ABSTRACT
This article investigates the logarithmic interval estimation of a ratio of two binomial proportions in dependent samples. Previous studies suggest that the confidence intervals of the difference between two correlated proportions and their ratio typically do not possess closed-form solutions. Moreover, the computation process is complex and often based on a maximum likelihood estimator, which is a biased estimator of the ratio. We look at the data from two dependent samples and explore the general problem of estimating the ratio of two proportions. Each sample is obtained in the framework of direct binomial sampling. Our goal is to demonstrate that the normal approximation for the estimation of the ratio is reliable for the construction of a confidence interval. The main characteristics of confidence estimators will be investigated by a Monte Carlo simulation. We also provide recommendations for applying the asymptotic logarithmic interval. The estimations of the coverage probability, average width, standard deviation of interval width, and index H are presented as the criteria of our judgment. The simulation studies indicate that the proposed interval performs well based on the aforementioned criteria. Finally, the confidence intervals are illustrated with three real data examples.
ABSTRACT
Genomic alteration in head and neck squamous cell carcinoma (HNSCC) was studied in two cell line pairs (HN30-HN31 and HN4-HN12) using conventional C-banding, multiplex fluorescence in situ hybridization (M-FISH), and array comparative genomic hybridization (array CGH). HN30 and HN4 were derived from primary lesions in the pharynx and base of tongue, respectively, and HN31 and HN12 were derived from lymph-node metastatic lesions belonging to the same patients. Gain of chromosome 1, 7, and 11 were shared in almost all cell lines. Hierarchical clustering revealed that HN31 was closely related to HN4, which shared eight chromosome alteration cases. Large C-positive heterochromatins were found in the centromeric region of chromosome 9 in HN31 and HN4, which suggests complex structural amplification of the repetitive sequence. Array CGH revealed amplification of 7p22.3p11.2, 8q11.23q12.1, and 14q32.33 in all cell lines involved with tumorigenesis and inflammation genes. The amplification of 2p21 (SIX3), 11p15.5 (H19), and 11q21q22.3 (MAML2, PGR, TRPC6, and MMP family) regions, and deletion of 9p23 (PTPRD) and 16q23.1 (WWOX) regions were identified in HN31 and HN12. Interestingly, partial loss of PTPRD (9p23) and WWOX (16q23.1) genes was identified in HN31 and HN12, and the level of gene expression tended to be the down-regulation of PTPRD, with no detectable expression of the WWOX gene. This suggests that the scarcity of PTPRD and WWOX genes might have played an important role in progression of HNSCC, and could be considered as a target for cancer therapy or a biomarker in molecular pathology.
