Semiparametric estimation of the attributable fraction when there are interactions under monotonicity constraints
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(2020) 20:236
TECHNICA L A DVA NCE
Open Access
Semiparametric estimation of the attributable fraction when there are interactions under monotonicity constraints Wei Wang1*
, Dylan S. Small2 and Michael O. Harhay1,3
Abstract Background: The 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. Methods: We 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. Results: The 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. Conclusions: The developed approach is easy to implement and supports flexible modeling of possible non-linear relationships between a disease and an exposure of interest. Keywords: Attributable fraction, B-splines, Interaction, Monotonicity constraint, Quadratic programming
Background The population attributable fraction (PAF) is the fraction of disease cases in a sample that can be attributed to the exposure. The PAF is an important measure of the public health impact of an exposure on disease burden, and thus it is useful to prioritize public health interventions *Correspondence: [email protected] Palliative and Advanced Illness Research (PAIR) Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA Full list of author information is available at the end of the article 1
[1, 2]. The maximum likelihood method is commonly used to estimate the PAF. However, this approach to estimation requires a correct model for the probability of disease given the exposure and other covariates subject to the ignorable treatment assignment assumption [3] (to be reviewed in the next section). Logistic regression is typically used to model the probability of disease given the exposure and the other
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