Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper, we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves.Comment: Published in at http://dx.doi.org/10.1214/11-AOS937 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic Properties of the Sequential Empirical ROC and PPV Curves

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three common measures of performance for a diagnostic biomarker. The independent increments covariance structure assumption is common in the group sequential study design literature. Showing that summary measures of the ROC, PPV and NPV curves have an independent increments covariance structure will provide the theoretical foundation for designing group sequential diagnostic biomarker studies. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. In this paper we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves. These results are used to show that the independent increments assumption holds for some summary measures of the ROC, PPV and NPV curves when estimated empirically

Population-based study of the association of variants in mismatch repair genes with prostate cancer risk and outcomes.

BACKGROUND: Mismatch repair (MMR) gene activity may be associated with prostate cancer risk and outcomes. This study evaluated whether single nucleotide polymorphisms (SNP) in key MMR genes are related to prostate cancer outcomes. METHODS: Data from two population-based case-control studies of prostate cancer among Caucasian and African-American men residing in King County, Washington were combined for this analysis. Cases (n = 1,458) were diagnosed with prostate cancer in 1993 to 1996 or 2002 to 2005 and were identified through the Seattle-Puget Sound Surveillance Epidemiology and End Results cancer registry. Controls (n = 1,351) were age-matched to cases and were identified through random digit dialing. Logistic regression was used to assess the relationship between haplotype-tagging SNPs and prostate cancer risk and disease aggressiveness. Cox proportional hazards regression was used to assess the relationship between SNPs and prostate cancer recurrence and prostate cancer-specific death. RESULTS: Nineteen SNPs were evaluated in the key MMR genes: five in MLH1, 10 in MSH2, and 4 in PMS2. Among Caucasian men, one SNP in MLH1 (rs9852810) was associated with overall prostate cancer risk [odds ratio, 1.21; 95% confidence interval (95% CI), 1.02, 1.44; P = 0.03], more aggressive prostate cancer (odds ratio, 1.49; 95% CI, 1.15, 1.91; P < 0.01), and prostate cancer recurrence (hazard ratio, 1.83; 95% CI, 1.18, 2.86; P < 0.01), but not prostate cancer-specific mortality. A nonsynonymous coding SNP in MLH1, rs1799977 (I219V), was also found to be associated with more aggressive disease. These results did not remain significant after adjusting for multiple comparisons. CONCLUSION: This population-based case-control study provides evidence for a possible association with a gene variant in MLH1 in relation to the risk of overall prostate cancer, more aggressive disease, and prostate cancer recurrence, which warrants replication

Analysis of recently identified prostate cancer susceptibility loci in a population-based study: Associations with family history and clinical features.

Purpose: Two recent genome-wide association studies have highlighted several SNPs purported to be associated with prostate cancer risk. We investigated the significance of these SNPs in a population-based study of Caucasian men, testing the effects of each SNP in relation to family history of prostate cancer and clinicopathological features of disease. Experimental Design: We genotyped 13 SNPs in 1,308 prostate cancer patients and 1,267 unaffected controls frequency matched to cases by five-year age groups. The association of each SNP with disease risk and stratified by family history of prostate cancer and clinicopathological features of disease was calculated using logistic and polytomous regression. Results: These results confirm the importance of multiple previously reported SNPs in relation to prostate cancer susceptibility; 11 of the 13 SNPs were significantly associated with risk of developing prostate cancer. However, none of the SNP associations were of comparable magnitude to that associated with having a first-degree family history of the disease. Risk estimates associated with SNPs rs4242382 and rs2735839 varied by family history, while risk estimates for rs10993994 and rs5945619 varied by Gleason score. Conclusions: Our results confirm that several recently identified SNPs are associated with prostate cancer risk; however the variant alleles only confer a low to moderate relative risk of disease and are generally not associated with more aggressive disease features

Association of FGFR4 genetic polymorphisms with prostate cancer risk and prognosis

The fibroblast growth factor receptor 4 (FGFR4) is thought to be involved in many critical cellular processes and has been associated with prostate cancer risk. Four single nucleotide polymorphisms within or near FGFR4 were analysed in a population-based study of 1458 prostate cancer patients and 1352 age-matched controls. We found no evidence to suggest that any of the FGFR4 SNP genotypes were associated with prostate cancer risk or with disease aggressiveness, Gleason score or stage. A weak association was seen between rs351855 and prostate cancer-specific mortality. Subset analysis of cases that had undergone radical prostatectomy revealed an association between rs351855 and prostate cancer risk. While our results confirm an association between FGFR4 and prostate cancer risk in radical prostatectomy cases, they suggest that the role of FGFR4 in disease risk and outcomes at a population-based level appears to be minor