Evaluating subject-level incremental values of new markers for risk classification rule

Abstract

Suppose that we need to classify a population of subjects into several well-defined ordered risk categories for disease prevention or management with their "baseline" risk factors/markers. In this article, we present a systematic approach to identify subjects using their conventional risk factors/markers who would benefit from a new set of risk markers for more accurate classification. Specifically for each subgroup of individuals with the same conventional risk estimate, we present inference procedures for the reclassification and the corresponding correct re-categorization rates with the new markers. We then apply these new tools to analyze the data from the Cardiovascular Health Study sponsored by the US National Heart, Lung, and Blood Institute. We used Framingham risk factors plus the information of baseline anti-hypertensive drug usage to identify adult American women who may benefit from the measurement of a new blood biomarker, CRP, for better risk classification in order to intensify prevention of coronary heart disease for the subsequent 10 years.

Fig. 1

Evaluating CRP incremental values for female participants from Cardiovascular Heath Study by treating non-CHD death as non-event; (a)-(c): ${\eta }_l^{\left(y\right)}(\cdot )$, l = 1, 2, 3, (solid lines for y = 1 and dashed lines for y = 0; thick lines for point estimators and thinner lines for 95% confidence intervals); (d) proportion of reclassification to other risk categories; (e) net gain in reclassification as measured by D₊(s) (point estimator: thick solid line, 95% point wise confidence intervals: dashed lines, and simultaneous confidence intervals: shaded region); (f) density function of the initial risks.

Fig. 2

Evaluating CRP incremental values for female participants from Cardiovascular Heath Study by treating non-CHD death as censoring; (a)-(c): ${\eta }_l^{\left(y\right)}(\cdot )$, l = 1, 2, 3, (solid lines for y = 1 and dashed lines for y = 0; thick lines for point estimators and thinner lines for 95% confidence intervals); (d) proportion of reclassification to other risk categories; (e) net gain in reclassification as measured by D₊(s) (point estimator: thick solid line, 95% point wise confidence intervals: dashed lines, and simultaneous confidence intervals: shaded region); (f) density function of the initial risks.

Fig. 3

Performance of the proposed procedure under a mis-specified model with sample size 3000 where the underlying effect of CRP is twice as big as that estimated from CHS data: (a,b,c) the sample average of ${\widehat{\eta }}_l^{\left(1\right)}\left(s\right)(\mathrm{l}=1,2,3)$ (solid curve) compared to the truth (gray dashed curve); (d,e,f) the average of the estimated standard errors (solid curve) for ${\widehat{\eta }}_l^{\left(1\right)}\left(s\right)$ compared to the empirical standard error estimates (gray dashed curves); and (g,h,i) the empirical coverage of the 95% confidence intervals based on the proposed resampling procedures. The three columns represents l = 1, 2 and 3, respectively.

Fig. 4

Evaluating CRP incremental values with respect to improvement in mean risk among cases with Y = 1 (dashed curve) and among controls with Y = 0 (dotted curve) for female participants from Cardiovascular Heath Study by treating non-CHD death as non-event.