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  • 1.
    Doretti, Marco
    et al.
    Department of Statistics, Computer Science, and Applications, University of Florence, Florence, Italy.
    Genbäck, Minna
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Stanghellini, Elena
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet. Department of Economics, University of Perugia, Perugia, Italy.
    Mediation analysis with case–control sampling: identification and estimation in the presence of a binary mediator2024Ingår i: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 66, nr 1, artikel-id 2300089Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    With reference to a stratified case–control (CC) procedure based on a binary variable of primary interest, we derive the expression of the distortion induced by the sampling design on the parameters of the logistic model of a secondary variable. This is particularly relevant when performing mediation analysis (possibly in a causal framework) with stratified case–control (SCC) data in settings where both the outcome and the mediator are binary. Despite being designed for parametric identification, our strategy is general and can be used also in a nonparametric context. With reference to parametric estimation, we derive the maximum likelihood (ML) estimator and the M-estimator of the joint outcome–mediator parameter vector. We then conduct a simulation study focusing on the main causal mediation quantities (i.e., natural effects) and comparing M- and ML estimation to existing methods, based on weighting. As an illustrative example, we reanalyze a German CC data set in order to investigate whether the effect of reduced immunocompetency on listeriosis onset is mediated by the intake of gastric acid suppressors.

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  • 2.
    Genbäck, Minna
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Uncertainty intervals and sensitivity analysis for missing data2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    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.

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  • 3.
    Genbäck, Minna
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Uncertainty intervals for mixed effects models with non-ignorable missingnessManuskript (preprint) (Övrigt vetenskapligt)
    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.

  • 4.
    Genbäck, Minna
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    de Luna, Xavier
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Bounds and sensitivity analysis when estimating average treatment effects with imputation and double robust estimatorsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    When estimating average causal effects of treatments with observational data, scientists often rely on the assumption of unconfoundedness. We propose a sensitivity analysis for imputation estimators and doubly robust estimators, based on bounds (defining an identification interval) for the causal effect of interest, which allow for unobserved confounders. The bounds are derived from the bias of the estimators, expressed as a function of a sensitivity parameter. We describe how such bounds can take into account sampling variation, thereby yielding an uncertainty interval. We are also able to contrast the size of potential bias due to violation of the unconfoundedness assumption, to the misspecification of the models used to explain outcome with the observed covariates. While the latter bias can in principle be made arbitrarily small with increasing sample size (by increasing the flexibility of the models used), the bias due to unobserved confounding does not disappear with increasing sample size. Through numerical experiments we illustrate the relative size of the biases due to unobserved confounders and model misspecification, as well as the empirical coverage of the uncertainty interval on which the proposed sensitivity analysis is based.

  • 5.
    Genbäck, Minna
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Enheten för demografi och åldrandeforskning (CEDAR).
    de Luna, Xavier
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Causal inference accounting for unobserved confounding after outcome regression and doubly robust estimation2019Ingår i: Biometrics, ISSN 0006-341X, E-ISSN 1541-0420, Vol. 75, nr 2, s. 506-515Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We therefore develop uncertainty intervals for average causal effects based on outcome regression estimators and doubly robust estimators, which provide inference taking into account both sampling variability and uncertainty due to unobserved confounders. In contrast with sampling variation, uncertainty due to unobserved confounding does not decrease with increasing sample size. The intervals introduced are obtained by modeling the treatment assignment mechanism and its correlation with the outcome given the observed confounders, allowing us to derive the bias of the estimators due to unobserved confounders. We are thus also able to contrast the size of the bias due to violation of the unconfoundedness assumption, with bias due to misspecification of the models used to explain potential outcomes. This is illustrated through numerical experiments where bias due to moderate unobserved confounding dominates misspecification bias for typical situations in terms of sample size and modeling assumptions. We also study the empirical coverage of the uncertainty intervals introduced and apply the results to a study of the effect of regular food intake on health. An R-package implementing the inference proposed is available.

  • 6.
    Genbäck, Minna
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Ng, Nawi
    Umeå universitet, Medicinska fakulteten, Institutionen för folkhälsa och klinisk medicin, Epidemiologi och global hälsa.
    Stanghellini, Elena
    de Luna, Xavier
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Predictors of decline in self-reported health: addressing non-ignorable dropout in longitudinal studies of ageing2018Ingår i: European Journal of Ageing, ISSN 1613-9372, E-ISSN 1613-9380, Vol. 15, nr 2, s. 211-220Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Predictors of decline in health in older populations have been investigated in multiple studies before. Most longitudinal studies of aging, however, assume that dropout at follow-up is ignorable (missing at random) given a set of observed characteristics at baseline. The objective of this study was to address non-ignorable dropout in investigating predictors of declining self-reported health (SRH) in older populations (50 years or older) in Sweden, the Netherlands, and Italy. We used the SHARE panel survey, and since only 2895 out of the original 5657 participants in the survey 2004 were followed up in 2013, we studied whether the results were sensitive to the expectation that those dropping out have a higher proportion of decliners in SRH. We found that older age and a greater number of chronic diseases were positively associated with a decline in self-reported health in the three countries studies here. Maximum grip strength was associated with decline in self-reported health in Sweden and Italy, and self-reported limitations in normal activities due to health problems were associated with decline in self-reported health in Sweden. These results were not sensitive to non-ignorable dropout. On the other hand, although obesity was associated with decline in a complete case analysis, this result was not confirmed when performing a sensitivity analysis to non-ignorable dropout. The findings, thereby, contribute to the literature in understanding the robustness of longitudinal study results to non-ignorable dropout while considering three different population samples in Europe.

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  • 7.
    Genbäck, Minna
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Stanghellini, Elena
    University of Perugia, Perugia, Italy.
    de Luna, Xavier
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Uncertainty intervals for regression parameters with non-ignorable missingness in the outcome2015Ingår i: Statistical papers, ISSN 0932-5026, E-ISSN 1613-9798, Vol. 56, nr 3, s. 829-847Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    When estimating regression models with missing outcomes, scientists usually have to rely either on a missing at random assumption (missing mechanism is independent from the outcome given the observed variables) or on exclusion restrictions (some of the covariates affecting the missingness mechanism do not affect the outcome). Both these hypotheses are controversial in applications since they are typically not testable from the data. The alternative, which we pursue here, is to derive identification sets (instead of point identification) for the parameters of interest when allowing for a missing not at random mechanism. The non-ignorability of this mechanism is quantified with a parameter. When the latter can be bounded with a priori information, a bounded identification set follows. Our approach allows the outcome to be continuous and unbounded and relax distributional assumptions. Estimation of the identification sets can be performed via ordinary least squares and sampling variability can be incorporated yielding uncertainty intervals achieving a coverage of at least (1-α) probability. Our work is motivated by a study on predictors of body mass index (BMI) change in middle age men allowing us to identify possible predictors of BMI change even when assuming little on the missing mechanism.

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