Methods for Modelling Non-Linear Relationships

2:00 pm to 4:00 pm EST | The session will be delivered live and online via the Gotowebinar system.

This webinar is part of the Advanced Methods Webinar Series

This webinar will discuss the options for including continuous covariates in a regression model, and in particular, methods for modeling non-linear relationships.  In his book, 'Clinical Prediction Models,' Ewout Steyerberg presents a hierarchy of procedures for including a continuous predictor, starting with dichotomizing the variable and moving to modeling the variable using restricted cubic splines or using a fractional polynomial model. This presentation discusses all of the choices, with a focus on the last two.

Restricted cubic splines express the relationship between the continuous covariate and the outcome using a set of cubic polynomials, which are constrained to meet at pre-specified points, called knots. Between the knots, each curve can take on the shape that best describes the data.

A fractional polynomial model is another flexible method for modeling a relationship that is possibly nonlinear. In this model, polynomials with non-integer and negative powers are considered, along with the more conventional square and cubic polynomials, and the small subset of powers that best fits the data is selected.

The webinar will describe and illustrate these methods at an introductory level intended to be useful to anyone who is familiar with regression analyses.

The webinar will:

  • Provide an overview of options to be used for modeling non-linear relationships
  • Discuss the pros and cons of dichotomizing continuous variables and of using simple polynomials or transformations
  • Explain what restricted cubic splines are, how to calculate and use them in a regression, and how to interpret the results
  • Explain what fractional polynomials are, how to select a regression model using fractional polynomials, and how to interpret the results
  • The examples will use some SAS code to make the methods easier to understand, but familiarity with SAS is not needed


Ruth CroxfordRuth Croxford is a Senior Epidemiologist at ICES.  She has Master’s degrees in Statistics from the University of Toronto and in Computer Science from Queen’s University, and will try not to embarrass any of these institutions during this webinar.  At ICES, she has contributed to the design and analysis of projects covering a wide variety of topics in health care.   In the process, she’s been extremely fortunate to continually learn from colleagues and researchers.  She is pleased to participate in this webinar series, as we all continue to learn from one another.

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