Description Usage Arguments Value References See Also Examples
Often in the risk prediction setting, there is interest in combining several predictors (e.g., biomarkers) into a single tool for prognosis, diagnosis or screening. One way to accomplish this is by targeting a measure of predictive capacity. In many cases, there is interest in the true positive rate (TPR; sensitivity) for a clinically meaningful false positive rate (FPR; 1-specificity). This function estimates a linear combination of predictors by maximizing a smooth approximation to the empirical TPR (sTPR) while constraining a smooth approximation to the empirical FPR (sFPR). Furthermore, since the TPR and FPR are determined both by the linear combination and the threshold (i.e., TPR is the proportion of diseased individuals whose linear combination value exceeds some threshold), this function estimates the combination and the threshold simultaneously. Estimates from robust logistic regression, specifically the method of Bianco and Yohai (implemented via the aucm
package), are used as starting values for the linear combination.
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data |
An object of class ‘data.frame’ where the first column contains the outcome (disease) indicator (1 for diseased, 0 for non-diseased), and the subsequent columns are the predictors. Note that missing observations are allowed, but they will be automatically removed. All columns of |
tval |
The acceptable FPR value. The method constrains the smooth approximation to the FPR to be less than or equal to |
initialval |
Starting values of the predictor combination for the smooth TPR maximization algorithm. Default value is |
alpha |
To improve performance, a small buffer may be added to |
approxh |
The tuning parameter for the smooth approximations is the ratio of the standard deviation of the linear combination (based on the starting values) to n^{approxh}, where n is the sample size. In particular, larger values of |
tolval |
Controls the tolerance on feasibility and optimality for the optimization procedure (performed by |
stepsz |
Controls the step size for the optimization procedure (performed by |
multiplier |
Used to provide an initial value for the threshold to the optimization procedure. Using the starting values for the linear combination (based on robust logistic regression), a reasonable choice for this initial value is the threshold such that sFPR = |
A list with the following components:
sTPRrslt |
The results from the smooth TPR maximization procedure, including 'delta' (the threshold estimated by the maximization procedure), 'deltaRE' (the threshold estimated based on quantiles of the combination estimated by the maximization procedure), the estimated combination coefficients, and an indicator of convergence for the optimization procedure. |
rGLMrslt |
The results from the robust logistic regression model (fit using |
GLMrslt |
The results from the (standard) logistic regression model, including 'delta' (the threshold estimated based on quantiles of the combination estimated by (standard) logistic regression), the estimated combination coefficients, and an indicator of convergence for |
Nobs |
The number of observations remaining after observations with missing values were removed. |
For all three methods, the combination coefficients are reported in the same order as the columns of data
.
Meisner, A., Carone, M., Pepe, M., and Kerr, K.F. (2017). Combining biomarkers by maximizing the true positive rate for a fixed false positive rate. UW Biostatistics Working Paper Series, Working Paper 420.
Bianco, A.M. and Yohai, V.J. (1996) Robust estimation in the logistic regression model. In Robust statistics, data analysis, and computer intensive methods (ed H. Rieder), pp 17-34. Springer.
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