Use of Stabilized Inverse Propensity Scores as Weights to Directly Estimate Relative Risk and Its Confidence Intervals

Abstract

Objectives Inverse probability of treatment weighting (IPTW) has been used in observational studies to reduce selection bias. To obtain estimates of the main effects, a pseudo data set is created by weighting each subject by IPTW and analyzed with conventional regression models. Currently variance estimation requires additional work depending on type of outcomes. Our goal is to demonstrate a statistical approach to directly obtain appropriate estimates of variance of the main effects in regression models. Methods We carried out theoretical and simulation studies to show that the variance of the main effects estimated directly from regressions using IPTW is underestimated, and that the type I error rate is higher due to the inflated sample size in the pseudo data. The robust variance estimator using IPTW often slightly overestimates the variance of the main effects. We propose to use the stabilized weights to directly estimate both the main effect and its variance from conventional regression models. Results We applied the approach to a study examining the effectiveness of serum potassium monitoring in reducing hyperkalemia-associated adverse events among 27,355 diabetic patients newly-prescribed a renin-angiotensin-aldosterone system (RAAS) inhibitor. The incidence rate ratio (with monitoring versus without monitoring) and confidence intervals were 0.46 (0.34, 0.61) using the stabilized weights compared to 0.46 (0.38, 0.55) using typical inverse probability of treatment weighting. Conclusions Our theoretical, simulation results and real data example demonstrate that the use of the stabilized weights in the pseudo data preserves the sample size of the original data, produces appropriate estimation of the variance of main effect, and maintains an appropriate type I error rate.

Impact of Surgical Approach on Patient-Reported Outcomes after Radical Prostatectomy: A Propensity Score-Weighted Analysis from a Multicenter, Prospective, Observational Study (The Pros-IT CNR Study)

“…Second, propensity scores weighting was used to minimize baseline differences, since it was found to work better when small sample sizes were considered [20]. Propensity scores were estimated by logistic regression models with the type of RP as dependent variable and pre-treatment characteristics, which exceeded 10% of difference at univariate analyses as independent variables [21]. Stabilized inverse weights equal to (1/propensity DOI: 10.1159/000496980 scoreLRP) and (1/propensity scoreRARP) were assigned to LRP and RARP patients, respectively, and weight of (1/1-[propensity scoreLRP + propensity scoreRARP]) to ORP patients, with weights stabilized for the observed frequencies in each group [22].…”

Impact of Extended-Spectrum β-Lactamase Production on Treatment Outcomes of Acute Pyelonephritis Caused by Escherichia coli in Patients without Health Care-Associated Risk Factors

“…The weights for the CA-ESBL group were the inverse of the propensity scores, and those for the CA-non-ESBL group were the inverse of 1 Ϫ the propensity scores. The stabilized weights were calculated by replacing the numerator with the marginal probability of actually having CA-ESBL-EC (16). After weighting, the variables were tested for balance using the absolute standardized mean difference, whereby differences of Ͼ20% represent a meaningful imbalance.…”

Reducing Pain Experienced During Potassium Chloride Infusion in the Emergency Department

“…In other words, the risk of experiencing pain for patients who were not assigned to the lignocaine group was 2.4 times the risk of those who were given lignocaine. The numbers needed to treat was 5 (95% C.I., [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], suggesting that on average, for every five patients who were treated with lignocaine prior to the initiation of potassium chloride infusion, one will benefit from the treatment.…”

“…Propensity scores of the subjects were estimated using the multivariable logistic regression where the status of treatment was regressed on the measured baseline covariates. Stabilized IPTWs will reduce variability due to instability in estimation that could be induced either by those treated subjects with low propensity scores or untreated subjects with high propensity scores (18,19). Absolute standardized difference was calculated for each of the baseline covariates to assess the balance be- …”