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Consistency of the propensity score estimators rely on correct specification of the propensity score model. The propensity score is frequently estimated using a main effect logistic regression. It has recently been shown that the use of ensemble machine learning algorithms, such as the Super Learner, could improve covariate balance and reduce bias in a meaningful manner in the case of serious model misspecification for treatment assignment. However, the loss functions normally used by the Super Learner may not be appropriate for propensity score estimation since the goal in this problem is not to optimize propensity score prediction but rather to achieve the best possible balance in the covariate distribution between treatment groups. In a simulation study, we evaluated the benefit of a modification of the Super Learner by propensity score estimation geared toward achieving covariate balance between the treated and untreated after matching on the propensity score. Our simulation study included six different scenarios characterized by various degrees of deviation from the usual main term logistic model for the true propensity score and outcome as well as the presence (or not) of instrumental variables. Our results suggest that the use of this adapted Super Learner to estimate the propensity score can further improve the robustness of propensity score matching estimators.

Objective: Propensity score matching is typically used to estimate the average treatment effect for the treated while inverse probability of treatment weighting aims at estimating the population average treatment effect. We illustrate how different estimands can result in very different conclusions., Study Design: We applied the two propensity score methods to assess the effect of continuous positive airway pressure on mortality in patients hospitalized for acute heart failure. We used Monte Carlo simulations to investigate the important differences in the two estimates., Results: Continuous positive airway pressure application increased hospital mortality overall, but no continuous positive airway pressure effect was found on the treated. Potential reasons were (1) violation of the positivity assumption; (2) treatment effect was not uniform across the distribution of the propensity score. From simulations, we concluded that positivity bias was of limited magnitude and did not explain the large differences in the point estimates. However, when treatment effect varies according to the propensity score (E[Y(1)-Y(0)|g(X)] is not constant, Y being the outcome and g(X) the propensity score), propensity score matching ATT estimate could strongly differ from the inverse probability of treatment weighting-average treatment effect estimate. We show that this empirical result is supported by theory., Conclusion: Although both approaches are recommended as valid methods for causal inference, propensity score-matching for ATT and inverse probability of treatment weighting for average treatment effect yield substantially different estimates of treatment effect. The choice of the estimand should drive the choice of the method., (© The Author(s) 2013.)

Objectives: The propensity score (PS) is a balancing score. Following PS matching, balance checking usually relies on estimating separately the standardized absolute mean difference for each baseline characteristic. The average standardized absolute mean difference and the Mahalanobis distances have been proposed to summarize the information across the covariates. However, they might be minimized when nondesirable variables such as instrumental variables (IV) are included in the PS model. We propose a new weighted summary balance measure that takes into account, for each covariate, its strength of association with the outcome., Study Design and Setting: This new measure was evaluated using a simulation study to assess whether minimization of the measure coincided with minimally biased estimates. All measures were then applied to a real data set from an observational cohort study., Results: Contrarily to the other measures, our proposal was minimized when including the confounders, which coincided with minimal bias and mean squared error, but increased when including an IV in the PS model. Similar findings were observed in the real data set., Conclusion: A balance measure taking into account the strength of association between the covariates and the outcome may be helpful to identify the most parsimonious PS model., (Copyright © 2015 Elsevier Inc. All rights reserved.)

The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed better for highly unbalanced variables. The SL-based estimators were associated with the smallest bias in cases of severe model misspecification. Our results suggest that use of SL to estimate the PS can improve covariate balance and reduce bias in a meaningful manner in cases of serious model misspecification for treatment assignment., (© The Author 2014. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: The best catecholamine regimen for cardiogenic shock has been poorly evaluated. When a vasopressor is required to treat patients with the most severe form of cardiogenic shock, whether inodilators should be added or whether inopressors can be used alone has not been established. The purpose of this study was to compare the impact of these two strategies on short-term mortality in patients with severe cardiogenic shocks., Methods and Results: Three observational cohorts of patients with decompensated heart failure were pooled to comprise a total of 1,272 patients with cardiogenic shocks. Of these 1,272 patients, 988 were considered to be severe because they required a vasopressor during the first 24 hours. We developed a propensity-score (PS) model to predict the individual probability of receiving one of the two regimens (inopressors alone or a combination) conditionally on baseline-measured covariates. The benefit of the treatment regimen on the mortality rate was estimated by fitting a weighted Cox regression model. A total of 643 patients (65.1%) died within the first 30 days (inopressors alone: 293 (72.0%); inopressors and inodilators: 350 (60.0%)). After PS weighting, we observed that the use of an inopressor plus an inodilator was associated with an improved short-term mortality (HR: 0.66 [0.55-0.80]) compared to inopressors alone., Conclusions: In the most severe forms of cardiogenic shock where a vasopressor is immediately required, adding an inodilator may improve short-term mortality. This result should be confirmed in a randomized, controlled trial.

