Variance estimation for stratified propensity score estimators

E J Williamson, R Morley, A Lucas, J R Carpenter
Statistics in Medicine 2012 July 10, 31 (15): 1617-32
Propensity score methods are increasingly used to estimate the effect of a treatment or exposure on an outcome in non-randomised studies. We focus on one such method, stratification on the propensity score, comparing it with the method of inverse-probability weighting by the propensity score. The propensity score--the conditional probability of receiving the treatment given observed covariates--is usually an unknown probability estimated from the data. Estimators for the variance of treatment effect estimates typically used in practice, however, do not take into account that the propensity score itself has been estimated from the data. By deriving the asymptotic marginal variance of the stratified estimate of treatment effect, correctly taking into account the estimation of the propensity score, we show that routinely used variance estimators are likely to produce confidence intervals that are too conservative when the propensity score model includes variables that predict (cause) the outcome, but only weakly predict the treatment. In contrast, a comparison with the analogous marginal variance for the inverse probability weighted (IPW) estimator shows that routinely used variance estimators for the IPW estimator are likely to produce confidence intervals that are almost always too conservative. Because exact calculation of the asymptotic marginal variance is likely to be complex, particularly for the stratified estimator, we suggest that bootstrap estimates of variance should be used in practice.

Full Text Links

Find Full Text Links for this Article


You are not logged in. Sign Up or Log In to join the discussion.

Related Papers

Remove bar
Read by QxMD icon Read

Save your favorite articles in one place with a free QxMD account.


Search Tips

Use Boolean operators: AND/OR

diabetic AND foot
diabetes OR diabetic

Exclude a word using the 'minus' sign

Virchow -triad

Use Parentheses

water AND (cup OR glass)

Add an asterisk (*) at end of a word to include word stems

Neuro* will search for Neurology, Neuroscientist, Neurological, and so on

Use quotes to search for an exact phrase

"primary prevention of cancer"
(heart or cardiac or cardio*) AND arrest -"American Heart Association"