Adaptive Fractional Polynomial Modeling

Knafl, George J.

doi:10.4236/ojs.2018.81011

Cited by 6 publications

(7 citation statements)

References 23 publications

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“…Knafl and Ding [ 12 ] formulate adaptive regression methods for searching through alternative models for means and dispersions in a variety of contexts. These methods use adaptive fractional polynomial models [ 21 ]. A short overview is provided here (for details, see Chapter 20, [ 12 ]).…”

Section: Methodsmentioning

confidence: 99%

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Regression Modeling of Individual-Patient Correlated Discrete Outcomes with Applications to Cancer Pain Ratings

Knafl¹,

Meghani²

2022

OJS

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Purpose: To formulate and demonstrate methods for regression modeling of probabilities and dispersions for individual-patient longitudinal outcomes taking on discrete numeric values. Methods: Three alternatives for modeling of outcome probabilities are considered. Multinomial probabilities are based on different intercepts and slopes for probabilities of different outcome values. Ordinal probabilities are based on different intercepts and the same slope for probabilities of different outcome values. Censored Poisson probabilities are based on the same intercept and slope for probabilities of different outcome values. Parameters are estimated with extended linear mixed modeling maximizing a likelihood-like function based on the multivariate normal density that accounts for within-patient correlation. Formulas are provided for gradient vectors and Hessian matrices for estimating model parameters. The likelihood-like function is also used to compute cross-validation scores for alternative models and to control an adaptive modeling process for identifying possibly nonlinear functional relationships in predictors for probabilities and dispersions. Example analyses are provided of daily pain ratings for a cancer patient over a period of 97 days. Results: The censored Poisson approach is preferable for modeling these data, and presumably other data sets of this kind, because it generates a competitive model with fewer parameters in less time than the other two approaches. The generated probabilities for this model are distinctly nonlinear in time while the dispersions are distinctly non-constant over time, demonstrating the need for adaptive modeling of such data. The analyses also address the dependence of these daily pain ratings on time and the daily numbers of pain flares. Probabilities and dispersions change differently over time for different numbers of pain flares. Conclusions: Adaptive modeling of daily pain ratings for individual cancer patients is an effective way to identify nonlinear relationships in time as well as in other predictors such as the number of pain flares.

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Section: Methodsmentioning

confidence: 99%

“…thods use adaptive fractional polynomial models [21]. A short overview is provided here (for details, see Chapter 20, [12]).…”

Section: Likelihood-like Cross-validationmentioning

confidence: 99%

Regression Modeling of Individual-Patient Correlated Discrete Outcomes with Applications to Cancer Pain Ratings

Knafl¹,

Meghani²

2022

OJS

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“…Let u be a primary predictor and q a real-valued power. As in [7], define the associated general power transform ( ) ; g u q as ( ) ( ) cos , 0 ; 0, 0 , 0 q q q u u g u q u u u…”

Section: Fractional Polynomial Hazard Rate Modelingmentioning

confidence: 99%

“…The objectives of this article are to formulate an adaptive approach for hazard regression modeling based on fractional polynomials [6] [7] and then to demonstrate this approach using two survival time data sets, one for lung cancer patients and one for multiple myeloma patients. This is a novel, original approach accounting for the dependence of the hazard rate on time while allowing for non-proportionality of the hazard rate as well as for nonlinearity in time and in other available predictors.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Approach for Hazard Regression Modeling

Knafl¹

2023

OJS

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Regression models for survival time data involve estimation of the hazard rate as a function of predictor variables and associated slope parameters. An adaptive approach is formulated for such hazard regression modeling. The hazard rate is modeled using fractional polynomials, that is, linear combinations of products of power transforms of time together with other available predictors. These fractional polynomial models are restricted to generating positive-valued hazard rates and decreasing survival times. Exponentially distributed survival times are a special case. Parameters are estimated using maximum likelihood estimation allowing for right censored survival times. Models are evaluated and compared using likelihood cross-validation (LCV) scores. LCV scores and tolerance parameters are used to control an adaptive search through alternative fractional polynomial hazard rate models to identify effective models for the underlying survival time data. These methods are demonstrated using two different survival time data sets including survival times for lung cancer patients and for multiple myeloma patients. For the lung cancer data, the hazard rate depends distinctly on time. However, controlling for cell type provides a distinct improvement while the hazard rate depends only on cell type and no longer on time. Furthermore, Cox regression is unable to identify a cell type effect. For the multiple myeloma data, the hazard rate also depends distinctly on time. Moreover, consideration of hemoglobin at diagnosis provides a distinct improvement, the hazard rate still depends distinctly on time, and hemoglobin distinctly moderates the effect of time on the hazard rate. These results indicate that adaptive hazard rate modeling can provide unique insights into survival time data.

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“…Knafl and Ding [ 3 ] provide a detailed formulation for adaptively searching through alternative regression models for means and dispersions in a variety of contexts using adaptive fractional polynomial models [ 9 ]. A brief overview is provided here.…”

Section: Modeling Possibly Nonlinear Means and Dispersion Over Timementioning

confidence: 99%

Modeling Individual Patient Count/Rate Data over Time with Applications to Cancer Pain Flares and Cancer Pain Medication Usage

Knafl¹,

Meghani²

2021

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The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non-constant dispersions while requiring reasonable amounts of time to search over alternative models for those data. This research addresses formulations for two approaches for extending generalized estimating equations (GEE) modeling. These approaches use a likelihood-like function based on the multivariate normal density. The first approach augments standard GEE equations to include equations for estimation of dispersion parameters. The second approach is based on estimating equations determined by partial derivatives of the likelihood-like function with respect to all model parameters and so extends linear mixed modeling. Three correlation structures are considered including independent, exchangeable, and spatial autoregressive of order 1 correlations. The likelihood-like function is used to formulate a likelihood-like cross-validation (LCV) score for use in evaluating models. Example analyses are presented using these two modeling approaches applied to three data sets of counts/rates over time for individual cancer patients including pain flares per day, as needed pain medications taken per day, and around the clock pain medications taken per day per dose. Means and dispersions are modeled as possibly nonlinear functions of time using adaptive regression modeling methods to search through alternative models compared using LCV scores. The results of these analyses demonstrate that extended linear mixed modeling is preferable for modeling individual patient count/rate data over time, because in example analyses, it either generates better LCV scores or more parsimonious models and requires substantially less time.

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Adaptive Fractional Polynomial Modeling

Cited by 6 publications

References 23 publications

Regression Modeling of Individual-Patient Correlated Discrete Outcomes with Applications to Cancer Pain Ratings

Regression Modeling of Individual-Patient Correlated Discrete Outcomes with Applications to Cancer Pain Ratings

An Adaptive Approach for Hazard Regression Modeling

Modeling Individual Patient Count/Rate Data over Time with Applications to Cancer Pain Flares and Cancer Pain Medication Usage

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