Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Use of Survival Data in Multivariate Adaptive Regression Analysis: Simulation Study
Yaşam Süresi Verilerinin Çok Değişkenli Uyumlu Regresyon Analizinde Kullanımı: Simülasyon Çalışması
Merve TÜRKEGÜN ŞENGÜLa, Gülhan TEMELa, İrem ERSÖZ KAYAb
aDepartment of Biostatistics and Medical Informatics, Mersin University Faculty of Medicine, Mersin, Türkiye
bDepartment of Computer Engineering, Tarsus University Faculty of Engineering, Mersin, Türkiye
Turkiye Klinikleri J Biostat. 2023;15(1):42-51
doi: 10.5336/biostatic.2022-94594
Article Language: EN
Full Text
ABSTRACT
 Objective: The multivariate adaptive regression splines (MARS) is very effective in order to model linear or nonlinear relationships. The Cox regression residuals-based MARS model, which integrates Cox regression and MARS approaches, was created to assess the relationships between efficient risk factors on the survival. The purpose of this study is to introduce the Survival-MARS (SM) model which uses the Cox-Snell, Martingale, and deviance residuals. Also,our aim is to compare the performance of the models created with residuals at different sample sizes and correlation levels with the simulation study in order to determine the most effective residual type that can be used in the SM model. Material and Methods: Performances of SM models that use CoxSnell,Martingale, and deviance residual types were compared at different sample sizes (n = 30, 100, 150, 250, 500, 1.000), with both no correlation (r = 0.00) and medium (r = 0.50) and high (r = 0.90) correlations between predictors. SM model performances were compared via minimum generalized cross-validation and the sum of mean squared error values.. Results: In all scenarios, SM models with Cox-Snell residuals have the best performance compared to other models established with other residuals. Martingale and deviance residuals were affected by high correlation and low sample sizes. Conclusion: In case of linear relationship between risk factors, SM models with Cox-Snell residuals are quite successful in explaining these relationship structures and enable the effects on the dependent variable to easily interpret.

Keywords: Multivariate adaptive regression splines; Cox regression; Cox-Snell residual; Martingale residual; deviance residual
ÖZET
 Amaç: Çok değişkenli uyumlu regresyon uzanımları tekniği [multivariate adaptive regression splines (MARS)], doğrusal ya da doğrusal olmayan ilişkileri modellemede oldukça etkilidir. Sağkalım üzerinde etkili risk faktörleri arasındaki bu tür ilişkileri değerlendirebilmek amacıyla her iki yöntemi birleştiren ve Cox regresyon artıklarına dayanan Survival-MARS (SM) modeli geliştirilmiştir. Bu çalışmanın amacı, Cox-Snell, Martingale ve sapma artıklarını kullanan Survival-MARS (SM) modelini tanıtmaktır. Ayrıca amacımız, SM modelinde kullanılabilecek en etkili artık türünü belirlemek için artıklarla oluşturulan modellerin, farklı örneklem genişliklerinde ve korelasyon düzeylerindeki performanslarını simülasyon çalışması ile karşılaştırmaktır. SM model performansları, minimum genelleştirilmiş çapraz geçerlilik ve minimum hata kareleri toplamı değerlerine bakılarak karşılaştırılmıştır. Bulgular: SM modellerinde ele alınan tüm senaryolar için Cox-Snell artıkları ile kurulan modellerin, diğer artıklarla kurulan modellere göre daha iyi performans gösterdiği görülmüştür. Martingale ve sapma artıklarının güçlü korelasyon ve küçük örneklem genişliklerinden etkilendiği gözlemlenmiştir. Sonuç: Risk faktörleri arasında lineer ilişki olması durumunda, Cox-Snell artıklı SM modeli bu ilişki yapılarını açıklamada oldukça başarılı olup bağımlı değişken üzerindeki etkilerinin de kolaylıkla yorumlanabilmesini sağlamaktadır.

