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Correction
Author(s) -
Senn Stephen,
Graf Erika,
Caputo Angelika
Publication year - 2008
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3321
Subject(s) - covariate , estimator , statistics , mathematics , linear regression , linear model
‘Stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure’ ( Statistics in Medicine 2007; 26 :5529–5544, DOI: 10.1002/sim.3133 ). In Section 4.2.1 entitled ‘ Marginal inference ’, \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}${\rm{Var}}(\hat{\beta_{1}})$\end{document} is incorrect. It should read\documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}\begin{eqnarray*}{\rm{Var}}(\hat{\beta_1})=\frac{4\sigma^2}{n}\left\{\frac{n-3}{n-4}\right\} \end{eqnarray*}\end{document}Therefore, ${\rm{Var}}(\hat{\Delta}){<}{\rm{Var}}(\hat{\beta_1})$ if and only if $1 + {\tilde{\beta}{}^2}/{\sigma^2}{<}(n-3)/(n-4)$ . If $|\tilde{\beta}|$ , the effect of the covariate, is sufficiently small, its inclusion in the linear model will inflate the marginal variance, so that the PS estimator outperforms the LS estimator for the linear model including the covariate in terms of marginal variance. However, provided $\tilde{\beta} \neq 0$ , for sufficiently large sample size, the inclusion of the covariate in the linear model will be beneficial.

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