Journal ArticleDOI
Flexible regression models with cubic splines
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In this article, the authors describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates, which can help prevent the problems that result from inappropriate linearity assumptions.Abstract:
We describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates. This simple method can help prevent the problems that result from inappropriate linearity assumptions. We compare restricted cubic spline regression to non-parametric procedures for characterizing the relationship between age and survival in the Stanford Heart Transplant data. We also provide an illustrative example in cancer therapeutics.read more
Citations
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Journal ArticleDOI
Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors
TL;DR: In this article, an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities are discussed, which are particularly needed for binary, ordinal, and time-to-event outcomes.
Book ChapterDOI
Prognostic/Clinical Prediction Models: Multivariable Prognostic Models: Issues in Developing Models, Evaluating Assumptions and Adequacy, and Measuring and Reducing Errors
TL;DR: An easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities are discussed, applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes.
Tutorial in biostatistics multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors
Kerry L. Lee,Daniel B. Mark +1 more
TL;DR: An easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities are discussed, which are applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes.
BookDOI
Regression Modeling Strategies
TL;DR: Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas.
Journal ArticleDOI
The APACHE III prognostic system. Risk prediction of hospital mortality for critically ill hospitalized adults.
William A. Knaus,Douglas P. Wagner,Elizabeth A. Draper,Jack E. Zimmerman,Marilyn Bergner,Paulo G. Bastos,Carl A. Sirio,Donaldj Murphy,Ted Lotring,Anne M. Damiano +9 more
TL;DR: The overall predictive accuracy of the first-day APACHE III equation was such that, within 24 h ofICU admission, 95 percent of ICU admissions could be given a risk estimate for hospital death that was within 3 percent of that actually observed.
References
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Journal ArticleDOI
Applied regression analysis 2nd ed.
Norman R. Draper,Smith H +1 more
TL;DR: This book brings together a number of procedures developed for regression problems in current use and includes material that either has not previously appeared in a textbook or if it has appeared is not generally available.
Journal ArticleDOI
Generalized Additive Models
Trevor Hastie,Robert Tibshirani +1 more
TL;DR: The class of generalized additive models is introduced, which replaces the linear form E fjXj by a sum of smooth functions E sj(Xj), and has the advantage of being completely auto- matic, i.e., no "detective work" is needed on the part of the statistician.
Journal ArticleDOI
Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting
TL;DR: The topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology.
Journal ArticleDOI
Chi-squared goodness-of-fit tests for the proportional hazards regression model
TL;DR: In this article, a class of omnibus chi-squared goodness-of-fit tests is presented for the model, relating failure time to covariate values, proposed by Cox (1972), which are based on the expected and observed frequency that a data point, representing a failure with associated covariates, falls into one of L mutually exclusive categories.