Comparing high-dimensional propensity score versus lasso

variable selection for confounding adjustment in a novel simulation

frameworkJessica Franklin

Instructor in MedicineDivision of Pharmacoepidemiology & Pharmacoeconomics

Brigham and Women’s Hospital and Harvard Medical School

QMC, Department of Quantitative Health SciencesUniversity of Massachusetts Medical School

April 15, 2014

Background

• Administrative healthcare claims data are a popular data source for nonrandomized studies of interventions.

• Because treatments are not randomized, addressing confounding is the primary methodological challenge.

Claims Data

• Comprehensive claims databases contain information on patient insurance enrollment and demographics, as well as every healthcare encounter, including:• Diagnoses• Procedures• Hospitalizations• Medications dispensed

• Dates of encounters provide a complete longitudinal record of patients’ healthcare interactions.

New user design

• Potential confounders are measured prior to initiation of exposure.

• Active treatment comparator group reduces biases associated with non-user comparators.Exposur

e initiation

Covariates assessed

Follow-up for outcome events

End of:• Data• Enrollmen

t

Principles of variable selection

• Brookhart et al. (2006) showed that the best PS model is the model that includes all predictors of outcome (regardless of whether they are associated with exposure).

• Pearl (2010) and Myers et al. (2011) further noted that including instrumental varaibles (IVs) can increase bias from unmeasured confounding.• IVs are associated with exposure, but not

associated with outcome except through exposure.

hd-PS variable selection

• The high-dimensional propensity score (hd-PS) algorithm screens thousands of diagnoses, medications, and procedure codes and ranks variables according to likelihood of confounding.

• Relies on the idea that a large number of “proxy” variables can reduce bias from unmeasured confounding.

• Empirical evidence has shown a reduction in bias.

Shrinkage methods

• Greenland (2008) suggested regularization methods as preferable to variable selection.

• Shrinking coefficients allows for efficient estimation, even in models with many degrees of freedom.

• Lasso regression provides both shrinkage and principled variable selection.• Shrinkage allows for direct modeling of the

outcome even with many potential confounders• Some coefficients are shrunk all the way to 0.

Objective

• To compare the performance of • hd-PS variable selection• Ridge regression of the outcome on all

potential confounders• Lasso regression of the outcome on all

potential confounders

• The goal is maximum reduction in confounding bias.

Comparing high-dimensional methods

• How can we answer this question?

• Empirical studies are useful when we “know” the true treatment effect, but even then we can’t determine the contributions of bias and variance to overall error.

• Ordinary simulation techniques with completely synthetic data cannot capture the complex correlation structure among covariates in claims data.

Plasmode simulation• We start with a real empirical cohort study:• 49,653 patients• Exposed to either ns-NSAIDs or Cox-2 inhibitors (X)• Followed for gastrointestinal events (Y)• Pre-defined covariates include age, sex, race, and 16

diagnosis/medication/procedure variables (C1)

• To get reasonable values for associations between covariates and outcome, we estimated a model with:• Y ~ X + all pre-defined covariates + interactions

between age and binary covariates

Simulation setup• True outcome generation model:

• Estimated coefficient values from the observed outcome model

• Except for the coefficient on exposure: .

• To create simulated datasets:• Sample with replacement rows from (X, C)• Calculate for each patient in the

sample.• Simulate outcome

• We created 500 datasets, each of size 30,000, outcome prevalence set to 5%, exposure prevalence set to 40%.

True causal diagram

C1

X Y

CAny variables associated with exposure remain associated with exposure.

Any correlations among covariates and true confounders remain intact.

C1 = True confounders, a subset of C = all measured covariates.

Associations with outcome are determined by chosen simulation model.

Outcome generation

Variable True OR

Age1.03092841

3

Black race0.66838508

2

Male gender1.41899133

3

Congestive heart failure1.22057522

9

Coronary disease1.18463300

1

Prior bleeding10.6247019

5

Prior ulcer0.77770424

9

Recent hospitalization4.53710606

9Recent nursing home admission

2.222756726

Warfarin1.01149407

2

Gastrointestinal drugs1.85852810

1

The mechanics of hd-PS

• For each diagnosis, procedure, medication code, hd-PS creates 3 potential variables:• Code observed ≥ 1 time during baseline period• Code observed ≥ median number of times• Code observed ≥ 75th percentile number of

times

• There are 2 potential ranking methods:• Exposure-based: A simple RR association

measure between exposure and each variable.• Bias-based: Bross’s bias formula that considers

the association of each varaible with exposure and outcome

hd-PS Analyses

• PSs were constructed using:• The top 500 exposure-ranked variables +

demographics• The top 500 bias-ranked variables +

demographics• The top 30 exposure-ranked variables +

demographics• The top 30 bias-ranked variables +

demographics

• Logistic regression on exposure + deciles of each PS

Shrinkage analyses

• Regression of the outcome on all hdPS-screened variables (4800 – those that never occur) + exposure + demographics• Ridge regression • Lasso regression

• We apply no shrinkage to the coefficient on exposure.

• Calculate the crude estimate for comparison

Combination approaches

• Using the variables selected by the lasso regression:• Include them in a PS analysis• Include them in an ordinary logistic regression

outcome model

• Using the 500 variables chosen by bias-based hd-PS:• Include them in an ordinary logistic regression

outcome model• Include them in a lasso outcome model• Include them in a ridge outcome model

Results – Variable selection

• Lasso selected 103 variables on average.

• 66% were also selected by at least one hdPS algorithm• IQR: 62-70%

• Age was selected in 100% of simulations.

• Race was selected in 28%.

Results - Bias

Results - Bias

Crude confounding bias of 0.19.

Results - Bias

Ridge and lasso regression with all variables reduces bias by 41% and 63%, respectively.

Results - Bias

Ridge and lasso do better when they start with pre-screened variables. Bias is reduced by 70% and 83%, respectively.

Results - Bias

Ordinary regression and PS approaches performed better. Exposure-based hdPS with 500 variables completely eliminated bias.

Results - Bias

Bias-based hdPS varaible selection also performed well, with 93% and 91% bias reduction in the PS and ordinary regression models.

Results - Bias

PS and regular regression models performed well using lasso variable selection as well (95% and 96% bias reduction).

Results - Bias

When restricting variables to a very small set, bias-based hdPS was much preferred.

Conclusion

• The variable selection method had relatively little importance.

• The estimation method mattered much more.• Shrinkage of coefficient estimates led to

insufficient bias control.

• Focus on including a large number of potential confounders or confounder proxies.

Limitations

• There are many “instruments” in current simulation setup.• Variables associated with exposure that are

not included in the outcome simulation model are essentially IVs, which is unrealistic.

• There is no unmeasured confounding in these data.• Variable selection is an easier task when all

important confounders are measured.

Future work

• Enrich the outcome model• Non-linear associations, more interactions, more true confounders

• Vary the true treatment effect• Modify the coefficient on treatment in the outcome generation

model.

• Vary exposure prevalence • Can be accomplished by sampling within exposure group.

• Vary outcome prevalence• Modify the intercept in the outcome generation model.

• Unmeasured confounding• Set aside one or more true confounders and don’t allow methods to

utilize these variables.

• Other base datasets

Thanks!

• Co-authors:• Wesley Eddings• Jeremy A Rassen• Robert J Glynn• Sebastian Schneeweiss

• Contact:• jmfranklin@partners.org• www.drugepi.org/faculty-staff-trainees/faculty/

jessica-franklin/