Introductory Prompt for the Article:
Title: A General Regression Methodology for ROC Curve Estimation Authors: Anna N. Angelos Tosteson, MS, and Colin B. Begg, PhD Journal: Medical Decision Making Volume/Issue/Pages: 8(3): 204-215 Publication Year: 1988 DOI: 10.1177/0272989X8800800309
This influential article, published in Medical Decision Making in 1988, presents a novel and flexible general regression methodology for estimating and analyzing Receiver Operating Characteristic (ROC) curves. Authored by Anna N. Angelos Tosteson and Colin B. Begg, the paper addresses significant shortcomings of traditional ROC curve generation methods, particularly their inability to directly incorporate covariates that may influence diagnostic test accuracy.
The proposed methodology applies generalized ordinal regression models to categorical rating data. This approach offers several key advantages over conventional nonparametric and parametric methods, substantially improving the ability to assess diagnostic tests using ROC curves:
- Parsimony and Covariate Adjustment: It allows for the parsimonious adjustment of ROC curve parameters for relevant covariates through two distinct regression equations: location and scale. Unlike traditional methods that necessitate dividing data into potentially sparse subgroups, this new method can incorporate continuous and categorical covariates directly into the analysis.
- Flexibility in Model Shape: The model is not restricted to the common assumption of binormality, which is often employed in smoothed ROC curve estimation, yet it can still accommodate the binormal model as a specific form of the more general model. This flexibility allows for a wide variety of ROC curve shapes.
- Insights into Covariate Effects: The method provides a powerful mechanism for pinpointing the effect that interobserver variability has on the ROC curve. It also enables the adjustment of ROC curves for temporal variation and case mix, and facilitates the assessment of a test’s incremental diagnostic value by implicitly controlling for relevant clinical information (covariates) already available.
- Interpretable Parameters: The model employs an underlying mathematical function known as the “link function” (e.g., probit or logit) to introduce smoothness and provide meaningful interpretations for its parameters.
- Location regression parameters (α) represent the extent to which the test is associated with each covariate, loosely speaking, influencing the “separation” of the response variable. If only location terms are included, an individual covariate term (without an interaction with disease status) does not define a separate curve for each level of the covariate; instead, it merely changes the cutoff values, corresponding to movement along the ROC curve rather than creating a new one.
- Scale regression parameters (ß) represent the influence of each covariate on the “spread” of the response categories. Their inclusion can disrupt desirable qualities like symmetry and concavity, and they may lead to curves that cross the 45° line. To accommodate different shapes for the ROC curve according to the level of the covariate, a scale term for the interaction of disease and the covariate must be included in the model.
The article details how to construct an ROC curve from the model’s equations and illustrates the method using an example of ultrasonography in detecting hepatic metastases. Parameter estimation is achieved through maximum likelihood estimates via iteratively reweighted least squares, a process available in specialized software like PLUM.
Ultimately, Tosteson and Begg emphasize that this new methodology is a valuable tool that will enhance the ability to assess the value of diagnostic tests, offering many advantages over traditional methods, even though those methods can be accommodated as special cases of this new technique.
APA Reference:
Tosteson, A. N. A., & Begg, C. B. (1988). A general regression methodology for ROC curve estimation. Medical Decision Making, 8(3), 204–215. https://doi.org/10.1177/0272989X8800800309
