In this study, we introduce a new model called the Odd Burr Lindley distribution which extends the Lindley distribution and has increasing, bathtub and upside down shapes for the hazard rate function. It includes the odd Lindley distribution as a special case. Several statistical properties of the distribution are explored, such as the density, hazard rate, survival, quantile functions, and moments. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A simulation study is performed to compare the performance of the different parameter estimates in terms of bias and mean square error. Two real data applications are modelled with the proposed distribution to illustrate the performance of the new distribution. Based on goodness-of-fit statistics, the new distribution outperforms the generalized gamma, gamma Weibull, gamma exponentiated exponential, generalized Lindley, Kumaraswamy Lindley, and odd log-logistic Lindley distributions.

No abstract

The evolution of SNP-SNP interactions has become an interesting field in genetic epidemiology. Most of the studies, aimed to analyze the relationship between genetic factors and disease of interest, are focused on single SNP associations. However, for quantitative traits, influenced by the interplay of environmental and more than one genetic factors, interaction between the multi factors should be taken into consideration. In this study, symmetry models for square contingency tables are applied to the cross-classified SNP-SNP interactions data. Results from a genome-wide association analysis of blood pressure are used as a prior evidence for the interacted SNPs.

Background: To evaluate the accuracy of the diagnosis of peri-implant bone defects' severities in digital panoramic radiographs obtained at different tube voltage and/or tube current settings. Material and Methods: Two different sizes of peri-implant bone defects (type 1 and type 2) were prepared after the implants were inserted into 29 bovine rib blocks. Digital panoramic radiographs were obtained at eight different tube voltage and/or tube current settings for all rib blocks. Implant images were cropped separately. The average intensity value (AIV) of cropped images were analyzed using Adobe Photoshop CC software. The Kruskal-Wallis H test was used to compare AIVs. All cropped images were evaluated using a five-point Likert scale for the likelihood of a bone defect being absent or present. The weighted kappa values were calculated to compare observer agreement and ROC analysis was performed to determine the appropriate exposure parameters. Results: The lowest AIV was obtained at 72 kV/6.3 mA (92.162±16.016), and the highest AIV was obtained at 60 kV/3.2 mA (179.050±13.823). The Kruskal-Wallis H test showed significant differences in the AIVs according to the exposure parameters (p<0.001). The kappa coefficient for the inter-observer agreement was excellent (0.864, p<0.001). The AUC values for type 1 defects ranged from 0.778 and 0.860; for type 2 defects ranged from 0.920 and 0.967. The AUC value of type 1 defects was slightly better in panoramic images obtained with high kV and low mA levels (72 kV/3.2 mA), compared to others. Conclusions: In daily clinical routine, peri-implant bone defects might be evaluated by panoramic radiographs obtained with all kV and mA values tested. However, to avoid misdiagnosing and for better accuracy, panoramic radiographs obtained with high kV and low mA levels suitable for patients should be used, especially in the detection of small or initial bone defects.

ÖZET Amaç: Karesel olumsallık tabloları bağımlı örneklemlerde ortaya çıkan, satır ve sütun değiş-kenleri aynı düzeylere sahip olan çapraz tablolarıdır. Bu tablolarının çözümlenmesinde bazı özel modeller kullanılır. Bu modeller çoğunlukla simetri modelleridir. Bu çalışmada iki boyutlu karesel olumsallık tablolarında simetri yapısı bozulduğu durumlar için geliştirilen modeller tanıtılmıştır. Bu modellerde olumsallık tablosundaki değişkenlerin sıralabilir ölçekte olduğu varsayılır. Gereç ve Yön-temler: Karesel olumsallık tabloların çözümlenmesinde simetri yapısının bozulduğu durumlar için kullanılan asimetri ve çarpık simetri modelleri 280 kanser hastasına ait veriler üzerinde gösterilmiş ve sonuçlar tartışılmıştır. Bu modellerin çözümlenmesinde SPSS ve SAS programları kullanılmıştır. En uygun model için parametre tahmini ile yorumlama yapılmıştır. Bulgular: Veriler simetri yapısını ifaden modellere uyum sağlamamıştır. Asimetri ve çarpık simetri modellerinin bütün alt modelleri veriye uyum sağlarken tekdüze çarpık simetri modeli en uyumlu model olarak bulunmuştur. Tekdüze çarpık simetri modeli varsayımı altında odds oranı 1,34 olarak hesaplanmıştır. Sonuç: Sitolojik ve patalojik sınıflandırma arasındaki uyum %74 bulunmuştur, bu değer yüksek uyum olarak değerlendi-rilebilir. Sitolojik tanı ile şüpheli teşhisi konan vakalar patolojik tanı ile desteklenmeden kesinleştiri-lemez. Kanser tanısının doğruluğu açısından sitolojik ve patalojik sınıflama arasında mükemmel uyum olması beklendiğinden köşegen dışı elemanların da incelenmesi gerekmektedir. Bu da karesel olumsallık tabloları çözümlemeleri ile mümkündür.Anahtar Kelimeler: Karesel olumsallık tablosu; simetri modeli; asimetri modeli; çarpık simetri modeli ABSTRACT Objective: Square contingency tables that arise in dependent samples where the row and column variables have same level. Some specific models used in the analysis of these kinds of tables. These models are mostly in the symmetrical pattern. In this study, the models are introduced for two dimensional square contingency tables where the departure from the symmetry structure is observed. Models described in this paper assume ordinal categories for the contingency table. Material and Methods: Asymmetry and skew symmetry models used when the symmetry structure is distorted in analysis of square contingency tables are shown on a 280 cancer patient's dataset and the results are discussed. SPSS and SAS programs are used in the analysis of these models. The interpretations are made with the parameter estimation for the best fitting model. Results: Symmetry models do not hold for the data. While the sub models of asymmetry and skew symmetry models hold for the data, the best fitting model is determined as the uniform skew symmetry model for the cancer data. The odds ratio under uniform skew smmetry model is estimated as 1.34. Conclusion: The agreement between the cytological and pathalogical diagnosis of uterine cancer is 74% suggesting the high agreement. A cytological diagnosis recorded as suspicious is not consid...