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Point and interval estimation of baseline risk and treatment effect based on logistic model for observational studies
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. (Matematik)
Department of Medical Epidemiology and Biostatistics, Karolinska Institute, Stockholm, Sweden.
2015 (English)In: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 57, no 3, p. 441-452Article in journal (Refereed) Published
Abstract [en]

In observational studies with dichotomous outcome of a population, researchers usually report treatment effect alone, although both baseline risk and treatment effect are needed to evaluate the significance of the treatment effect to the population. In this article, we study point and interval estimates including confidence region of baseline risk and treatment effect based on logistic model, where baseline risk is the risk of outcome of the population under control treatment while treatment effect is measured by the risk difference between outcomes of the population under active versus control treatments. Using approximate normal distribution of the maximum-likelihood (ML) estimate of the model parameters, we obtain an approximate joint distribution of the ML estimate of the baseline risk and the treatment effect. Using the approximate joint distribution, we obtain point estimate and confidence region of the baseline risk and the treatment effect as well as point estimate and confidence interval of the treatment effect when the ML estimate of the baseline risk falls into specified range. These interval estimates reflect nonnormality of the joint distribution of the ML estimate of the baseline risk and the treatment effect. The method can be easily implemented by using any software that generates normal distribution. The method can also be used to obtain point and interval estimates of baseline risk and any other measure of treatment effect such as risk ratio and the number needed to treat. The method can also be extended from logistic model to other models such as log-linear model.

Place, publisher, year, edition, pages
2015. Vol. 57, no 3, p. 441-452
Keywords [en]
Confounding covariate, Point estimate, Interval estimate, Marginal risk difference
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hig:diva-14102DOI: 10.1002/bimj.201400019ISI: 000355610400006PubMedID: 25810034Scopus ID: 2-s2.0-84928011260OAI: oai:DiVA.org:hig-14102DiVA, id: diva2:615367
Available from: 2013-04-10 Created: 2013-04-10 Last updated: 2018-03-13Bibliographically approved

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Wang, Xiaoqin

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CiteExportLink to record
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Citation style
  • apa
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  • ieee
  • modern-language-association-8th-edition
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  • sv-SE
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  • nn-NB
  • de-DE
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