Using Marginal Structural Model to Estimate and Adjust for Causal Effect of Post-discontinuation Chemotherapy on Survival in Cancer Trials

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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

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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).

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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.

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PDC Confounding on Survival
Randomization
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PDC Confounding on Survival
Randomization
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Example Trial Phase III Study of
Alimta/Cisplatin vs Cisplatin in MPM
Alimta (500 mg/m2) Cis (75 mg/m2), day 1,
q3wks N228 (226 treated)
RANDOMIZE

• Balanced for key baseline prognostic factors

Cis (75 mg/m2), day 1, q3wks N228 (222 treated)
Version
Modified by Date
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MPM Trial ITT Survival Analysis
HR 0.77 95 CI of HR (0.61, 0.96)
Median 12.1 mo
Median 9.3 mo
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MPM Trial Survival by PDC Group
Alimta/Cis n MS Alimta/Cis n MS Alimta/Cis n MS Cis n MS Cis n MS
No PDC 141 141 9.8 mo 119 6.9 mo
Any PDC Median time to PDC 85 7.6 mo 85 7.6 mo 14.9 mo 103 3.2 mo 12.5 mo



Version
Modified by Date
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Cox Model to Adjust for PDC

• The hazard function for the time-dependent Cox
  model
• R is (randomized) treatment group A(t)A(u)
  0ultt 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.

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MPM Trial Cox Model
Model includes treatment group and time-dependent
PDC.
Effect HR 95 CI
Alimta/Cis vs Cis (Cox) 0.82 0.66, 1.04
Alimta/Cis vs Cis (ITT) 0.77 0.61, 0.96
PDC vs no PDC (Cox) 1.61 1.26, 2.07

Version
Modified by Date
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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).

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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 Wi(t)Wi(t).
• Wi(t) is the inverse of the probability of
  having patient is observed history of PDC up to
  time t.
• Wi(t) is the inverse of the probability of that
  patient i remained uncensored up to time t.

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Marginal Structural (Cox) Model (2)

• This weighting approach creates a
  pseudo-population which consists of Wi(t)Wi(t)
  copies of patient is data.
• In this population, time-dependent confounders
  dont 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.

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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.

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Weighted Cox Model

• SAS Proc PHREG does not implement weighted Cox
  regression.
• Easy solution equivalence between Cox model and
  pooled logistic regression (DAgostino, 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 (Hernán, 2000).

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MPM Trial MSCM Results
Model includes treatment group and time-dependent
PDC.
Effect HR 95 CI
Alimta/Cis vs Cis (Cox) 0.82 0.66, 1.04
Alimta/Cis vs Cis (ITT) 0.77 0.61, 0.96
Alimta/Cis vs Cis (MSCM) 0.66 0.46, 0.95
PDC vs no PDC (Cox) 1.61 1.26, 2.07
PDC vs no PDC (MSCM) 0.60 0.34, 1.04
Version
Modified by Date
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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?