1 1 Using Marginal Structural Model to Estimate and Adjust for Causal Effect of Post- discontinuation Chemotherapy on Survival in Cancer Trials Y. Wang, S. Hong, I. Lipkovich, D. Faries Eli Lilly and Company ICSA 2007 Y. Wang, S. Hong, I. Lipkovich, D. Faries Eli Lilly and Company ICSA 2007

Survival as an Endpoint Survival is measured by the time from randomization to death from any cause. Universally accepted measure of clinical benefit; easily and precisely measured. Require larger/longer studies; treatment effect on survival is potentially confounded by subsequent cancer therapies such as post- discontinuation chemo (PDC). Survival is measured by the time from randomization to death from any cause. Universally accepted measure of clinical benefit; easily and precisely measured. Require larger/longer studies; treatment effect on survival is potentially confounded by subsequent cancer therapies such as post- discontinuation chemo (PDC).

Intent-to-Treat Analysis of Survival Intent-to-treat analysis, simply ignoring potential PDC confounding, is the standard approach. Most closely models the real clinical scenario. Estimated treatment effect may not have causal interpretation due to potential confounding of PDC. Intent-to-treat analysis, simply ignoring potential PDC confounding, is the standard approach. Most closely models the real clinical scenario. Estimated treatment effect may not have causal interpretation due to potential confounding of PDC.

Patient dies on study chemo 1 Randomization Discontinuation Patient censored in follow-up 3 Patient dies in follow-up 2 PDC Confounding on Survival

Randomization Discontinuation Patient censored in follow-up 5 Patient dies in follow-up 4 Patient begins subsequent chemo PDC Confounding on Survival

Alimta (500 mg/m 2 ) + Cis (75 mg/m 2 ), day 1, q3wks N=228 (226 treated) Balanced for key baseline prognostic factors Example Trial: Phase III Study of Alimta/Cisplatin vs Cisplatin in MPM RANDOMIZERANDOMIZE Cis (75 mg/m 2 ), day 1, q3wks N=228 (222 treated)

MPM Trial: ITT Survival Analysis HR % CI of HR (0.61, 0.96) Median 12.1 mo Median 9.3 mo

MPM Trial: Survival by PDC Group Alimta/Cis n MS Cis n MS No PDC mo mo Any PDC Median time to PDC mo 14.9 mo mo 12.5 mo

Cox Model to Adjust for PDC The hazard function for the time-dependent Cox model: R is (randomized) treatment group; A(t)={A(u): 0≤u<t} is the observed PDC history prior to time t. For simplicity, assume all PDCs are the same and the effect of PDC is maintained up to death once initiated. The hazard function for the time-dependent Cox model: R is (randomized) treatment group; A(t)={A(u): 0≤u<t} is the observed PDC history prior to time t. For simplicity, assume all PDCs are the same and the effect of PDC is maintained up to death once initiated.

10 EffectHR 95% CI Alimta/Cis vs Cis (Cox) , 1.04 Alimta/Cis vs Cis (ITT) , 0.96 PDC vs no PDC (Cox) , 2.07 MPM Trial: Cox Model Model includes treatment group and time-dependent PDC.

11 Time-dependent Confounders for PDC A time-dependent confounder for PDC is (a) a time- dependent risk factor for survival that also predicts initiation of PDC, and (b) past history of PDC also affects subsequent level of the risk factor. In oncology, potential time-dependent confounders for PDC include clinical conditions, occurrence of AEs or abnormal lab/biomarker values, effectiveness of the study treatment, etc. When there exist time-dependent confounders for PDC, the Cox model may produce biased estimate of the causal effect of PDC, even in the absence of unmeasured confounding and model misspecification (Robins 1997, 2000). A time-dependent confounder for PDC is (a) a time- dependent risk factor for survival that also predicts initiation of PDC, and (b) past history of PDC also affects subsequent level of the risk factor. In oncology, potential time-dependent confounders for PDC include clinical conditions, occurrence of AEs or abnormal lab/biomarker values, effectiveness of the study treatment, etc. When there exist time-dependent confounders for PDC, the Cox model may produce biased estimate of the causal effect of PDC, even in the absence of unmeasured confounding and model misspecification (Robins 1997, 2000).

