Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Some Aspects of Propensity Score-based Estimators for Causal Inference
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers that are related to commonly used propensity score-based estimators for average causal effects.

The first paper starts with the observation that researchers often have access to data containing lots of covariates that are correlated. We therefore study the effect of correlation on the asymptotic variance of an inverse probability weighting and a matching estimator. Under the assumptions of normally distributed covariates, constant causal effect, and potential outcomes and a logit that are linear in the parameters we show that the correlation influences the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Further, the strength of the confounding towards the outcome and the treatment plays an important role.

The second paper extends the first paper in that the estimators are studied under the more realistic setting of using the estimated propensity score. We also relax several assumptions made in the first paper, and include the doubly robust estimator. Again, the results show that the correlation may increase or decrease the variances of the estimators, but we also observe that several aspects influence how correlation affects the variance of the estimators, such as the choice of estimator, the strength of the confounding towards the outcome and the treatment, and whether constant or non-constant causal effect is present.

The third paper concerns estimation of the asymptotic variance of a propensity score matching estimator. Simulations show that large gains can be made for the mean squared error by properly selecting smoothing parameters of the variance estimator and that a residual-based local linear estimator may be a more efficient estimator for the asymptotic variance. The specification of the variance estimator is shown to be crucial when evaluating the effect of right heart catheterisation, i.e. we show either a negative effect on survival or no significant effect depending on the choice of smoothing parameters.  

In the fourth paper, we provide an analytic expression for the covariance matrix of logistic regression with normally distributed regressors. This paper is related to the other papers in that logistic regression is commonly used to estimate the propensity score.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. , 24 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 99
Keyword [en]
correlation, treatment effect, inverse probability weighting, local linear estimator, matching, multicollinearity, observational study.
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-229341ISBN: 978-91-554-8990-8 (print)OAI: oai:DiVA.org:uu-229341DiVA: diva2:736335
Public defence
2014-09-19, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2014-08-29 Created: 2014-08-06 Last updated: 2014-09-08
List of papers
1. Effects of correlated covariates on the asymptotic efficiency of matching and inverse probability weighting estimators for causal inference
Open this publication in new window or tab >>Effects of correlated covariates on the asymptotic efficiency of matching and inverse probability weighting estimators for causal inference
2015 (English)In: Statistics (Berlin), ISSN 0233-1888, E-ISSN 1029-4910, Vol. 49, no 4, 795-814 p.Article in journal (Refereed) Published
Abstract [en]

In observational studies, the overall aim when fitting a model for the propensity score is to reduce bias for an estimator of the causal effect. To make the assumption of an unconfounded treatment plausible researchers might include many, possibly correlated, covariates in the propensity score model. In this paper, we study how the asymptotic efficiency of matching and inverse probability weighting estimators for average causal effects change when the covariates are correlated. We investigate the case with multivariate normal covariates, a logistic model for the propensity score and linear models for the potential outcomes and show results under different model assumptions. We show that the correlation can both increase and decrease the large sample variances of the estimators, and that the correlation affects the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Moreover, the strength of the confounding towards the outcome and the treatment plays an important role.

Keyword
correlation, efficiency bound, observational study, propensity score
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-226274 (URN)10.1080/02331888.2014.925899 (DOI)000357649900005 ()
Note

Funding: Institute for Evaluation of Labour Market and Education Policy, Sweden

Available from: 2014-06-14 Created: 2014-06-14 Last updated: 2017-12-05Bibliographically approved
2. Correlation and efficiency of propensity score-based estimators for average causal effects
Open this publication in new window or tab >>Correlation and efficiency of propensity score-based estimators for average causal effects
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Propensity score based-estimators are commonly used to estimate causal effects in evaluation research. To reduce bias in observational studies researchers might be tempted to include many, perhaps correlated, covariates when estimating the propensity score model. Taking into account that the propensity score is estimated, this study investigates how the efficiency of matching, inverse probability weighting and doubly robust estimators change under the case of correlated covariates. Propositions regarding the large sample variances under certain assumptions of the data generating process are given. The propositions are supplemented by several numerical large sample and finite sample results from a wide range of models. The results show that the correlation may increase or decrease the variances of the estimators. There are several factors that influence how correlation affects the variance of the estimators, including the choice of estimator, the strength of the confounding towards outcome and treatment, and whether a constant or non-constant treatment effect is present.

Keyword
doubly robust, inverse probability weighting, matching, observational study
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-229340 (URN)
Available from: 2014-08-06 Created: 2014-08-06 Last updated: 2014-08-29Bibliographically approved
3. Estimating the variance of a propensity score matching estimator: A new look at right heart catheterisation data
Open this publication in new window or tab >>Estimating the variance of a propensity score matching estimator: A new look at right heart catheterisation data
2014 (English)Report (Other academic)
Abstract [en]

This study considers the implementation of a variance estimator when estimating the asymptotic variance of a propensity score matching estimator for the average treatment effect. We investigate the role of smoothing parameters in the variance estimator and propose using local linear estimation. Simulations demonstrate that large gains can be made in terms of mean squared error by properly selecting smoothing parameters and that local linear estimation may lead to a more efficient estimator of the asymptotic variance. The choice of smoothing parameters in the variance estimator is shown to be crucial when evaluating the effect of right heart catheterisation, i.e. we show either a negative effect on survival or no significant effect depending on the choice of smoothing parameters.

Publisher
50 p.
Series
Working paper / Department of Statistics, Uppsala University, 2014:3
Keyword
average treatment effect, causal inference, kernel, local linear
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-229146 (URN)
Available from: 2014-08-06 Created: 2014-08-01 Last updated: 2014-09-11Bibliographically approved
4. Some approximations of the logistic distribution with application to the covariance matrix of logistic regression
Open this publication in new window or tab >>Some approximations of the logistic distribution with application to the covariance matrix of logistic regression
2014 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 85, 63-68 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we show that a two-component normal mixture model provides a good approximation to the logistic distribution. This approximation is an improvement over using the normal distribution and is comparable to using the t-distribution as approximating distributions. The results from using the mixture model is exemplified by finding an approximative analytic expression for the covariance matrix of logistic regression using normally distributed random regressors.

Keyword
Density, Gaussian, Mixture, Normal, t -distribution
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-221566 (URN)10.1016/j.spl.2013.11.007 (DOI)000331665000009 ()
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2017-12-05Bibliographically approved

Open Access in DiVA

fulltext(448 kB)351 downloads
File information
File name FULLTEXT01.pdfFile size 448 kBChecksum SHA-512
1110de70dae2eb7b647c9dbcbb20f6d7fa0d801d3ef543f9aa74e221fc13c7fcc31f9dba032858d3565f804f81568c1da42d6cf30f64d168a2a9bbad141fa929
Type fulltextMimetype application/pdf