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Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples.

Austin PC - Stat Med (2009)

Bottom Line: Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates.Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed.Inferences about treatment effect made using propensity-score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates.

View Article: PubMed Central - PubMed

Affiliation: Institute for Clinical Evaluative Sciences, G1 06, 2075 Bayview Avenue, Toronto, Ontario, Canada M4N 3M5. peter.austin@ices.on.ca

ABSTRACT
The propensity score is a subject's probability of treatment, conditional on observed baseline covariates. Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity-score matching is a popular method of using the propensity score in the medical literature. Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed. Inferences about treatment effect made using propensity-score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates. In this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified: comparing means and prevalences of baseline characteristics using standardized differences; ratios comparing the variance of continuous covariates between treated and untreated subjects; comparison of higher order moments and interactions; five-number summaries; and graphical methods such as quantile-quantile plots, side-by-side boxplots, and non-parametric density plots for comparing the distribution of baseline covariates between treatment groups. We describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero, thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified. We highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity-score model. In particular, methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative.

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Distribution of estimated propensity score in treated and untreated subjects in different matched samples.
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fig05: Distribution of estimated propensity score in treated and untreated subjects in different matched samples.

Mentions: We examined one of the simulated data sets generated in Scenario B (in the true propensity-score model there exists an interaction between two continuous covariates) described in Section 4.1. The top two panels of Figure 5 describes non-parametric estimates of the distribution of the propensity score in treated and untreated subjects in the two propensity-score matched samples (mis-specified and correctly specified propensity-score models). Under both propensity score models, the distribution of the estimated propensity score was similar between treated and untreated subjects in the matched sample. The lower two panels of Figure 5 describe quantile–quantile plots comparing the distribution of the estimated propensity score in the two matched samples. Regardless of whether the propensity-score model was correctly specified, the quantile–quantile plots demonstrate the distribution of the estimated propensity score was essentially identical between treated and untreated subjects in the matched sample.


Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples.

Austin PC - Stat Med (2009)

Distribution of estimated propensity score in treated and untreated subjects in different matched samples.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3472075&req=5

fig05: Distribution of estimated propensity score in treated and untreated subjects in different matched samples.
Mentions: We examined one of the simulated data sets generated in Scenario B (in the true propensity-score model there exists an interaction between two continuous covariates) described in Section 4.1. The top two panels of Figure 5 describes non-parametric estimates of the distribution of the propensity score in treated and untreated subjects in the two propensity-score matched samples (mis-specified and correctly specified propensity-score models). Under both propensity score models, the distribution of the estimated propensity score was similar between treated and untreated subjects in the matched sample. The lower two panels of Figure 5 describe quantile–quantile plots comparing the distribution of the estimated propensity score in the two matched samples. Regardless of whether the propensity-score model was correctly specified, the quantile–quantile plots demonstrate the distribution of the estimated propensity score was essentially identical between treated and untreated subjects in the matched sample.

Bottom Line: Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates.Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed.Inferences about treatment effect made using propensity-score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates.

View Article: PubMed Central - PubMed

Affiliation: Institute for Clinical Evaluative Sciences, G1 06, 2075 Bayview Avenue, Toronto, Ontario, Canada M4N 3M5. peter.austin@ices.on.ca

ABSTRACT
The propensity score is a subject's probability of treatment, conditional on observed baseline covariates. Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity-score matching is a popular method of using the propensity score in the medical literature. Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed. Inferences about treatment effect made using propensity-score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates. In this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified: comparing means and prevalences of baseline characteristics using standardized differences; ratios comparing the variance of continuous covariates between treated and untreated subjects; comparison of higher order moments and interactions; five-number summaries; and graphical methods such as quantile-quantile plots, side-by-side boxplots, and non-parametric density plots for comparing the distribution of baseline covariates between treatment groups. We describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero, thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified. We highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity-score model. In particular, methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative.

Show MeSH