Anahtar Kelimeler: Çok değişkenli uyumlu regresyon; Cox regresyon; Cox-Snell artığı; Martingale artığı; sapma artığı
REFERENCES:
  1. Clark TG, Bradburn MJ, Love SB, Altman DG. Survival analysis part I: basic concepts and first analyses. Br J Cancer. 2003;89(2):232-8. [Crossref]  [PubMed]  [PMC] 
  2. Cox DR. Regression models and life-tables. Journal of the Royal Statistical Society Series B. 1972;34(2):187-220. [Crossref] 
  3. Monika Kriner. Survival analysis with multivariate adaptive regression splines [PhD thesis]. Munich: Ludwig Maximilian University of Munich; 2007. [Cited: Jun 9, 2022]. Available from: [Link] 
  4. LeBlanc M, Crowley J. Adaptive regression splines in the Cox model. Biometrics. 1999;55(1):204-13. [Crossref]  [PubMed] 
  5. Friedman JH. Multivariate adaptive regression splines. The Annals of Statistics. 1991;19(1):1-67. [Crossref] 
  6. Temel Orekici G, Ankaralı H, Yazıcı AC. Regresyon Modellerine alternatif bir yaklaşım: MARS [An alternative approach to regression models: MARS]. Turkiye Klinikleri J Biostat. 2010;2(2):58-66. [Link] 
  7. Chou SM, Lee TS, Shao YE, Chen IF. Mining the breast cancer pattern using artificial neural networks and multivariate adaptive regression splines. Expert Systems with Applications. 2004;27(1):133-42. [Crossref] 
  8. Craven P, Wahba G. Smoothing noisy data with spline function, estimating the correct degree of smoothing by the method of generalized cross-validation. Numer Math. 1979;31:377-403. [Crossref] 
  9. Altınok G, Karagöz P, Batmaz İ. Learning to rank by using multivariate adaptive regression splines and conic multivariate adaptive regression splines. Computational Intelligence. 2021;37(1):371-408. [Crossref] 
  10. Kleinbaum D, Klein M. Evaluating the proportional hazards assumption. Survival Analysis: A Self-Learning Text. 3rd ed. New York: Springer; 1996. p.164-87. [Crossref] 
  11. Bradburn MJ, Clark TG, Love SB, Altman DG. Survival analysis part II: multivariate data analysis--an introduction to concepts and methods. Br J Cancer. 2003;89(3):431-6. [Crossref]  [PubMed]  [PMC] 
  12. Nardi A, Schemper M. New residuals for Cox regression and their application to outlier screening. Biometrics. 1999;55(2):523-9. [Crossref]  [PubMed] 
  13. Collett D. Text in Statistical Science: Modelling Survival Data in Medical Research. 2nd ed. Boca Raton: Taylor & Francis Inc.; 2003.
  14. Barlow WE, Prentice RL. Residuals for relative risk regression. Biometrika. 1988;75(1):65-74. [Crossref] 
  15. Therneau TM, Grambsch PM, Fleming TR. Martingale-based residuals for survival models. Biometrika. 1990;77(1):147-60. [Crossref] 
  16. Alpar R. Uygulamalı Çok Değişkenli İstatistiksel Yöntemler. 5. Baskı. Ankara: Detay Anatolia Akademik Yayıncılık LTD.ŞTİ.; 2017.
  17. Dauda KA, Yahya WB, Banjoko AW. Survival analysis with multivariate adaptive regression splines using cox-snell residual. Anale Seria Informatică. 2015;3(2):25-41. [Link] 
  18. Irwansyah E, Stefani D, Bekti RD. Cox proportional hazard with multivarite adaptive regression splines to analyze the product sales time in E-commerce. Int J Appl Math Stat. 2015;53(5).109-15. [Crossref] 
  19. Austin PC, Fang J, Lee DS. Using fractional polynomials and restricted cubic splines to model non-proportional hazards or time-varying covariate effects in the Cox regression model. Stat Med. 2022;41(3):612-24. [Crossref]  [PubMed]  [PMC] 

.: Up To Date

.: Process List

Login

 Forgot your password?

 New Registration  

Contact

Ortadoğu Reklam Tanıtım Yayıncılık Turizm Eğitim İnşaat Sanayi ve Ticaret A.Ş.

.: Address

Turkocagi Caddesi No:30 06520 Balgat / ANKARA
Phone: +90 312 286 56 56
Fax: +90 312 220 04 70
E-mail: info@turkiyeklinikleri.com

.: Manuscript Editing Department

Phone: +90 312 286 56 56/ 2
E-mail: yaziisleri@turkiyeklinikleri.com

.: English Language Redaction

Phone: +90 312 286 56 56/ 145
E-mail: tkyayindestek@turkiyeklinikleri.com

.: Marketing Sales-Project Department

Phone: +90 312 286 56 56/ 142
E-mail: reklam@turkiyeklinikleri.com

.: Subscription and Public Relations Department

Phone: +90 312 286 56 56/ 118
E-mail: abone@turkiyeklinikleri.com

.: Customer Services

Phone: +90 312 286 56 56/ 118
E-mail: satisdestek@turkiyeklinikleri.com

1. TERMS OF USE

1.1. To use the web pages with http://www.turkiyeklinikleri.com domain name or the websites reached through the sub domain names attached to the domain name (They will be collectively referred as "SITE"), please read the conditions below. If you do not accept these terms, please cease to use the "SITE." "SITE" owner reserves the right to change the information on the website, forms, contents, the "SITE," "SITE" terms of use anytime they want.

