Monotone B-Spline Smoothing for a Generalized Linear Model Response

Wang, Wei; Small, Dylan S.

doi:10.1080/00031305.2014.969445

Cited by 7 publications

(7 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using a boosting technique [ 38 , 39 ] implement a similar approach to estimate β under the same constraint A β ≥ 0 to solve the problem defined in equation (3) of the supplementary material. In the settings that have been tried, a comparison of fitting a univariate generalized linear model under the monotonicity constraint showed that the boosting algorithm is computationally intensive [ 23 ]. A summary of other approaches in the literature for estimation when there are monotonicity constraints and interactions is provided in Section S8 of the supplementary material.…”

Section: Discussionmentioning

confidence: 99%

“…Semiparametric approaches have been applied to estimate relative risk functions [ 19 ], to calculate odds ratios [ 20 ], and to estimate effect measures in the presence of interactions [ 21 ]. Herein, we use B-splines [ 22 ] (see also [ 23 , 24 ] and references therein), to develop a semiparametric approach to estimate the PAF in the presence of interactions with confounding. The model fitting procedure is formulated as a well studied quadratic programming problem, and, thus, can be easily solved using standard optimization packages.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Wang

Small

Harhay

2020

BMC Med Res Methodol

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Wang

Small

Harhay

2020

BMC Med Res Methodol

Self Cite

View full text Add to dashboard Cite

show abstract

“…We require monotone functions so we can take inverses for calibration later, but this only requires the spline coefficients to be non-decreasing ie. β 1 ≤ β 2 ≤ … ≤ β k [ 35 ] as used in similar applications [ 28 , 36 , 37 ]. Our approach has three benefits.…”

Section: Methodsmentioning

confidence: 99%

Modeling energy balance while correcting for measurement error via free knot splines

2018

View full text Add to dashboard Cite

Measurements of energy balance components (energy intake, energy expenditure, changes in energy stores) are often plagued with measurement error. Doubly-labeled water can measure energy intake (EI) with negligible error, but is expensive and cumbersome. An alternative approach that is gaining popularity is to use the energy balance principle, by measuring energy expenditure (EE) and change in energy stores (ES) and then back-calculate EI. Gold standard methods for EE and ES exist and are known to give accurate measurements, albeit at a high cost. We propose a joint statistical model to assess the measurement error in cheaper, non-intrusive measures of EE and ES. We let the unknown true EE and ES for individuals be latent variables, and model them using a bivariate distribution. We try both a bivariate Normal as well as a Dirichlet Process Mixture Model, and compare the results via simulation. Our approach, is the first to account for the dependencies that exist in individuals’ daily EE and ES. We employ semiparametric regression with free knot splines for measurements with error, and linear components for error free covariates. We adopt a Bayesian approach to estimation and inference and use Reversible Jump Markov Chain Monte Carlo to generate draws from the posterior distribution. Based on the semiparameteric regression, we develop a calibration equation that adjusts a cheaper, less reliable estimate, closer to the true value. Along with this calibrated value, our method also gives credible intervals to assess uncertainty. A simulation study shows our calibration helps produce a more accurate estimate. Our approach compares favorably in terms of prediction to other commonly used models.

show abstract

“…Depending on the research question and nature of the variable on which we want to impose a monotonicity constraint, different techniques may be more favorable. If the variable is essentially continuous, such as time intervals or the dose of a drug, we can use parametric functions which are known to be monotonic (e.g., the log or logistic functions in simple cases) or use semi-parametric approaches such as monotonic splines (Gu, 2013;He & Shi, 1998;Helwig, 2017;Kelly & Rice, 1990;Lee, 1996;Leitenstorfer & Tutz, 2006, 2007Pya & Wood, 2015;Ramsay, 1988;Wang & Small, 2015). If the variable under study is categorical, the monotonicity assumption reduces to an ordering constraint on the predicted category means.…”

mentioning

confidence: 99%

Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

Bürkner¹,

Charpentier²

2018

Preprint

View full text Add to dashboard Cite

Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the contained information. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modeling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter $b$ representing the direction and size of the effect and a simplex parameter $\zeta$ modeling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may not only be applied to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies, we show that the model is well calibrated and, in case of monotonicity, has similar or even better predictive performance than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects, which allows to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.

show abstract

Monotone B-Spline Smoothing for a Generalized Linear Model Response

Cited by 7 publications

References 38 publications

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

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

Modeling energy balance while correcting for measurement error via free knot splines

Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

Contact Info

Product

Resources

About