Robustness against outliers in ordinal response model via divergence approach

This study deals with the problem of outliers in ordinal response model, which is a regression on ordered categorical data as the response variable. ``Outlier" means that the combination of ordered categorical data and its covariates is heterogeneous compared to other pairs. Although the ordinal response model is important for data analysis in various fields such as medicine and social sciences, it is known that the maximum likelihood method with probit, logit, log-log and complementary log-log link functions, which are often used, is strongly affected by outliers, and statistical analysts are forced to limit their analysis when there may be outliers in the data. To solve this problem, this paper provides inference methods with two robust divergences (the density-power and $\gamma$-divergences). We also derive influence functions for the proposed methods and show conditions on the link function for them to be bounded and to redescendence. Since the commonly used link functions satisfy these conditions, the analyst can perform robust and flexible analysis with our methods. In addition, and this is a result that further highlights our contributions, we show that the influence function in the maximum likelihood method does not have redescendence for any link function in the ordinal response model. Through numerical experiments using artificial and two real data, we show that the proposed methods perform better than the maximum likelihood method with and without outliers in the data for various link functions.Comment: 30 page

Androgen’s effects in female

The metabolic effects of androgens and their underlying mechanisms in females have been revealed by recent studies. An excess of androgens can have adverse effects on feeding behavior and metabolic functions and induce metabolic disorders / diseases, such as obesity, insulin resistance, and diabetes, in women and experimental animals of reproductive age. Interestingly, these effects of androgens are not observed in ovariectomized animals, indicating that their effects might be dependent on the estrogen milieu. Central and peripheral mechanisms, such as alterations in the activity of hypothalamic factors, reductions in energy expenditure, skeletal muscle insulin resistance, and β-cell dysfunction, might be related to these androgens’ effects

Association Between PSCA Variants and Duodenal Ulcer Risk

Background: While duodenal ulcer (DU) and gastric cancer (GC) are both H. pylori infection-related diseases, individuals with DU are known to have lower risk for GC. Many epidemiological studies have identified the PSCA rs2294008 T-allele as a risk factor of GC, while others have found an association between the rs2294008 C-allele and risk of DU and gastric ulcer (GU). Following these initial reports, however, few studies have since validated these associations. Here, we aimed to validate the association between variations in PSCA and the risk of DU/GU and evaluate its interaction with environmental factors in a Japanese population. Methods: Six PSCA SNPs were genotyped in 584 DU cases, 925 GU cases, and 8,105 controls from the Japan Multi-Institutional Collaborative Cohort (J-MICC). Unconditional logistic regression models were applied to estimate odds ratios (ORs) and 95% confidence intervals (CIs) for the association between the SNPs and risk of DU/GU. Results: PSCA rs2294008 C-allele was associated with per allele OR of 1.34 (95% CI, 1.18–1.51; P = 2.28 × 10−6) for the risk of DU. This association was independent of age, sex, study site, smoking habit, drinking habit, and H. pylori status. On the other hand, we did not observe an association between the risk of GU and PSCA SNPs. Conclusions: Our study confirms an association between the PSCA rs2294008 C-allele and the risk of DU in a Japanese population

Generalized Cram\'er's coefficient via ff-divergence for contingency tables

This study proposes measures describing the strength of association between the row and column variables via the $f$-divergence. Cram\'er's coefficient is a possible mechanism for the analysis of two-way contingency tables. Tomizawa et al. (2004) proposed more general measures, including Cram\'er's coefficient, using the power-divergence. In this paper, we propose more general measures and show some of their properties, demonstrating that the proposed measures are beneficial for comparing the strength of association in several tables.Comment: 20 page

An Index for the Degree and Directionality of Asymmetry for Square Contingency Tables with Ordered Categories

For square contingency tables with ordered categories, an index based on Cressie and Read's power divergence (or Patil and Taillie's diversity index) has been proposed in order to measure the degree of departure from symmetry. Although there are two types of maximum asymmetry (i.e., whether (1) all the observations concentrate in the top-right cell in the table, or (2) they concentrate in the bottom-left cell), the existing index cannot distinguish the two directions of maximum asymmetry. This paper proposes a directional index based on an arc-cosine function in order to simultaneously represent the degree and directionality of asymmetry. The proposed index would be useful for comparing degrees of asymmetry for several square contingency tables. Numerical examples show the utility of the proposed index using some datasets. We evaluate the usefulness of the proposed index by applying it to real data of the clinical study. The proposed index provides analysis results that are easier to interpret than the existing index

Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories

In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other hand, in the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from symmetry rather than independence. Over past years, many studies have proposed various types of indexes based on their power divergence (or diversity index) to represent the degree of departure from symmetry. This study proposes a two-dimensional index to measure the degree of departure from symmetry in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes. Numerical experiments show the utility of the proposed two-dimensional index. We show the usefulness of the proposed two-dimensional index by using real data

Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories

In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other hand, in the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from symmetry rather than independence. Over past years, many studies have proposed various types of indexes based on their power divergence (or diversity index) to represent the degree of departure from symmetry. This study proposes a two-dimensional index to measure the degree of departure from symmetry in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes. Numerical experiments show the utility of the proposed two-dimensional index. We show the usefulness of the proposed two-dimensional index by using real data

Schwannoma-like uterine leiomyoma with fever of unknown origin and surgical management in a middle-aged woman: A case report

Herein, we describe a 42-year-old woman with multiple uterine leiomyomas with interesting clinical and histologic findings. She had no medical history, except for uterine myomas, which were diagnosed in her early 30s. She presented with fever and lower abdominal pain, and her symptoms did not respond to antibiotics and antipyretics. The clinical evaluation suggested that degeneration of the largest myoma might be the cause of her symptoms, and pyomyoma was suspected. As she had sustained lower abdominal pain, hysterectomy and bilateral salpingectomy were performed. Histopathological examination confirmed the presence of usual-type uterine leiomyomas without suppurative inflammation. The largest tumor showed a rare morphology with a predominant schwannoma-like growth pattern and infarct-type necrosis. Thus, schwannoma-like leiomyoma was diagnosed. This rare tumor might be one of the manifestations of hereditary leiomyomatosis and renal cell cancer syndrome; however, this patient was unlikely to have that rare syndrome. Herein, the clinical, radiological, and pathologic findings of a schwannoma-like leiomyoma are presented and we have raised the question of whether patients with schwannoma-like uterine leiomyoma are more likely to be associated with hereditary leiomyomatosis and renal cell cancer syndrome than those with usual-type uterine leiomyoma