Department of Statistical Science Duke University Propensity score weighting for CER Challenges in o bservational comparative effectiveness studies treatment and control groups are different in baseline characteristics ID: 1048587
Download Presentation The PPT/PDF document "Overlap Weighting Fan Li" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
1. Overlap WeightingFan LiDepartment of Statistical ScienceDuke University
2. Propensity score weighting for CERChallenges in observational comparative effectiveness studies: treatment and control groups are different in baseline characteristics Apply analysis methods to balance covariates between groupsPropensity score weightingMain idea: re-weigh the subjects so that the weighted treatment and control groups are balancedTreatment effect is estimated by the weighted average difference of outcomes between groups The weighted population is the “target population”Dominated by inverse probability of treatment weight (IPTW/IPW)
3. IPW: what is it and what’s the matter?Propensity score: probability of a subject getting treatment given covariates, denoted by PS is usually unknown and need to be estimated, e.g. via a logistic model IPW: for treated subjects; for control subjectsProblem of IPW when the groups are poor overlapped Extreme weights when is close to 0 or 1 – analysis can be dominated by a few outliers Trimming: drop the subjects with extreme PSWhere to trim? 0.01, 0.05, 0.1? Results can be sensitive to the cutoff pointHow to trim? Symmetric or asymmetric trimming Interpretation: how to interpret the population with propensity score (0.05, 0.95)
4. Overlap Weight (OW)Overlap weight: for treated subjects; for control subjects OW: weigh each subject by its probability of being in the opposite group Who are up-weighted? Subjects with PS close to 0.5, i.e. those who are mostly likely to be assigned to either treatment, namely, population in clinical equipoise, or overlap populationImplementation: crucial to normalize the weights so that the sum of the weights in each group is 1Literally one line change of code from IPW
5. Visualize a Simulated Example
6. Overlap Weight: AdvantagesMinimum variance: among all balancing propensity score weights methods (including IPW, matching weights, trimming), OW has the minimum variance of the weighted estimator of causal effects Exact balance: when PS is estimated via a logistic regression, OW leads to exact balance of each covariate in the modelStandardized difference is exactly zero Exact balance holds for any sample size, you don’t need a large sampleOW is bounded, no extreme weightsNo need to choose artificial cutoff point as trimming: continuous version of trimming
7. Overlap Weight: Interpretation Who are up-weighted? Subjects with PS close to 0.5 Target population: those who are mostly likely to be assigned to either treatment; people who are “on the fence” of treatment choiceScientific meaning of the overlap populationPopulation in clinical equipoise: target population in clinical trialsObservational CER studies: population whom doctors particularly want to learn the comparative effectiveness Policy: population who would be most responsive to a policy change Estimand: average treatment effect of the overlap population (ATO)
8. OW vs. IPWIPW: target population is the population represented by the study sampleWhat if the sample is just a convenience sample?Trimming in effect changes the target population, focusing on subpopulation with adequate overlap, but in an opaque fashion Relationship between OW and IPW varies by the degree of overlap Good overlap: similar results. In the extreme case of a randomized trial, OW=IPW Poor overlap: large difference
9. Simulations (Li, Thomas, Li, 2019, AJE)
10.
11. Case study: Framingham Heart StudyGoal: evaluate the effect of statins on health outcomes Patients: cross-sectional population from the offspring cohort with a visit 6 (1995-1998)Treatment: statin use at visit 6 vs. no statin useOutcomes: CV death, myocardial infarction (MI), strokeConfounders: sex, age, body mass index, diabetes, history of MI, history of PAD, history of stroke...Significant imbalance between treatment and control groups in covariates
12.
13.
14.
15. OW for Multiple TreatmentsWhen there are treatment: for treatment OW is where , the generalized propensity score (Imbens, 2000), usually estimated via multinomial logistic modelImportant to normalize the weights so that sum of OW in each treatment is 1Treatment effect estimate: Pairwise comparison of the weighted average of the outcome in each treatment Details in Li and Li (2019, AOAS)
16. Visualize OW with Multiple Treatments
17. OW for survival outcomesSimple approaches: Calculate Kaplan-Meier on the OW weighted sampleFit a Cox proportional hazards model to the OW weighted sample Cheng et al. (2021): counterfactual survival probabilities (curves) where is the estimated censoring processThe pseudo-observation approach: “once for all” method for several estimands: survival probability, restricted mean causal effect, etc. Zeng et al. (2021) proved the optimal variance property
18. OW for subgroup analysisBalance in overall population not necessarily leads to subgroup balanceOW leads to exact balance in subgroupsYang et al. (2021, SIM) proposed a general algorithmFirst use LASSO to select important covariate-subgroup interactions in the propensity score modelUse OW with PS estimated from the LASSO-selected model Case study: Compare-UF 1430 women with fibroids: 567 myomectomy; 863 hysterectomy 35 subgroups, 20 confounders: 700 subgroup-confounder interactionsSevere imbalance in confounders Outcome: quality of life 1-year after treatment
19. Subgroup balance under IPW (Yang et al. 2021)
20. Subgroup balance under OW (Yang et al. 2021)
21.
22. R package: PSweight PSweight (Zhou et al. 2020): available on CRANhttps://cran.r-project.org/web/packages/PSweight/index.html Implement a wide range of propensity score weighting methodsOW, IPW, MW, trimmingBalance metric and plotsBinary treatment and multiple treatmentsContinuous, binary, count, survival outcome (to be implemented)Subgroup analysis
23. Key ReferencesLi F, Morgan KL, Zaslavsky AM. (2018). Balancing covariates via propensity score weighting. Journal of the American Statistical Association. 113(521), 390-400. Li F, Thomas LE, Li F. (2019). Addressing extreme propensity scores via the overlap weights. American Journal of Epidemiology. 188(1), 250-257.Li F, Li F. (2019). Propensity score weighting for causal inference with multiple treatments. Annals of Applied Statistics. 13(4), 2389-2415.Thomas LE, Li F, Pencina M. (2020). Overlap weighting: a propensity score method that mimics attributes of a randomized clinical trial. Journal of American Medical Association. 323(23):2417-2418.Cheng C, Li F, Thomas LE, Li F. (2021). Addressing extreme propensity scores in estimating counterfactual survival functions via the overlap weights. American Journal of Epidemiology. Under revision.Yang S, Lorenzi E, Papadogeorgou G, Wojdyla D, Li F, Thomas LE. (2021). Propensity score weighting for causal subgroup analysis. Statistics in Medicine. 40:4294-4309.All references, slides, example R, SAS code are available at:http://www2.stat.duke.edu/~fl35/OW.html
24. AcknowledgementsAlan Zaslavsky (Harvard)Laine Thomas (Duke)Fan Li (Yale)Michael Pencina (Duke)Shuxi Zeng (Facebook)Siyun Yang (Duke)