Introduction: Continuous positive airway pressure (CPAP) improves patients' condition in case of cardiogenic pulmonary edema (CPE). However, the impact of CPAP on short-term mortality remains a matter of debate. We aimed at estimating the effect of CPAP on short-term mortality in patients treated for a CPE., Methods and Results: We pooled the data from the Acute Heart Failure Global Registry of Standard Treatment and the Etude Francaise l'Innsuficiens Cardiaque Aigue observational cohorts to compare the estimations of the effect on short-term mortality of CPAP, before and after propensity score (PS) matching. A total of 2286 patients with a cardiogenic pulmonary edema were included in the analysis, of whom 321 (14%) received CPAP. Of these, 314 could be matched to a control patient (matched population: n = 628) and were included in the PS analysis. In naive analysis, CPAP application influenced neither short-term mortality (HR: 1.03, 95% CI: 0.73-1.46; P = .86) nor the need for tracheal intubation (OR: 1.04, 95% CI: 0.78-1.40; P = .78). After PS matching, CPAP was associated with a reduction in the need for tracheal intubation (OR: 0.56, 95% CI: 0.37-0.84; P = .005) but it did not reduce short-term mortality (HR: 0.77, 95% CI: 0.47-1.26; P = .30)., Conclusions: Despite a reduction in the need for tracheal intubation, CPAP application may not reduce short-term mortality in patients suffering from cardiogenic pulmonary edema., (Copyright © 2013 Elsevier Inc. All rights reserved.)

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.

Objective: When analyzing observational databases, marginal structural models (MSMs) may offer an appealing approach to estimate causal effects. We aimed at evaluating MSMs, in accounting for confounding when assessing the benefit of intensive care unit (ICU) admission and on its interaction with patient age, as compared with propensity score (PS) matching., Study Design and Setting: PS and inverse-probability-of-treatment weights for MSMs were derived from an observational study designed to evaluate the benefit of ICU admission on in-hospital mortality. Only first ICU triages (time-fixed weights) or whole triage history (time-dependent weights) were considered. Weights were stabilized by either the prevalence of the actual treatment or the probability of the actual treatment given baseline covariates. Risk difference (RD) was the main outcome measure., Results: MSMs with time-dependent weights offered the best reduction in the baseline imbalances as compared with PS matching. No effect of ICU admission on in-hospital mortality was found (RD=0.010; 95% confidence interval=-0.038, 0.052) with no interaction between age and treatment., Conclusion: MSMs appear interesting to handle selection bias in observational studies. When confounding evolves over time, the use of time-dependent weights should be stressed out., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Background: The assessment of the causal effect of Intensive Care Unit (ICU) admission generally involves usual observational designs and thus requires controlling for confounding variables. Instrumental variable analysis is an econometric technique that allows causal inferences of the effectiveness of some treatments during situations to be made when a randomized trial has not been or cannot be conducted. This technique relies on the existence of one variable or "instrument" that is supposed to achieve similar observations with a different treatment for "arbitrary" reasons, thus inducing substantial variation in the treatment decision with no direct effect on the outcome. The objective of the study was to assess the benefit in terms of hospital mortality of ICU admission in a cohort of patients proposed for ICU admission (ELDICUS cohort)., Methods: Using this cohort of 8,201 patients triaged for ICU (including 6,752 (82.3%) patients admitted), the benefit of ICU admission was evaluated using 3 different approaches: instrumental variables, standard regression and propensity score matched analyses. We further evaluated the results obtained using different instrumental variable methods that have been proposed for dichotomous outcomes., Results: The physician's main specialization was found to be the best instrument. All instrumental variable models adequately reduced baseline imbalances, but failed to show a significant effect of ICU admission on hospital mortality, with confidence intervals far higher than those obtained in standard or propensity-based analyses., Conclusions: Instrumental variable methods offer an appealing alternative to handle the selection bias related to nonrandomized designs, especially when the presence of significant unmeasured confounding is suspected. Applied to the ELDICUS database, this analysis failed to show any significant beneficial effect of ICU admission on hospital mortality. This result could be due to the lack of statistical power of these methods.

Introduction: Propensity score methods have been increasingly used in the last 10 years. However, the practical use of the propensity score (PS) has been reported as heterogeneous in several papers reviewing the use of propensity scores and giving some advice. No precedent work has focused on the specific application of PS in intensive care and anaesthesiology literature., Objectives: After a brief development of the theory of propensity score, to assess the use and the quality of reporting of PS studies in intensive care and anaesthesiology, and to evaluate how past reviews have influenced the quality of the reporting., Study Design and Setting: Forty-seven articles published between 2006 and 2009 in the intensive care and anaesthesiology literature were evaluated. We extracted the characteristics of the report, the type of analysis, the details of matching procedures, the number of patients in treated and control groups, and the number of covariates included in the PS models., Results: Of the 47 articles reviewed, 26 used matching on PS, 12 used stratification on PS and 9 used adjustment on PS. The method used was reported in 81% of the articles, and the choice to conduct a paired analysis or not was reported in only 15%. The comparison with the previously published reviews showed little improvement in reporting in the last few years., Conclusion: The quality of reporting propensity scores in intensive care and anaesthesiology literature should be improved. We provide some recommendations to the investigators in order to improve the reporting of PS analyses.