Use of Residuals and Rank Product in Detection of Outlier in Survival Analysis with Crimean-Congo Hemorrhagic Fever Data

Abstract

Purpose: Survival analysis is a statistical method used in many fields, especially in the field of health. It involves modeling the relationship between the survival time of individuals after a treatment or procedure and the event called response. The presence of outliers in the data may cause biased parameter estimations of the established models. Also, this situation causes the proportional hazards assumption to be violated especially in Cox regression analysis. Outlier(s) are identified with the help of residuals, Bootstrap Hypothesis test and Rank product test. Method: In R.4.0.3 software, outlier(s) are determined on a clinical dataset by the Schoenfeld residual, Martingale residual, Deviance residual method and Bootstrap Hypothesis test (BHT) based on Concordance index, and Rank product test. Results: After the cox regression established by the backward stepwise and robust cox regression, it was observed that the established models did not fit. So, the outlier(s) determined by the methods mentioned. Conclusion: It was decided that only one observation could be excluded from the study. As in the survival data, in many data types, outliers can be detected and further analyzes can be applied by using the methods mentioned.

Keywords

• Outliers
• Residuals
• Concordance index
• Rank product

Kırım-Kongo Kanamalı Ateşi Verileri ile Sağkalım Analizinde Aykırı Değer Tespitinde Artıklar ve Sıra Çarpımı Kullanımı

Abstract

Giriş: Sağkalım analizi sağlık alanında başta olmak üzere pek çok alanda kullanılan istatistiksel bir yöntemdir. Bir tedavi ya da işlemden sonra bireylerin hayatta kalması ile yanıt denilen olay arasındaki ilişkinin modellenmesini içermektedir. Veride aykırı değerlerin varlığı, kurulan modellerin yanlış parametre kestirimlerine neden olabilmektedir. Özellikle Cox regresyon analizinde orantılı risk varsayımının bozulmasına neden olmaktadır. Artıklar, Bootstrap Hipotez testi ve Rank çarpımı testi yardımıyla aykırı değer(ler) tespit edilmektedir. Gereç ve Yöntemler: R.4.0.3 yazılımında, klinik bir veri kümesi üzerinde, Schoenfeld artığı, Martingale artığı, Sapma artığı ve Uyum indeksi tabanlı Bootstrap Hipotez test (BHT) ve Sıra çarpımı testi ile aykırı değer(ler) belirlenmektedir. Bulgular: Geriye doğru adım adım ve Robust Cox regresyonu ile kurulan cox regresyonu sonrasında, kurulan modellerin uymadığı görülmüştür. Bu nedenle, söz konusu yöntemlerle aykırı değer(ler) belirlenmiştir. Sonuç: Sadece bir gözlemin çalışma dışı bırakılabileceğine karar verilmiştir. Hayatta kalma verilerinde olduğu gibi birçok veri türünde aykırı değerler tespit edilebilmekte ve bahsedilen yöntemler kullanılarak ileri analizler uygulanabilmektedir.

Keywords

• Aykırı değerler
• Artıklar
• Uyum indeksi
• Sıra çarpımı

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