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The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in the analysis of observational data. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimated treatment effects. We introduce covariate balancing propensity score (CBPS) methodology, which models treatment assignment while optimizing the covariate balance. The CBPS exploits the dual characteristics of the propensity score as a covariate balancing score and the conditional probability of treatment assignment. The estimation of the CBPS is done within the generalized method‐of‐moments or empirical likelihood framework. We find that the CBPS dramatically improves the poor empirical performance of propensity score matching and weighting methods reported in the literature. We also show that the CBPS can be extended to other important settings, including the estimation of the generalized propensity score for non‐binary treatments and the generalization of experimental estimates to a target population. Open source software is available for implementing the methods proposed.

Background Propensity score matching is a statistical method that is often used to make inferences on the treatment effects in observational studies. In recent years, there has been widespread use of the technique in the cardiothoracic surgery literature to evaluate to potential benefits of new surgical therapies or procedures. However, the small sample size and the strong dependence of the treatment assignment on the baseline covariates that often characterize these studies make such an evaluation challenging from a statistical point of view. In such settings, the use of propensity score matching in combination with oversampling and replacement may provide a solution to these issues by increasing the initial sample size of the study and thus improving the statistical power that is needed to detect the effect of interest. In this study, we review the use of propensity score matching in combination with oversampling and replacement in small sample size settings. Methods We performed a series of Monte Carlo simulations to evaluate how the sample size, the proportion of treated, and the assignment mechanism affect the performances of the proposed approaches. We assessed the performances with overall balance, relative bias, root mean squared error and nominal coverage. Moreover, we illustrate the methods using a real case study from the cardiac surgery literature. Results Matching without replacement produced estimates with lower bias and better nominal coverage than matching with replacement when 1:1 matching was considered. In contrast to that, matching with replacement showed better balance, relative bias, and root mean squared error than matching without replacement for increasing levels of oversampling. The best nominal coverage was obtained by using the estimator that accounts for uncertainty in the matching procedure on sets of units obtained after matching with replacement. Conclusions The use of replacement provides the most reliable treatment effect estimates and that no more than 1 or 2 units from the control group should be matched to each treated observation. Moreover, the variance estimator that accounts for the uncertainty in the matching procedure should be used to estimate the treatment effect.

Examining covariate balance is the prescribed method for determining the degree to which propensity score methods should be successful at reducing bias. This study assessed the performance of various balance measures, including a proposed balance measure based on the prognostic score (similar to a disease risk score), to determine which balance measures best correlate with bias in the treatment effect estimate. The correlations of multiple common balance measures with bias in the treatment effect estimate produced by weighting by the odds, subclassification on the propensity score, and full matching on the propensity score were calculated. Simulated data were used, based on realistic data settings. Settings included both continuous and binary covariates and continuous covariates only. The absolute standardized mean difference (ASMD) in prognostic scores, the mean ASMD (in covariates), and the mean t-statistic all had high correlations with bias in the effect estimate. Overall, prognostic scores displayed the highest correlations with bias of all the balance measures considered. Prognostic score measure performance was generally not affected by model misspecification, and the prognostic score measure performed well under a variety of scenarios. Researchers should consider using prognostic score–based balance measures for assessing the performance of propensity score methods for reducing bias in nonexperimental studies.

Background\\nTo better understand the epidemiology and patterns of tracheostomy practice for patients with acute respiratory distress syndrome (ARDS), we investigated the current usage of tracheostomy in patients with ARDS recruited into the Large Observational Study to Understand the Global Impact of Severe Acute Respiratory Failure (LUNG-SAFE) study.\\nMethods\\nThis is a secondary analysis of LUNG-SAFE, an international, multicenter, prospective cohort study of patients receiving invasive or noninvasive ventilation in 50 countries spanning 5 continents. The study was carried out over 4 weeks consecutively in the winter of 2014, and 459 ICUs participated. We evaluated the clinical characteristics, management and outcomes of patients that received tracheostomy, in the cohort of patients that developed ARDS on day 1–2 of acute hypoxemic respiratory failure, and in a subsequent propensity-matched cohort.\\nResults\\nOf the 2377 patients with ARDS that fulfilled the inclusion criteria, 309 (13.0%) underwent tracheostomy during their ICU stay. Patients from high-income European countries (n = 198/1263) more frequently underwent tracheostomy compared to patients from non-European high-income countries (n = 63/649) or patients from middle-income countries (n = 48/465). Only 86/309 (27.8%) underwent tracheostomy on or before day 7, while the median timing of tracheostomy was 14 (Q1–Q3, 7–21) days after onset of ARDS. In the subsample matched by propensity score, ICU and hospital stay were longer in patients with tracheostomy. While patients with tracheostomy had the highest survival probability, there was no difference in 60-day or 90-day mortality in either the patient subgroup that survived for at least 5 days in ICU, or in the propensity-matched subsample.\\nConclusions\\nMost patients that receive tracheostomy do so after the first week of critical illness. Tracheostomy may prolong patient survival but does not reduce 60-day or 90-day mortality.

Propensity score analysis is a popular method to control for confounding in observational studies. A challenge in propensity methods is missing values in confounders. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. Concurrently, we aimed to provide guidance in choosing the optimal strategy. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Additionally, we demonstrated how missingness graphs help clarifying the missing structure. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random. In some situations, complete case analysis was also able to partially correct for unmeasured confounding. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation may fail when data are missing not at random. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random.

