Nonparametric estimation of time-dependent ROC curves conditional on a continuous covariate

The receiver-operating characteristic (ROC) curve is the most widely used measure for evaluating the performance of a diagnostic biomarker when predicting a binary disease outcome. The ROC curve displays the true positive rate (or sensitivity) and the false positive rate (or 1-specificity) for different cut-off values used to classify an individual as healthy or diseased. In time-to-event studies, however, the disease status (e.g. death or alive) of an individual is not a fixed characteristic, and it varies along the study. In such cases, when evaluating the performance of the biomarker, several issues should be taken into account: first, the time-dependent nature of the disease status; and second, the presence of incomplete data (e.g. censored data typically present in survival studies). Accordingly, to assess the discrimination power of continuous biomarkers for time-dependent disease outcomes, time-dependent extensions of true positive rate, false positive rate, and ROC curve have been recently proposed. In this work, we present new nonparametric estimators of the cumulative/dynamic time-dependent ROC curve that allow accounting for the possible modifying effect of current or past covariate measures on the discriminatory power of the biomarker. The proposed estimators can accommodate right-censored data, as well as covariate-dependent censoring. The behavior of the estimators proposed in this study will be explored through simulations and illustrated using data from a cohort of patients who suffered from acute coronary syndrome.

Impact of TGF-ß1 -509C/T and 869T/C polymorphisms on glioma risk and patient prognosis

Transforming growth factor beta (TGF-ß) plays an important role in carcinogenesis. Two polymorphisms in the TGF-ß1 gene (-509C/T and 869T/C) were described to influence susceptibility to gastric and breast cancers. The 869T/C polymorphism was also associated with overall survival in breast cancer patients. In the present study, we investigated the relevance of these TGF-ß1 polymorphism in glioma risk and prognosis. A case-control study that included 114 glioma patients and 138 cancer-free controls was performed. Single nucleotide polymorphisms (SNPs) were evaluated by polymerase chain reaction followed by restriction fragment length polymorphism (PCR-RFLP). Univariate and multivariate logistic regression analyses were used to calculate odds ratio (OR) and 95 % confidence intervals (95 % CI). The influence of TGF-ß1 -509C/T and 869T/C polymorphisms on glioma patient survival was evaluated by a Cox regression model adjusted for patients' age and sex and represented in Kaplan-Meier curves. Our results demonstrated that TGF-ß1 gene polymorphisms -509C/T and 869T/C are not significantly associated with glioma risk. Survival analyses showed that the homozygous -509TT genotype associates with longer overall survival of glioblastoma (GBM) patients when compared with patients carrying CC + CT genotypes (OR, 2.41; 95 % CI, 1.06-5.50; p = 0.036). In addition, the homozygous 869CC genotype is associated with increased overall survival of GBM patients when compared with 869TT + TC genotypes (OR, 2.62; 95 % CI, 1.11-6.17; p = 0.027). In conclusion, this study suggests that TGF-ß1 -509C/T and 869T/C polymorphisms are not significantly associated with risk for developing gliomas but may be relevant prognostic biomarkers in GBM patients.