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Semiparametric estimation of the attributable fraction when there are interactions under monotonicity constraints

Authors
  • Wang, Wei1
  • Small, Dylan S.2
  • Harhay, Michael O.1, 1
  • 1 Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA , Philadelphia (United States)
  • 2 The Wharton School, University of Pennsylvania, Philadelphia, PA, USA , Philadelphia (United States)
Type
Published Article
Journal
BMC Medical Research Methodology
Publisher
Springer (Biomed Central Ltd.)
Publication Date
Sep 21, 2020
Volume
20
Issue
1
Identifiers
DOI: 10.1186/s12874-020-01118-4
Source
Springer Nature
Keywords
License
Green

Abstract

BackgroundThe population attributable fraction (PAF) is the fraction of disease cases in a sample that can be attributed to an exposure. Estimating the PAF often involves the estimation of the probability of having the disease given the exposure while adjusting for confounders. In many settings, the exposure can interact with confounders. Additionally, the exposure may have a monotone effect on the probability of having the disease, and this effect is not necessarily linear.MethodsWe develop a semiparametric approach for estimating the probability of having the disease and, consequently, for estimating the PAF, controlling for the interaction between the exposure and a confounder. We use a tensor product of univariate B-splines to model the interaction under the monotonicity constraint. The model fitting procedure is formulated as a quadratic programming problem, and, thus, can be easily solved using standard optimization packages. We conduct simulations to compare the performance of the developed approach with the conventional B-splines approach without the monotonicity constraint, and with the logistic regression approach. To illustrate our method, we estimate the PAF of hopelessness and depression for suicidal ideation among elderly depressed patients.ResultsThe proposed estimator exhibited better performance than the other two approaches in the simulation settings we tried. The estimated PAF attributable to hopelessness is 67.99% with 95% confidence interval: 42.10% to 97.42%, and is 22.36% with 95% confidence interval: 12.77% to 56.49% due to depression.ConclusionsThe developed approach is easy to implement and supports flexible modeling of possible non-linear relationships between a disease and an exposure of interest.

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