![]() ![]() the true PS models) and generating the outcome.I wrote Part 1 a couple of years ago, so I guess I’m due for a part 2. Logistic models were used for treatment assignment ( i.e. We generated a binary treatment variable Z ( Z = 1 denotes treated units, Z = 0 denotes control units) and a binary outcome variable Y ( Y = 1 denotes the occurrence, Y = 0 denotes the non-occurrence). One of the covariates ( W 14) did not follow this generation process, but was defined as a combination of the others, mimicking the revised cardiac risk index of Lee et al. Of these, some were defined as continuous variables with distributions approximating biological markers, while others were binary variables, the prevalence of which approximated comorbidities reported in perioperative studies (Additional file 1: Table S1). We designed 15 explanatory variables ( W 1 to W 15) by generating a set of 14 normal random variables correlated by different degrees (Additional file 1: Figure S1) and adjusting and dichotomizing them to obtain distributions similar to real perioperative variables, (Additional file 1: Table S1). We conducted a series of Monte Carlo experiments based on simulated data sets that mimicked real clinical settings in the perioperative field, by using an approach similar to Setoguchi’s method. The threshold should be the highest tolerable standardized difference that does not compromise treatment effect estimation. We hypothesize that a threshold would have to be respected to ensure unbiased estimate of treated effect.Īs not all covariates can be adjusted, we aimed to determine the optimal imbalance threshold for choosing the covariates for regression adjustment to remove residual confounding. However, small samples, which are more likely to suffer imbalance, limit the number of covariates that can be included, and specifying criterion strict enough to remove sufficient residual confounding is problematic. If a sample is large enough to contain sufficient outcomes, all of the covariates can be adjusted. Īlthough arbitrary thresholds for standardized differences have been proposed for detecting residual imbalance across groups in matched samples, there is no consensus on which threshold value should be used to choose the covariates for regression adjustment. In a next step, any unbalanced covariates can be adjusted within the PS-matched sample. If balance is not possible, PS models can be re-specified until a correct balance is achieved. If balance is achieved across all of the confounders, the treatment effect can be estimated without bias. However, King and Nielsen showed that PS matching was likely to be concerned by covariates imbalance. Īpproximating completely randomized experiment, a fundamental step in PS matching analysis is to ensure that the covariate balance across the treatment groups is achieved, by using diagnostics that have been described in the literature. Under the assumption of no unmeasured confounders, treated and control units with the same PS are matched, removing confounding and allowing an unbiased estimation of the treatment effect. ![]() ![]() Defined as the conditional probability of receiving the treatment of interest given a set of confounders, the PS aims to balance confounding covariates across treatment groups. Propensity score (PS) matching analysis is a popular method for estimating the treatment effect in observational studies. In case of remaining imbalance, a double adjustment might be worth considering. If covariate balance is not achieved, we recommend reiterating PS modeling until standardized differences below 0.10 are achieved on most covariates. We found that the mean squared error of the estimates was minimized under the same conditions. The additional benefit was negligible when we also adjusted for covariates with less imbalance. We showed that regression adjustment could dramatically remove residual confounding bias when it included all of the covariates with a standardized difference greater than 0.10. The treatment effect was estimated using logistic regression that contained only those covariates considered to be unbalanced by these thresholds. We examined 25 thresholds (from 0.01 to 0.25, stepwise 0.01) for considering residual imbalance. We calculated standardized mean differences across groups to detect any remaining imbalance in the matched samples. We performed PS 1:1 nearest-neighbor matching on each sample. We conducted a series of Monte Carlo simulations on virtual populations of 5,000 subjects. We aimed to find the optimal imbalance threshold for entering covariates into regression. However, it is not always possible to include all covariates in adjustment. Double-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching. ![]()
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