implemented in SAS proc phreg Counting process input format weight statement cov(aggregate) option Robust output standard errors will be conservative but work well in practice Treatment Effects/Premature Discontinuation 27

28 Application to SYNERGY All-cause mortality within t max = 365 days (1 year): n = 9784 subjects, 4899 (4885) randomized to UFH (ENOX) 27.6% UFH, 28.6% ENOX subjects censored before t max 65.5% UFH, 63.6% ENOX subjects adminstratively censored at t max 95% of subjects censored before t max within 2 months of t max ; 75% within 1 month Protocol: Last visit within 2 months, close enough = assuming all censoring administrative not unreasonable Treatment Effects/Premature Discontinuation 28

29 Application to SYNERGY Discontinuation: Overall: 706 (14.4%) UFH, 1194 (24.4%) ENOX Mandatory: 337 (6.9%) UFH, 551 (11.3%) ENOX Optional: 369 (7.5%) UFH, 594 (12.2%) ENOX Optional at time 0 : 39 (< 1%) UFH, 90 (1.8%) ENOX Mean times to discontinuation from days (SD days) Treatment Effects/Premature Discontinuation 29

30 Application to SYNERGY Model for K{u, Z, Q( ), S}: Numerous baseline covariates X, several time-dependent covariates V H (u) post-randomization q{u,z, Q(u)}, u > 0: Proportional hazards model Subset of X identified by forward selection Included with Z and V H (u) in a final PH model Baseline: Gender, height, troponin levels, smoking status, diabetes, Killip class, race, region, prior hypertension, prior CABG, prior ENOX, prior UFH, rales Time-dependent: Transfusion status, creatine kinase (CK) levels, CK-MB levels p 0 (Z, X), u = 0: Logistic regression model Subset of X identified by forward selection Prior ENOX, age, region, race, height, prior hypertension, prior angina w(u, Z): PH model Treatment Effects/Premature Discontinuation 30

31 Application to SYNERGY Hazard ratio, one year all-cause mortality Method Estimate 95% confidence interval p-value intent-to-treat 1.06 ( ) 0.44 censor, all 1.03 ( ) 0.77 censor, optional 1.08 ( ) 0.33 time dependent 1.03 ( ) 0.77 inverse weighted w(u, Z) ( ) 0.36 w(u,z) depends on Z 1.07 ( ) 0.42 All results similar Treatment Effects/Premature Discontinuation 31

32 Application to SYNERGY Possible explanations: %age of subjects who optionally discontinued either treatment = 9.8% overall; not large Important covariates may not have been measured = ineffective adjustment Important covariates in model for K{u, Z, Q( ), S} and those retained in a naive PH model ignoring discontinuation do not overlap Bottom line: Although all analyses do not find ENOX/UFH difference only the weighted analysis is designed to address the well-formulated question of interest Allows confirmation that the negative trial outcome was not an artifact of differential rates of discontinuation Treatment Effects/Premature Discontinuation 32

33 Simulation studies 2000 Monte Carlo data sets, n = 2000: β = 0.5, t max = Z Bernoulli(0.5), X = (X 1, X 2 ) standard normal Potential failure times T (Z): Generate uniform Υ correlated with X via Υ = Φ 1 (0.6X X ǫ), ǫ N(0,1), transform Υ using inverse cdf of exponential(0.0025e βz ) Potential times to mandatory discontinuation/completion M (Z): exponential{exp(0.4x X 2 2.8)} Potential censoring times C (Z): 90+exponential(0.0012e 0.4Z ) Observed time to optional discontinuation O: Generate O with hazard exp( 5)exp{0.9Z + 0.1X 1 0.4X 1 Z + 0.5X 2 + ( Z)V H (u)}, V H (u) = I(D u), D exponential{2exp(0.5x Z 0.8ǫ)} = V H (u) is time-dependent confounder If O all above, O = ; else O = O Treatment Effects/Premature Discontinuation 33

34 Simulation studies 2000 Monte Carlo data sets, n = 2000: β = 0.5, t max = If O min(m, T ), T = T with time after O discounted by exp(0.8) = optional discontinuation has negative effect on survival Else, T = T U = min(t, C ) 32% censored, 23% optionally discontinued Treatment Effects/Premature Discontinuation 34

35 Simulation studies Log hazard ratio Method True Mean Est. MC SD Ave. SE Cov. Prob intent-to-treat censor, optional inverse weighting w(u, Z) w(u, Z) depends on Z Intent-to-treat, ad hoc estimators biased Inverse weighted estimators consistent Choice between unstabilized and stabilized weights? Treatment Effects/Premature Discontinuation 35

36 Simulation studies Logrank test : Under β = 0, 0.05 level test Method p-value intent-to-treat censor, optional inverse weighting Treatment Effects/Premature Discontinuation 36

37 Discussion Sensible conceptualization of treatment effect had no subject discontinued his/her assigned treatment Critical: Distinguish optional vs. mandatory discontinuation, focus on dynamic treatment regimes = Should collect reasons for discontinuation and covariates that may be associated with decisions Justification of inverse probability risk set weighting Treatment Effects/Premature Discontinuation 37

38 Discussion The analysis that would have been done under the standard assumption of independent censoring if there were no optional discontinuation Informative censoring : Inverse weighting for censoring (Robins, 1993; Hernán et al., 2006) Key assumption: Optional discontinuation is at random Augmentation not worth added complexity Zhang, M., Tsiatis, A.A., Davidian, M., Pieper, K.S., and Mahaffey, K.W. (2011). Inference on Treatment Effects from a Randomized Clinical Trial in the Presence of Premature Treatment Discontinuation: The SYNERGY Trial. Biostatistics 12, Treatment Effects/Premature Discontinuation 38

39 References Cole, S.R. and Hernán, M.A. (2003). Adjusted survival curves with inverse probability weights. Computer Methods and Programs in Biomedicine 75, Hernán, M.A., Lanoy, E., Costagliola, D. and Robins, J.M. (2006). Comparison of dynamic treatment regimes via inverse probability weighting. Basic and Clinical Pharmacology and Toxicology 98, Robins, J.M.(1993). Analytic methods for estimating HIV-treatment and cofactor effects. In Methodological Issues in AIDS Behavioral Research, Ostrow DG, Kessler RC (eds.) Plenum Press: New York, pp Robins, J., Orellana, L., and Rotnitzky, A. (2008). Estimation and extrapolation of optimal treatment and testing strategies. Statistics in Medicine 27, Robins, J. and Rotnitzky, A. (1992). Recovery of information and adjustment for dependent censoring using surrogate markers. In AIDS Epidemiology, Jewell NP, Dietz K, Farewell V (eds.) Birkauser: Boston. The SYNERGY Trial Investigators. (2004). Enoxaparin vs. unfractionated heparin in high-risk patients with non-st-segment elevation acute coronary syndromes managed with an intended early invasive strategy: Primary results of the SYNERGY randomized trial. Journal of the American Medical Association 292, Treatment Effects/Premature Discontinuation 39

40 References van der Laan, M.J. and Petersen, M.L. (2007). Causal effect models for realistic individualized treatment and intention to treat rules. The International Journal of Biostatistics, Article 3. Treatment Effects/Premature Discontinuation 40