Nonparametric Adjustment for Measurement Error in Time-to-Event Data: Application to Risk Prediction Models

<p>Mismeasured time-to-event data used as a predictor in risk prediction models will lead to inaccurate predictions. This arises in the context of self-reported family history, a time-to-event predictor often measured with error, used in Mendelian risk prediction models. Using validation data, we propose a method to adjust for this type of error. We estimate the measurement error process using a nonparametric smoothed Kaplan–Meier estimator, and use Monte Carlo integration to implement the adjustment. We apply our method to simulated data in the context of both Mendelian and multivariate survival prediction models. Simulations are evaluated using measures of mean squared error of prediction (MSEP), area under the response operating characteristics curve (ROC-AUC), and the ratio of observed to expected number of events. These results show that our method mitigates the effects of measurement error mainly by improving calibration and total accuracy. We illustrate our method in the context of Mendelian risk prediction models focusing on misreporting of breast cancer, fitting the measurement error model on data from the University of California at Irvine, and applying our method to counselees from the Cancer Genetics Network. We show that our method improves overall calibration, especially in low risk deciles. Supplementary materials for this article are available online.</p

Sample characteristics of ABBY project participants; reported as mean (SD) for continuous variables or number and percent for categorical variables.

†<p>indicates statistical difference between Sylheti and the other group at the p<0.05 cut off.</p><p>Sample characteristics of ABBY project participants; reported as mean (SD) for continuous variables or number and percent for categorical variables.</p

Lowess smoother of the log of DHEAS by age among all girls Aged 5–16 years.

<p>Triangle shows inflection point where log salivary DHEAS reaches 5.5–6 pg/ml, signifying the clinical threshold for adrenarche.</p

Height and Weight by among girls aged 5–6 in the ABBY Project.

<p>(Upper) Lowess smoother of height and age for each group compared with the UK 1990 Growth References, (Lower) Lowess smoother of weight and age for each group compared with the UK 1990 Growth References.</p

Test performance characteristics.

<p>A. Crude estimates among women with full colposcopic and histologic evaluation (N = 675). B. Verification-biased adjusted estimates among total screened population (N = 2331).</p><p>CIN: cervical intraepithelial neoplasia, CI: confidence interval, PPV: positive predictive value, NPV: negative predictive value</p

Hazard ratios (95% C I) of adrenarche onset among girls <9.5 years adjusted for height, weight, BMI, and waist circumference.

<p>Hazard ratios (95% C I) of adrenarche onset among girls <9.5 years adjusted for height, weight, BMI, and waist circumference.</p

Salivary DHEAS pg/ml by age groups in Sylheti, first-generation, second-generation and European girls, aged 5-16 years.

†<p>indicates statistical difference between Sylheti and first-generation girls at the p<0.05 cut off.</p><p>Salivary DHEAS pg/ml by age groups in Sylheti, first-generation, second-generation and European girls, aged 5-16 years.</p

Demographics of study population.

<p>Demographics of study population.</p

Participation in screening and follow-up (colposcopy and biopsy where recommended) by randomization arm and screening result.

<p>Screen positive indicates positive result on VIA, Pap, and/or HPV DNA testing. Colposcopy normal indicates no area of abnormality identified, no biopsy recommended. Colposcopy abnormal-biopsy taken indicates that a biopsy was successfully obtained from all visually identified areas of abnormality. Colposcopically abnormal-biopsy refused indicates that a lesion was visualized and biopsy recommended, but the patient refused.</p

Estimated proportion of cases of CIN2+ observed and estimated via population weighting for verification bias adjustment.

<p><i>Screen detected</i> indicates proportion of cases of CIN2+ detected by hc2, and <i>screen undetected</i> indicates the proportion of CIN2+ cases detected through the screening program, but missed by hc2. <i>Refused biopsy</i> indicates the proportion of CIN2+ cases estimated among those who refused biopsy, <i>refused colposcopy</i> indicates the proportion of CIN2+ cases estimated among those who screened positive, but refused colposcopic exam, and <i>refused involvement</i> indicates the proportion of CIN2+ cases estimated among those who refused participation in the program (i.e., not screened).</p