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Maximum likelihood estimation of correction for dilution bias in simple linear regression using replicates from subjects with extreme first measurements
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Public Health and Caring Sciences. (Geriatrics)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Public Health and Caring Sciences, Family Medicine and Clinical Epidemiology.
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2008 (English)In: Statistics in Medicine, ISSN 0277-6715, E-ISSN 1097-0258, Vol. 27, no 22, 4397-4407 p.Article in journal (Refereed) Published
Abstract [en]

The least-squares estimator of the slope in a simple linear regression model is biased towards zero when the predictor is measured with random error. A corrected slope may be estimated by adding data from a reliability study, which comprises a subset of subjects from the main study. The precision of this corrected slope depends on the design of the reliability study and estimator choice.Previous work has assumed that the reliability study constitutes a random sample from the main study. A more efficient design is to use subjects with extreme values on their first measurement. Previously, we published a variance formula for the corrected slope, when the correction factor is the slope in the regression of the second measurement on the first. In this paper we show that both designs improve by maximum likelihood estimation (MLE). The precision gain is explained by the inclusion of data from all subjects for estimation of the predictor's variance and by the use of the second measurement for estimation of the covariance between response and predictor. The gain of MLE enhances with stronger true relationship between response and predictor and with lower precision in the predictor measurements. We present a real data example on the relationship between fasting insulin, a surrogate market, and true insulin sensitivity measured by a gold-standard euglycaemic insulin clamp, and simulations, where the behavior of profile-likelihood-based confidence intervals is examined. MLE was shown to be a robust estimator for non-normal distributions and efficient for small sample situations.

Place, publisher, year, edition, pages
2008. Vol. 27, no 22, 4397-4407 p.
Keyword [en]
regression dilution bias, maximum likelihood estimation, reliability study, extreme selection, corrected regression coefficient
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:uu:diva-17699DOI: 10.1002/sim.3312ISI: 000259550200002PubMedID: 18618419OAI: oai:DiVA.org:uu-17699DiVA: diva2:45470
Available from: 2008-08-15 Created: 2008-08-15 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Measurement Variability Related to Insulin Secretion and Sensitivity: Assessment and Implications in Epidemiological Studies
Open this publication in new window or tab >>Measurement Variability Related to Insulin Secretion and Sensitivity: Assessment and Implications in Epidemiological Studies
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

There is a growing interest in random measurement variability of biological variables. In regression models, such variability of the predictors yields biased estimators of coefficients (regression dilution bias). The objectives of this thesis were to develop an efficient method to correct for such bias, to reveal the relative importance of insulin sensitivity and insulin secretion, corrected for regression dilution bias, on glucose tolerance, and to explore the seasonal nature of the variability of insulin sensitivity.

A reliability study is often designed to randomly select subjects from the main study. Our idea was to collect replicates for subjects with extreme values on their first measurement. The extreme selection design, in combination with maximum likelihood estimation, resulted in an efficient estimator of a corrected regression coefficient in a simple linear regression model. Results were presented theoretically and with an application: The relation between insulin sensitivity and fasting insulin in Uppsala Longitudinal Study of Adult Men (ULSAM) where the extreme selection design decreased the standard error of the estimated regression coefficient with 28 per cent compared with the random sampling design.

We estimated the partial longitudinal effects of the predictors insulin sensitivity and insulin secretion, corrected for regression dilution bias, on glucose tolerance in ULSAM. The effects of the predictors, when corrected, were similar.

Insulin sensitivity in ULSAM increased during summer and decreased during winter and insulin secretion exposed opposite variation keeping glucose homeostasis nearly constant. Insulin sensitivity was related to outdoor temperature.

In summary, we developed a cost-efficient reliability design for correction for regression dilution bias. Insulin sensitivity and insulin secretion had similar longitudinal effects on glucose tolerance, which implies that interventions aimed at these targets are equally important. Further, we revealed the seasonal nature of variations of insulin sensitivity and insulin secretion. This result has implications on glycaemic control in diabetic patients.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2009. 67 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Medicine, ISSN 1651-6206 ; 440
National Category
Geriatrics
Research subject
Geriatrics
Identifiers
urn:nbn:se:uu:diva-99636 (URN)978-91-554-7469-0 (ISBN)
Public defence
2009-04-29, Enghoffsalen, Akademiska sjukhuset, Uppsala, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2009-04-07 Created: 2009-03-18 Last updated: 2012-07-26Bibliographically approved

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Berglund, LarsGarmo, HansLindbäck, JohanSvärdsudd, KurtZethelius, Björn

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