By Jonathan Chaffer, Karl Swedberg
As a diagnostic decision-making software, receiver working attribute (ROC) curves supply a finished and visually appealing method to summarize the accuracy of predictions. they're commonly utilized in scientific analysis and more and more in fields equivalent to information mining, credits scoring, climate forecasting, and psychometry. during this example-driven booklet, writer Mithat GÃ¶nen illustrates the numerous latest SAS strategies that may be adapted to supply ROC curves and expands upon additional analyses utilizing different SAS systems and macros. either parametric and nonparametric tools for reading ROC curves are coated intimately.
themes addressed contain:
- Appropriate equipment for binary, ordinal, and non-stop measures
- Computations utilizing PROC FREQ, PROC LOGISTIC, PROC NLMIXED, and macros
- Comparing the ROC curves of a number of markers and adjusting them for covariates
- ROC curves with censored facts
- Using the ROC curve for comparing multivariable prediction types through bootstrap and cross-validation
- ROC curves in SAS firm Miner
- And extra!
Written for any statistician drawn to studying extra approximately ROC curve method, the e-book assumes readers have a uncomplicated knowing of regression systems and reasonable familiarity with Base SAS and SAS/STAT. a few familiarity with SAS/GRAPH is useful yet now not crucial.
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Additional resources for Analyzing Receiver Operating Characteristic Curves With SAS
0172 Sample Size = 181 Two Somers’ statistics are reported: C|R uses the column variable as the predictor and the row variable as the gold standard, while R|C uses the row variable as the predictor and the column variable as the gold standard. 0523. If the table was constructed so that the marker (the SUV) was the column variable and the gold standard was the row variable, then we would have used the Somers’ D C|R statistic. 8713, identical to the LOGISTIC output, which was reported with three significant digits.
3 Empirical ROC Curve and the Conditional Distributions of the Marker A convenient mathematical representation of the empirical ROC curve yields further insight into many of its properties. 1 shows, the distribution of the marker should be examined based on the gold standard value. Let f(t|D=0) and f(t|D=1) be the conditional density of the marker for gold standard negative and positive patients. The upper histogram is an approximation for f(t|D=0) and the lower one for f(t|D=1). Now define F and G as the survival functions (one minus the cumulative distribution) corresponding to f(t|D=0) and f(t|D=1), that is Chapter 3: Single Continuous Predictor 21 ∞ F (t ) = ∫ f ( s | D = 0) ds t ∞ G (t ) = ∫ f ( s | D = 1) ds t Because all patients in G(t) are, by definition, gold standard positive, G(t) describes the proportion of positive patients whose SUV exceeds t out of all positive patients.
You can first plot the observed ROC points, as if for an empirical ROC curve, but instead of connecting them, you can fit a curve with the form above and find a and b such that the resulting fit is best. This process is further facilitated by the observation that Φ−1 ( y ) = a + bΦ−1 ( x) Therefore, if the ROC points are first transformed to the probit scale, then you only need to fit a line, which can be done, almost trivially, by using least squares. There are many SAS/STAT procedures available for this purpose, but PROC REG offers the simplest interface.