1.2. The owner of the "SITE" is Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. (From now on it is going to be referred as "Turkiye Klinikleri", shortly) and it resides at Turkocagi cad. No:30, 06520 Balgat Ankara. The services in the "SITE" are provided by "Turkiye Klinikleri."

1.3. Anyone accessing the "SITE" with or without a fee whether they are a natural person or a legal identity is considered to agree these terms of use. In this contract hereby, "Turkiye Klinikleri" may change the stated terms anytime. These changes will be published in the "SITE" periodically and they will be valid when they are published. Any natural person or legal identity benefiting from and reaching to the "SITE" are considered to be agreed to any change on hereby contract terms done by "Turkiye Klinikleri."

1.4. The "Terms of Use" hereby is published in the website with the last change on March 30th 2014 and the "SITE" is activated by enabling the access to everyone. The "Terms of Use" hereby is also a part of the any "USER Contract" was and/or will be done with the users using "Turkiye Klinikleri" services with or without a fee an inseparable.

2. DEFINITIONS

2.1. "SITE": A website offering different kind of services and context with a certain frame determined by "Turkiye Klinikleri" and it is accessible on-line on http://www.turkiyeklinikleri.com domain name and/or subdomains connected to the domain name.

2.2. USER: A natural person or a legal identity accessing to the "SITE" through online settings.

2.3. LINK: A link enabling to access to another website through the "SITE", the files, the context or through another website to the "SITE", the files and the context.

2.4. CONTEXT: Any visual, literary and auditory images published in the "Turkiye Klinikleri", "SITE" and/or any website or any accessible information, file, picture, number/figures, price, etc.

2.5. "USER CONTRACT": An electronically signed contract between a natural or a legal identity benefiting from special services "Turkiye Klinikleri" will provide and "Turkiye Klinikleri".

3. SCOPE OF THE SERVICES

3.1. "Turkiye Klinikleri" is completely free to determine the scope and quality of the services via the "SITE".

3.2. To benefit the services of "Turkiye Klinikleri" "SITE", the "USER" must deliver the features that will be specified by "Turkiye Klinikleri". "Turkiye Klinikleri" may change this necessity any time single-sided.

3.3. Not for a limited number, the services "Turkiye Klinikleri" will provide through the "SITE" for a certain price or for free are;

- Providing scientific articles, books and informative publications for health industry.

- Providing structural, statistical and editorial support to article preparation stage for scientific journals.

4. GENERAL PROVISIONS

4.1. "Turkiye Klinikleri" is completely free to determine which of the services and contents provided in the "SITE" will be charged.

4.2. People benefiting from the services provided by "Turkiye Klinikleri" and using the website can use the "SITE" only according to the law and only for personal reasons. Users have the criminal and civil liability for every process and action they take in the "SITE". Every USER agrees, declares and undertakes that they will not proceed by any function or action infringement of rights of "Turkiye Klinikleri"s and/or other third parties', they are the exclusive right holder on usage, processing, storage, made public and revealing any written, visual or auditory information reported to Turkiye Klinikleri" and/or "SITE" to the third parties. "USER" agrees and undertakes that s/he will not duplicate, copy, distribute, process, the pictures, text, visual and auditory images, video clips, files, databases, catalogs and lists within the "SITE", s/he will not be using these actions or with other ways to compete with "Turkiye Klinikleri", directly or indirectly.

4.3. The services provided and the context published within the "SITE" by third parties is not under the responsibility of "Turkiye Klinikleri", institutions collaborated with "Turkiye Klinikleri", "Turkiye Klinikleri" employee and directors, "Turkiye Klinikleri" authorized salespeople. Commitment to accuracy and legality of the published information, context, visual and auditory images provided by any third party are under the full responsibility of the third party. "Turkiye Klinikleri" does not promise and guarantee the safety, accuracy and legality of the services and context provided by a third party.

4.4. "USER"s cannot act against "Turkiye Klinikleri", other "USER"s and third parties by using the "SITE". "Turkiye Klinikleri" has no direct and/or indirect responsibility for any damage a third party suffered or will suffer regarding "USER"s actions on the "SITE" against the rules of the hereby "Terms of Use" and the law.

4.5. "USER"s accept and undertake that the information and context they provided to the "SITE" are accurate and legal. "Turkiye Klinikleri" is not liable and responsible for promising and guaranteeing the verification of the information and context transmitted to "Turkiye Klinikleri" by the "USER"s, or uploaded, changed and provided through the "SITE" by them and whether these information are safe, accurate and legal.

4.6. "USER"s agree and undertake that they will not perform any action leading to unfair competition, weakening the personal and commercial credit of "Turkiye Klinikleri" and a third party,  encroaching and attacking on personal rights within the "SITE" in accordance with the Turkish Commercial Code Law.

