Improving Analysis of Continuous Predictors: Advantages of Fractional Polynomial Transformations (FP) and Interpretation of “Non-Linear” Odds Ratios (OR) or Hazard Ratios (HR)

Author(s)

Valveny N1, O´Mahoney T2, Alfonso V1, Mansilla I1, Shala A1
1TFS HealthScience, Barcelona, Spain, 2TFS HealthScience, Newbridge, Ireland

OBJECTIVES: Assessing continuous predictors (e.g., cholesterol) with a categorical outcome (e.g., mortality) under a “linearity assumption” may lead to wrong decisions, especially if the variable is categorized (data-driven approach). We aimed to review methods for analyzing continuous predictors in regression models from RWE studies, to describe advantages of FP over traditional methods, and to develop a new visualization tool to help understanding “non-linear” ORs or HRs.

METHODS: We searched in Pubmed RWE studies from the last 2 years (2020-2022) and summarized main methods, including advantages and limitations. We described FP methodology and developed a “FP-Risk Score Calculator” to translate model parameters into 10 risk zones (intuitive, traffic-light-like ranging from green to dark red) for the predictor values.

RESULTS: Most common methods are, by decreasing order: 1) cut-points (49.7%); 2) untransformed variable (47.6%); 3) cubic-spline transformations (2.5%); 4) FP-transformations (0.2%). FP was the most efficient method selecting the best fit based on power and alpha error: 44 single or double-term transformations using “fraction powers” comprising most biologically plausible risk shapes (linear/non-linear, monotonic/unimodal). FP can be tested in univariate or multivariate models using a hierarchical function selection procedure, to select the best (and simplest) fit, which may also be linear (http://biom131.imbi.uni-freiburg.de/biom/mfp/). “Non-linear” OR/HRs are x-dependent, i.e., vary along X. We developed a “FP-Risk Score Calculator” to translate model parameters into 10 Risk Zones for the observed range of X values. Each zone is linked to 10 evenly divided outcome probabilities and (for simplicity) to the OR/HR of the mid-point.

CONCLUSIONS: Continuous variables should not be assumed by default to have a linear relationship with the outcome nor categorized using pre-defined or data-driven cut-points. Systematic FP-transformations are easy to implement and allow selecting the best (and simplest) fit. The new FP-Risk Score Calculator divides predictor values into 10 risk zones to facilitate clinical interpretation.

Conference/Value in Health Info

2023-11, ISPOR Europe 2023, Copenhagen, Denmark

Value in Health, Volume 26, Issue 11, S2 (December 2023)

Code

MSR33

Topic

Methodological & Statistical Research

Topic Subcategory

Confounding, Selection Bias Correction, Causal Inference

Disease

No Additional Disease & Conditions/Specialized Treatment Areas

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