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Uncertainty intervals for mixed effects models with non-ignorable missingness
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

When estimating regression models with missing outcomes, scientists usually rely on strong untestable assumptions such as missing at random, exclusion restrictions, or distributional assumptions on the missing data, in order to point identify the parameters of interest. An alternative is to estimate identification intervals under milder assumptions. In this paper, we use a sensitivity parameter, which quantifies the non-ignorability of the missingness mechanism, in order to estimate identification intervals for regression parameters in linear mixed effects models. By taking sampling variability into account, we obtain uncertainty intervals which can be used for a sensitivity analysis of the missing at random assumption or to draw conclusions from the data without making unnecessarily strong assumptions.

National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-127120OAI: oai:DiVA.org:umu-127120DiVA: diva2:1043966
Available from: 2016-11-01 Created: 2016-10-31 Last updated: 2016-11-01
In thesis
1. Uncertainty intervals and sensitivity analysis for missing data
Open this publication in new window or tab >>Uncertainty intervals and sensitivity analysis for missing data
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we develop methods for dealing with missing data in a univariate response variable when estimating regression parameters. Missing outcome data is a problem in a number of applications, one of which is follow-up studies. In follow-up studies data is collected at two (or more) occasions, and it is common that only some of the initial participants return at the second occasion. This is the case in Paper II, where we investigate predictors of decline in self reported health in older populations in Sweden, the Netherlands and Italy. In that study, around 50% of the study participants drop out. It is common that researchers rely on the assumption that the missingness is independent of the outcome given some observed covariates. This assumption is called data missing at random (MAR) or ignorable missingness mechanism. However, MAR cannot be tested from the data, and if it does not hold, the estimators based on this assumption are biased. In the study of Paper II, we suspect that some of the individuals drop out due to bad health. If this is the case the data is not MAR. One alternative to MAR, which we pursue, is to incorporate the uncertainty due to missing data into interval estimates instead of point estimates and uncertainty intervals instead of confidence intervals. An uncertainty interval is the analog of a confidence interval but wider due to a relaxation of assumptions on the missing data. These intervals can be used to visualize the consequences deviations from MAR have on the conclusions of the study. That is, they can be used to perform a sensitivity analysis of MAR.

The thesis covers different types of linear regression. In Paper I and III we have a continuous outcome, in Paper II a binary outcome, and in Paper IV we allow for mixed effects with a continuous outcome. In Paper III we estimate the effect of a treatment, which can be seen as an example of missing outcome data.

Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2016. 13 p.
Series
Statistical studies, ISSN 1100-8989 ; 50
Keyword
missing data, missing not at random, non-ignorable, set identification, uncertainty intervals, sensitivity analysis, self reported health, average causal effect, average causal effect on the treated, mixed-effects models
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-127121 (URN)978-91-7601-555-1 (ISBN)
Public defence
2016-11-25, Hörsal E, Humanisthuset, Umeå Universitet, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2016-11-04 Created: 2016-10-31 Last updated: 2016-11-30Bibliographically approved

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