Controlling for Time Dependent Confounding Using Marginal
Structural Models in the Case of a Continuous Treatment O Wang 1, T
McMullan 2 1 Amgen, Thousand Oaks, CA 2 inVentiv Clinical,
Collegeville,PA Slide 2 2 Background The management of anemia in
end stage renal disease is a continuous process over time
Physicians monitor patient characteristics such as hemoglobin
levels, iron, other co- morbid conditions regularly over time and
adjust their Epogen dosing behavior accordingly Modeling Epogen
over time provides a more realistic measure of its impact on
clinical outcomes Slide 3 3 Confounding by Indication Hemoglobin
measured over time is a good predictor of both Epogen dose and
patient outcome a confounder Hemoglobin is also impacted by
previous Epogen dose time- dependent confounding Standard time
dependent Cox PH models will produce biased parameter estimates
need another approach! Slide 4 4 Marginal Structural Models (MSM)
Censoring weights are created similarly This weighting creates a
pseudo-population, without confounding between A and L Stabilized
vs. non-stabilized weights History-adjusted MSM Slide 5 5 MSM
Illustrated Severely Sick PatientsMildly Sick Patients IPTW High
dose Low dose High dose Low dose High dose Low dose Slide 6 6 MSM
weight estimates Binary treatment: Logistic model that estimates
probability of on/off treatment Ordinal treatment categories:
Ordinal regression that estimates probability of receiving current
treatment category Continuous treatment: probability density at
current treatment could be very small! Slide 7 7 MSM weights For
patient i at time point K Slide 8 8 MSM for continuous treatment?
Theoretically MSM models can be applied to a continuous treatment
variable But MSM parameter estimates could be highly sensitive to a
number of issues Given the lack of reported statistical work in
this area, how good is our continuous MSM parameter estimate? in
other words how well is the MSM model adjusting for time dependent
confounding? 1.ETA assumption 2.Observed Counterfacturals is it a
representative sample Slide 9 9 Study design: Observed data 60,000
patients in the database 7/2000 ~ 6/2002: up to 2 years of data EPO
dose of every administration, Hb on average every 2 weeks 6 months
baseline, 12 months follow up Data aggregated to bi-weekly Slide 10
10 MSM Simulation Approach 1 Baseline Month i=1 Age ~ N(O mean, O
var ) truncated at 18 and 100 c 1 ~ 10 + 11 Age t 1 ~ 10 + 11 Age +
12 c 1 logit(Y 1 ) ~ 10 + 11 Age + 12 c 1 + t 1 logit(cen 1 ) ~ 10
+ 11 Age + 12 c 1 + 13 t 1 Months i=2 to 12 c i ~ i0 + i1 Age + i2
c i-1 + i3 t i-1 t i ~ i0 + i1 Age + i2 c i + i3 t i-1 logit(Y i )
~ i0 + i1 Age + i2 c i + t i logit(cen i ) ~ i0 + i1 Age + i2 c i +
i3 t i fixed at log(0.85) Slide 11 11 MSM Simulation 1 Results
Results: log(0.85) MSM Estimates: N=600 Mean=0.919 Median=0.908
CI=0.610:1.229 PHREG Estimates: N=600 Mean=0.859 Median=0.858
CI=0.846:0.871 Slide 12 12 MSM Simulation Approach 2 Design: Build
two simulated datasets. Dataset A: EPO~HGB independent. Dataset B:
EPO~HGB related as in obs data. Model datasets A & B with
PHREG/compare. Model dataset B with MSM/compare with A. Slide 13 13
MSM Simulation 2 Design: Dataset A 1.Sample log EPO, Hb, &
censoring separately from observed data. 2.Model Mortality ~ Curr
Log EPO + Curr Hb using observed data =0.73 for dose 3.Fit sampled
log EPO & Hb to model & obtain a predicted probability of
mortality. Slide 14 14 MSM Simulation 2 Design: Dataset B Keep
Mortality, Hb, & censoring as in dataset A. Model logEPO~Lag1
Hb using observed data. Fit bootstrapped Lag1 Hb to model &
obtain a predicted logEPO. Slide 15 15 MSM Simulation 2 : Results
Design: Dataset A Design: Dataset B n=520 runs PHREG: mean=0.750
median=0.750 CI=0.7456-0.7541 MSM: mean=0.737 median=0.737
CI=0.7314-0.7419 PHREG: mean=0.999 median=0.999 CI=0.9877-1.0112
MSM: mean=0.883 median=0.874 CI=0.7220-1.0434 Slide 16 16
Simulation Results Summary Simulation 1 hard to interpret as the
truth is unknown Simulation 2 Dataset A: MSM PHREG (as expected)
Simulation 2 Dataset B: Truth < MSM < PHREG Suggestion of
adjustment for confounding No over-adjustment, ie, not biased in
the other direction Slide 17 17 MSM Assumptions Consistency
Assumption (CA) the observed outcome equals the treatment regimen
counterfactural outcome a violation of the above would occur if the
patient was not treatment compliant Sequential Randomization
Assumption (SRA) at each time point, conditional on the observed
past, treatment assignment at this time point is strongly ignorable
and there are no unmeasured confounders Under SRA patients are
conditionally exchangeable Coarsening at Random (CAR) at each time
point, conditional on the observed past, the censoring mechanism at
this time point is strongly ignorable (missing at random MAR)
Experimental Treatment Assignment (ETA) the probability of
observing a specific treatment regimen is > 0 and < 1 that is
the treatment decision is not a deterministic function of the past
MSM Assumptions not easy or even impossible to check Slide 18 18
Observed data analysis Analysis model Mortality is modeled with
weighted, time- dependent, 2-month lagged EPO Treatment weight
models and censoring models 2-month lagged EPO and censoring are
modeled with 2.5-, 3-, 3.5-, and 4-month lagged EPO and Hb, plus
baseline covariates. MortalityEPO dose (for inference) Dose Hb Dose
Hb Dose Hb Dose Hb 2 wk 2 months Slide 19 19 Continuous MSM,
non-HA, 5% Truncation Slide 20 20 Continuous MSM, HA, 5% Truncation
Slide 21 21 Categorical MSM, Non-HA, 5% Truncation Slide 22 22
Marginal Structural Models (MSM) Censoring weights are created
similarly This weighting creates a pseudo-population, without
confounding between A and L Stabilized vs. non-stabilized weights
History-adjusted MSM Slide 23 23 Categorical MSM, HA, 5% Truncation
Slide 24 24 Categorical MSM, Non-HA, 2% Truncation Slide 25 25
Categorical MSM, HA, 2% Truncation Slide 26 26 Categorical MSM,
Non-HA, 1% Truncation Slide 27 27 Categorical MSM, HA, 1%
Truncation Slide 28 28 Continuous vs categorical: Caution! Slide 29
29 Conclusions The value of repeated Epogen and Hemoglobin data
over time, and the granularity of these data, are key to
understanding their relationship with mortality. MSM IPTW
estimation can be a challenging problem over time when there are
many time points and a large number of treatment levels. MSM models
are promising for adjusting for confounding by indication in a
variety of treatment variable types Simulations seem to point to
some adjustment for confounding by indication with continuous
treatment but residual bias may still be unaccounted for.