12 Marginal Structural (Cox) Model (1) The marginal structural (Cox) model (MSCM) adjust for time-dependent confounders using the inverse probability of treatment and censoring weighted estimation (IPTCW). Fit the weighted time-dependent Cox model with the contribution of patient i to the risk- set at time t weighted by W i (t)W i *(t). W i (t): is the inverse of the probability of having patient i’s observed history of PDC up to time t. W i *(t): is the inverse of the probability of that patient i remained uncensored up to time t. The marginal structural (Cox) model (MSCM) adjust for time-dependent confounders using the inverse probability of treatment and censoring weighted estimation (IPTCW). Fit the weighted time-dependent Cox model with the contribution of patient i to the risk- set at time t weighted by W i (t)W i *(t). W i (t): is the inverse of the probability of having patient i’s observed history of PDC up to time t. W i *(t): is the inverse of the probability of that patient i remained uncensored up to time t.

13 Marginal Structural (Cox) Model (2) This weighting approach creates a pseudo-population which consists of W i (t)W i *(t) copies of patient i’s data. In this population, time-dependent confounders don’t predict PDC. Causal effect of PDC in this population is the same as in the study population. The MSCM provides consistent estimate for the causal effect of PDC in the absence of unmeasured confounding and model misspecification (Robins 1997, 2000). Thus, the MSCM provides an approach for assessing causal effects of randomized therapies by appropriately adjusting for PDC. This weighting approach creates a pseudo-population which consists of W i (t)W i *(t) copies of patient i’s data. In this population, time-dependent confounders don’t predict PDC. Causal effect of PDC in this population is the same as in the study population. The MSCM provides consistent estimate for the causal effect of PDC in the absence of unmeasured confounding and model misspecification (Robins 1997, 2000). Thus, the MSCM provides an approach for assessing causal effects of randomized therapies by appropriately adjusting for PDC.

14 Estimation of Weights Weights are unknown and need to be estimated from data. Baseline and time-dependent covariates are used to estimate weights. A “stabilized” version of weights are typically used for smaller variability. Weights are unknown and need to be estimated from data. Baseline and time-dependent covariates are used to estimate weights. A “stabilized” version of weights are typically used for smaller variability.

15 Weighted Cox Model SAS Proc PHREG does not implement weighted Cox regression. Easy solution: equivalence between Cox model and pooled logistic regression (D’Agostino, 1990). Since weights are random variables, the standard errors from weighted logistic regression are invalid. The robust variance estimator for GEE provides valid but conservative confidence estimates (Hern á n, 2000). SAS Proc PHREG does not implement weighted Cox regression. Easy solution: equivalence between Cox model and pooled logistic regression (D’Agostino, 1990). Since weights are random variables, the standard errors from weighted logistic regression are invalid. The robust variance estimator for GEE provides valid but conservative confidence estimates (Hern á n, 2000).

16 EffectHR 95% CI Alimta/Cis vs Cis (Cox) , 1.04 Alimta/Cis vs Cis (ITT) , 0.96 Alimta/Cis vs Cis (MSCM) , 0.95 PDC vs no PDC (Cox) , 2.07 PDC vs no PDC (MSCM) , 1.04 MPM Trial: MSCM Results Model includes treatment group and time-dependent PDC.

17 Discussion Under certain assumptions, the causal effect of PDC on survival can be consistently estimated thru MSCM, and thus can be appropriately adjusted for. Some challenges and issues with MSCM: Assumption of no unmeasured confounding not testable. “Robust” estimate of the variance too conservative? Sensitivity to model (mis-)specification? Under certain assumptions, the causal effect of PDC on survival can be consistently estimated thru MSCM, and thus can be appropriately adjusted for. Some challenges and issues with MSCM: Assumption of no unmeasured confounding not testable. “Robust” estimate of the variance too conservative? Sensitivity to model (mis-)specification?