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Models for Additive and Sufficient Cause Interaction
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-2990-1959
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The aim of this thesis is to develop and explore models in, and related to, the sufficient cause framework, and additive interaction. Additive interaction is closely connected with public health interventions and can be used to make inferences about the sufficient causes in order to find the mechanisms behind an outcome, for instance a disease.

In paper A we extend the additive interaction, and interventions, to include continuous exposures. We show that there does not exist a model that does not lead to inconsistent conclusions about the interaction.

The sufficient cause framework can also be expressed using Boolean functions, which is expanded upon in paper B. In this paper we define a new model based on the multifactor potential outcome model (MFPO) and independence of causal influence models (ICI).

In paper C we discuss the modeling and estimation of additive interaction in relation to if the exposures are harmful or protective conditioned on some other exposure. If there is uncertainty about the effects direction there can be errors in the testing of the interaction effect.

Abstract [sv]

Målet med denna avhandling är att utveckla, och utforska modeller i det så kallade sufficent cause ramverket, och additiv interaktion. Additiv interaktion är nära kopplat till interventioner inom epidemiology och sociologi, men kan också användas för statistiska tester för sufficient causes för att förstå mekanimser bakom ett utfall, tex en sjukdom.

I artikel A så expanderar vi modellen för additiv interaktion och interventioner till att också inkludera kontinuerliga variabler. Vi visar att det inte finns någon modell som inte leder till motsägelser i slutsatsen om interaktionen.

Sufficient cause ramverket kan också utryckas via Boolska funktioner, vilket byggs vidare på i artikel B. I den artikeln definerar vi en modell baserad på mutltifactor potential outcome modellen (MFPO) och independence of causal influence modellen (ICI).

I artikel C diskuterar vi modelleringen och estimering av additiv interaktion i relation till om variablerna har skadlig eller skyddande effekt betingat på någon annan variabel. Om det finns osäkerhet kring en effekts riktning så kan det leda till fel i testerna för den additiva interaktionen.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. , p. 134
Series
TRITA-SCI-FOU ; 2019;43
Keywords [en]
Causal Inference, Sufficient Cause, Potential Outcomes, Counterfactual, Additive Interaction, Interaction, MFPO, ICI, Logistic Regression, Linear Odds, Public Health, Interventions, Probabilistic Potential Outcome
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics, Mathematical Statistics
Identifiers
URN: urn:nbn:se:kth:diva-259608ISBN: 978-91-7873-308-8 (electronic)OAI: oai:DiVA.org:kth-259608DiVA, id: diva2:1352480
Presentation
2019-10-10, F11, Lindstedtsvägen 22, KTH Stockholm, 10:00 (English)
Opponent
Supervisors
Note

Examinator: Professor Henrik Hult, Matematik, KTH

Available from: 2019-09-19 Created: 2019-09-18 Last updated: 2019-09-19Bibliographically approved
List of papers
1. On the Existence of Suitable Models for Additive Interaction with Continuous Exposures
Open this publication in new window or tab >>On the Existence of Suitable Models for Additive Interaction with Continuous Exposures
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Additive interaction can be of importance for public health interventions and it is commonly defined using binary exposures. There has been expansions of the models to also include continuous exposures, which could lead to better and more precise estimations of the effect of interventions. In this paper we define the intervention for a continuous exposure as a monotonic function. Based on this function for the interventions we prove that there is no model for estimating additive interactions with continuous exposures for which it holds that; (i) both exposures have marginal effects and no additive interaction on the exposure level for both exposures, (ii) neither exposure has marginal effect and there is additive interaction between the exposures. We also show that a logistic regression model for continuous exposures will always produce additive interaction if both exposures have marginal effects.

Keywords
Additive Interaction, Multiplicative Interaction, Logistic Regression, Linear Odds, Continuous Exposures, Public Health, Interventions
National Category
Probability Theory and Statistics Public Health, Global Health, Social Medicine and Epidemiology
Research subject
Applied and Computational Mathematics, Mathematical Statistics
Identifiers
urn:nbn:se:kth:diva-259549 (URN)
Note

QC 20190925

Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-25Bibliographically approved
2. On Probabilistic Multifactor Potential Outcome Models
Open this publication in new window or tab >>On Probabilistic Multifactor Potential Outcome Models
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The sufficient cause framework describes how sets of sufficient causes are responsible for causing some event or outcome. It is known that it is closely connected with Boolean functions. In this paper we define this relation formally, and show how it can be used together with Fourier expansion of the Boolean functions to lead to new insights. The main result is a probibalistic version of the multifactor potential outcome model based on independence of causal influence models and Bayesian networks.

Keywords
Causal Inference, Sufficient Cause, Potential Outcome, Boolean Function, MFPO, ICI, BCF, Probabilistic Potential Outcome, Qualitative Bayesian Network, Additive Interaction
National Category
Probability Theory and Statistics Public Health, Global Health, Social Medicine and Epidemiology
Identifiers
urn:nbn:se:kth:diva-259607 (URN)
Note

QC 20190925

Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-25Bibliographically approved
3. Measures of Additive Interactionand Effect Direction
Open this publication in new window or tab >>Measures of Additive Interactionand Effect Direction
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Measures for additive interaction are defined using risk ratios. These ratios need to be modeled so that all combinations of the exposures are harmful, as the scale between protective and harmful factors differs. This remodeling is referred to as recoding. Previously, recoding has been thought of as random. In this paper, we will examine and discuss the impact of recoding in studies with small effect sizes, such as genome wide association studies, and the impact recoding has on significance testing.

Keywords
Additive Interaction, Sufficient Cause, Logistic Regression, Linear Odds, RERI, Effect Direction
National Category
Public Health, Global Health, Social Medicine and Epidemiology Probability Theory and Statistics
Research subject
Applied and Computational Mathematics, Mathematical Statistics
Identifiers
urn:nbn:se:kth:diva-259606 (URN)
Note

QC 20190930

Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-30Bibliographically approved

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