Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Point and Confidence Interval Estimation of the Parameter and Survival Function for Lindley Distribution Under Censored and Uncensored Data
Lindley Dağılımında Sansürlü ve Sansürsüz Verilerde Parametre ve Sağ Kalım Fonksiyonları için Nokta ve Aralık Tahmini
Kamil ALAKUŞa, Necati Alp ERİLLİb
aDepartment of Statistics, Ondokuz Mayis University Faculty of Arts and Sciences, Samsun, TURKEY
bDepartment of Econometrics, Sivas Cumhuriyet University Faculty of Economic and Administrative, Sivas, TURKEY
Turkiye Klinikleri J Biostat. 2019;11(3):198-212
doi: 10.5336/biostatic.2019-70223
Article Language: EN
Full Text
ABSTRACT
 Objective: Survival analysis is a statistical method used to compare the life expectancy of patients in health studies and to investigate the effectiveness of the treatments. The Lindley distribution is a widely used distribution in survival analysis in recent years and is used to describe the life of a process or device. The Lindley distribution is a two-parameter continuous distribution that is widely used in a wide range of fields including biology, engineering and medicine. Material and Method: In this study, point and interval estimates of the Lindley distribution were examined for censored and uncensored data. Parameter inferences and confidence intervals are shown. In the application section, real-time data (uncensored) and a simulation data (uncensored and censored) are compared with other distributions of the exponential distribution family. Results: According to the results obtained from the analysis, it was observed that Lindley distribution gave better results in special data structures compared to other distributions of exponential family. Lindley distribution; For uncensored real-life data and censored and uncensored simulation data, it has a lower model selection criterion. Conclusion: The exact distribution of the data to be used in survival analysis is one of the prerequisites for the success of the analysis. The Lindley distribution, with its increasing popularity in recent years, is a distribution that gives successful results in survival analysis.

Keywords: Lindley Distribution; Survival Analysis; Censored Data; Point Estimation
ÖZET
 Amaç: Sağ Kalım analizi, sağlık çalışmalarında hastaların beklenen yaşam sürelerinin karşılaştırılmasında, uygulanacak tedavilerin etkinlikleinin araştırılmasında kullanılan istatistiksel yöntemlerdir. Lindley dağılımı, son yıllarda sağ kalım analizlerinde sık kullanılan bir dağılımdır ve bir işlem ya da cihazın ömrünü tanımlamada kullanılır. Biyoloji, mühendislik ve tıp da dahil olmak üzere çok çeşitli alanlarda uygulama alanı bulan Lindley dağılımı, iki parametreli sürekli bir dağılımdır. Gereç ve Yöntemler: Bu çalışmada, sansürlü ve sansürsüz veriler için Lindley dağılımının nokta ve aralık tahminleri incelenmiştir. Parametre çıkarımları ve güven aralıklarının bulunması gösterilmiştir. Uygulama bölümünde ise gerçek zamanlı veriler (sansürsüz) ve bir simülasyon verisi (sansürsüz ve sansürlü), üstel dağılım ailesinin diğer dağılımları ile karşılaştırılmıştır. Bulgular: Analizlerden elde edilen sonuçlara göre, Lindley dağılımının özel veri yapılarında üstel ailesinin diğer dağılımları ile karşılaştırıldığında daha iyi sonuçlar verdiği görülmüştür. Lindley dağılımı; Sansürsüz gerçek yaşam verisi ile sansürlü ve sansürsüz simülasyon verilerinde, daha düşük model seçme kriterine sahiptir. Sonuç: Sağkalım analizlerinde kullanılacak verilerin dağılımlarının tam olarak belirlenmesi, analizin daha başarılı olması için gereken ön şartlarından biridir. Lindley dağılımı da son yıllarda artan popülerliği ile sağ kalım analizlerinde başarılı sonuçlar veren bir dağılımdır.

Anahtar Kelimeler: Lindley Dağılımı; Sağ Kalım Analizi; Sansürlü Veri; Nokta Tahmini
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