Establishing causal links when experiments are not feasible is an important challenge for psychology researchers. The question of whether parents’ spanking causes children’s externalizing behavior problems poses such a challenge because randomized experiments of spanking are unethical, and correlational studies cannot rule out potential selection factors. This study used propensity score matching based on the lifetime prevalence and recent incidence of spanking in a large and nationally representative sample (N = 12,112) as well as lagged dependent variables to get as close to causal estimates outside an experiment as possible. Whether children were spanked at the age of 5 years predicted increases in externalizing behavior problems by ages 6 and 8, even after the groups based on spanking prevalence or incidence were matched on a range of sociodemographic, family, and cultural characteristics and children’s initial behavior problems. These statistically rigorous methods yield the conclusion that spanking predicts a deterioration of children’s externalizing behavior over time.

The sharing of patient-level data necessary for covariate-adjusted survival analysis between medical institutions is difficult due to privacy protection restrictions. We propose a privacy-preserving framework that estimates balanced Kaplan–Meier curves from distributed observational data without exchanging raw data. Each institution sends only the low-dimensional representation obtained through dimensionality reduction of the covariate matrix. Analysts reconstruct the aggregated dataset, perform propensity score matching, and estimate survival curves. Experiments using simulation datasets and five publicly available medical datasets showed that the proposed method consistently outperformed single-site analyses. This method can handle both horizontal and vertical data distribution scenarios and enables the collaborative acquisition of reliable survival curves with minimal communication and no disclosure of raw data.

Background Tumour perineural invasion (PNI) is a predictor of poor prognosis, but its effect on the prognosis of patients with colorectal cancer (CRC) has not yet been elucidated. Methods This retrospective study used propensity score matching (PSM). The clinical case data of 1470 patients with surgically treated stage I–IV CRC at Wuhan Union Hospital were collected. PSM was used to analyse and compare the clinicopathological characteristics, perioperative outcomes, and long-term prognostic outcomes of the PNI(+) and PNI(-) groups. The factors influencing prognosis were screened using Cox univariate and multivariate analyses. Results After PSM, 548 patients were included in the study (n = 274 in each group). Multifactorial analysis showed that neurological invasion was an independent prognostic factor affecting patients’ OS and DFS (hazard ratio [HR], 1.881; 95% confidence interval [CI], 1.35–2.62; P = 0.0001; HR, 1.809; 95% CI, 1.353–2.419; P < 0.001). Compared to PNI(+) patients without chemotherapy, those who received chemotherapy had a significant improvement in OS (P < 0.01). The AUROC curve of OS in the PNI(+) subgroup (0.802) was higher than that after PSM (0.743), while that of DFS in the PNI(+) subgroup (0.746) was higher than that after PSM (0.706). The independent predictors of PNI(+) could better predict the prognosis and survival of patients with PNI(+). Conclusions PNI significantly affects the long-term survival and prognosis of patients with CRC undergoing surgery and is an independent risk factor for OS and DFS in patients with CRC undergoing surgery. Postoperative chemotherapy significantly improved the OS of PNI(+) patients.

BackgroundTranscatheter tricuspid valve repair (TTVR) is a promising technique for the treatment of tricuspid regurgitation (TR). Data comparing the performance of novel edge-to-edge devices (PASCAL and MitraClip-XTR) are scarce.MethodsWe identified 80 consecutive patients who underwent TTVR using either the PASCAL or MitraClip-XTR system to treat symptomatic TR from July 2018 to June 2020. To adjust for baseline imbalances, we performed a propensity score (PS) 1:1 matching. The primary endpoint was a reduction in TR severity by at least one grade at 30 days.ResultsThe PS-matched cohort (n = 44) was at high-surgical risk (EuroSCORE II: 7.5% [interquartile range (IQR) 4.8–12.1%]) with a mean TR grade of 4.3 ± 0.8 and median coaptation gap of 6.2 mm [IQR 3.2–9.1 mm]. The primary endpoint was similarly observed in both groups (PASCAL: 91% vs. MitraClip-XTR: 96%). Multiple device implantation was the most common form (59% vs. 82%, p = 0.19), and the occurrence of SLDA was comparable between the PASCAL and MitraClip-XTR system (5.7% [2 of 35 implanted devices] vs. 4.4% [2 of 45 implanted devices], p = 0.99). No periprocedural death or conversions to surgery occurred, and 30-day mortality (5.0% vs. 5.0%, log-rank p = 0.99) and 3-month mortality (10.0% vs. 5.0%, log-rank p = 0.56) were similar between both groups. During follow-up, functional NYHA class, 6-min walking distance, and health status improved in both groups.ConclusionsBoth TTVR devices, PASCAL and MitraClip-XTR, appeared feasible and comparable for an effective TR reduction. Randomized head-to-head comparisons will help to further define the appropriate scope of application of each system.

Background Propensity score (PS) methods are increasingly used, even when sample sizes are small or treatments are seldom used. However, the relative performance of the two mainly recommended PS methods, namely PS-matching or inverse probability of treatment weighting (IPTW), have not been studied in the context of small sample sizes. Methods We conducted a series of Monte Carlo simulations to evaluate the influence of sample size, prevalence of treatment exposure, and strength of the association between the variables and the outcome and/or the treatment exposure, on the performance of these two methods. Results Decreasing the sample size from 1,000 to 40 subjects did not substantially alter the Type I error rate, and led to relative biases below 10%. The IPTW method performed better than the PS-matching down to 60 subjects. When N was set at 40, the PS matching estimators were either similarly or even less biased than the IPTW estimators. Including variables unrelated to the exposure but related to the outcome in the PS model decreased the bias and the variance as compared to models omitting such variables. Excluding the true confounder from the PS model resulted, whatever the method used, in a significantly biased estimation of treatment effect. These results were illustrated in a real dataset. Conclusion Even in case of small study samples or low prevalence of treatment, PS-matching and IPTW can yield correct estimations of treatment effect unless the true confounders and the variables related only to the outcome are not included in the PS model.