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

Year 2024, , 20 - 27, 31.03.2024

Osman Demir , Ünal Erkorkmaz

https://doi.org/10.31832/smj.1390306

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

References

• 1. Cox DR. Regression models and life-tables. Journal of Royal Statistical Society. 1972;34(2):187-202.
• 2. Pinto JD, Carvalho AM, Vinga S. Outlier detection in survival analysis based on the concordance c-index. SCITEPRESS-Science and Technology Publications, Lda; 2015:75-82.
• 3. Eo S-H, Hong S-M, Cho H. Identification of outlying observations with quantile regression for censored data. arXiv preprint arXiv:14047710. 2014.
• 4. Aktas T, Aktas F, Ozmen C, Ozmen Z, Kaya T, Demir O. Mean Platelet Volume (mpv): A New Predictor of Pulmonary Findings and Survival in Cchf Patients? Acta Medica Mediterranea. 2017;33(2):183-190.
• 5. Therneau TM. A Package for Survival Analysis in R. R package version 3.2-11. 2021.
• 6. Bednarski T, Borowicz F, Scogin S. Coxrobust: Fit Robustly Proportional Hazards Regression Model. 2022.
• 7. Pinto J. BCSOD: This packages provides 6 methods to perform outlier detection in survival context.. R package version 1.0. 2015.
• 8. Storey John D, Bass AJ, Dabney A, Robinson D. Qvalue: Q-value estimation for false discovery rate control. R package version 2.15.0. 2017.
• 9. Team RC. R: A language and environment for statistical computing. 2013.
• 10. Androulakis E, Koukouvinos C, Mylona K, Vonta F. A real survival analysis application via variable selection methods for Cox’s proportional hazards model. Journal of Applied Statistics. 2010;37(8):1399-1406.
• 11. Cox DR, Oakes D. Analysis of survival data. Chapman and Hall, London; 1984.
• 12. Bednarski T. Robust estimation in Cox’s regression model. Scandinavian Journal of Statistics. 1993;20:213-225.
• 13. Minder CE, Bednarski T. A robust method for proportional hazards regression. Statistics in medicine. 1996;15(10):1033-1047.
• 14. Carrasquinha E, Veríssimo A, Vinga S. Consensus outlier detection in survival analysis using the rank product test. bioRxiv. 2018:421917.
• 15. Schoenfeld D. Partial residuals for the proportional hazards regression model. Biometrika. 1982;69(1):239-241.
• 16. Kumar D, Klefsjö B. Proportional hazards model: A review. Reliability Engineering & System Safety. 1994;44(2):177-188.
• 17. Barlow WE, Prentice RL. Residuals for relative risk regression. Biometrika. 1988;75(1):65-74.
• 18. Carrasquinha E, Veríssimo A, Lopes MB, Vinga S. Variable selection and outlier detection in regularized survival models: Application to melanoma gene expression data. Springer; 2018:431-440.
• 19. Karasoy D, Tuncer N. Outliers in survival analysis. Alphanumeric journal. 2015;3(2):139-152.
• 20. Therneau TM, Grambsch PM, Fleming TR. Martingale- based residuals for survival models. Biometrika. 1990;77(1):147-160.
• 21. Harrell FE, Califf RM, Pryor DB, Lee KL, Rosati RA. Evaluating the yield of medical tests. Jama. 1982;247(18):2543- 2546.
• 22. Caldas J, Vinga S. Global meta-analysis of transcriptomics studies. PLoS One. 2014;9(2):e89318.
• 23. Breitling R, Armengaud P, Amtmann A, Herzyk P. Rank. Products: A simple, yet powerful, new method to detect differentially regulated genes in replicated microarray experiments. FEBS letters. 2004;573(1-3):83-92.
• 24. Carrasquinha E, Veríssimo A, Lopes MB, Vinga S. Identification of influential observations in high-dimensional cancer survival data through the rank product test. Bio- Data Mining. 2018;11(1):1.
• 25. A. KJ. Comments on the rank product method for analyzing replicated experiments. FEBS Letters. 2010;584(5):941.
• 26. Eisinga R, Breitling R, Heskes T. The exact probability distribution of the rank product statistics for replicated experiments. FEBS letters. 2013;587(6):677-682.
• 27. Storey JD. A direct approach to false discovery rates. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2002;64(3):479-498.
• 28. Halabi S, Dutta S, Wu Y, Liu A. Score and deviance residuals based on the full likelihood approach in survival analysis. Pharmaceutical statistics. 2020;19(6):940-954.