4.7. "Turkiye Klinikleri" reserves the right to change the services and the context within the "SITE"  anytime. "Turkiye Klinikleri" may use this right without any notification and timelessly. "USER"s have to make the changes and/or corrections "Turkiye Klinikleri" required immediately. Any changes and/or corrections that are required by "Turkiye Klinikleri", may be made by "Turkiye Klinikleri" when needed. Any harm, criminal and civil liability resulted or will result from changes and/or corrections required by "Turkiye Klinikleri" and were not made on time by the "USER"s belongs completely to the users.

4.8. "Turkiye Klinikleri" may give links through the "SITE" to other websites and/or "CONTEXT"s and/or folders that are outside of their control and owned and run by third parties. These links are provided for ease of reference only and do not hold qualification for support the respective web SITE or the admin or declaration or guarantee for the information inside. "Turkiye Klinikleri" does not hold any responsibility over the web-sites connected through the links on the "SITE", folders and context, the services or products on the websites provided through these links or their context.

4.9. "Turkiye Klinikleri" may use the information provided to them by the "USERS" through the "SITE" in line with the terms of the "PRIVACY POLICY" and "USER CONTRACT". It may process the information or classify and save them on a database. "Turkiye Klinikleri" may also use the USER's or visitor's identity, address, e-mail address, phone number, IP number, which sections of the "SITE" they visited, domain type, browser type, date and time information to provide statistical evaluation and customized services.

5. PROPRIETARY RIGHTS

5.1. The information accessed through this "SITE" or provided by the users legally and all the elements (including but not limited to design, text, image, html code and other codes) of the "SITE" (all of them will be called as studies tied to "Turkiye Klinikleri"s copyrights) belongs to "Turkiye Klinikleri". Users do not have the right to resell, process, share, distribute, display or give someone permission to access or to use the "Turkiye Klinikleri" services, "Turkiye Klinikleri" information and the products under copyright protection by "Turkiye Klinikleri". Within hereby "Terms of Use" unless explicitly permitted by "Turkiye Klinikleri" nobody can reproduce, process, distribute or produce or prepare any study from those under "Turkiye Klinikleri" copyright protection.

5.2. Within hereby "Terms of Use", "Turkiye Klinikleri" reserves the rights for "Turkiye Klinikleri" services, "Turkiye Klinikleri" information, the products associated with "Turkiye Klinikleri" copyrights, "Turkiye Klinikleri" trademarks, "Turkiye Klinikleri" trade looks or its all rights for other entity and information it has through this website unless it is explicitly authorized by "Turkiye Klinikleri".

6. CHANGES IN THE TERMS OF USE

"Turkiye Klinikleri" in its sole discretion may change the hereby "Terms of Use" anytime announcing within the "SITE". The changed terms of the hereby "Terms of Use" will become valid when they are announced. Hereby "Terms of Use" cannot be changed by unilateral declarations of users.

7. FORCE MAJEURE

"Turkiye Klinikleri" is not responsible for executing late or never of this hereby "Terms of Use", privacy policy and "USER Contract" in any situation legally taken into account as force majeure. Being late or failure of performance or non-defaulting of this and similar cases like this will not be the case from the viewpoint of "Turkiye Klinikleri", and "Turkiye Klinikleri" will not have any damage liability for these situations. "Force majeure" term will be regarded as outside of the concerned party's reasonable control and any situation that "Turkiye Klinikleri" cannot prevent even though it shows due diligence. Also, force majeure situations include but not limited to natural disasters, rebellion, war, strike, communication problems, infrastructure and internet failure, power cut and bad weather conditions.

8. LAW AND AUTHORISATION TO FOLLOW

Turkish Law will be applied in practicing, interpreting the hereby "Terms of Use" and managing the emerging legal relationships within this "Terms of Use" in case of finding element of foreignness, except for the rules of Turkish conflict of laws. Ankara Courts and Enforcement Offices are entitled in any controversy happened or may happen due to hereby contract.

9. CLOSING AND AGREEMENT

Hereby "Terms of Use" come into force when announced in the "SITE" by "Turkiye Klinikleri". The users are regarded to agree to hereby contract terms by using the "SITE". "Turkiye Klinikleri" may change the contract terms and the changes will be come into force by specifying the version number and the date of change on time it is published in the "SITE".

 

30.03.2014

Privacy Policy

We recommend you to read the terms of use below before you visit our website. In case you agree these terms, following our rules will be to your favor. Please read our Terms of Use thoroughly.

www.turkiyeklinikleri.com website belongs to Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. and is designed in order to inform physicians in the field of health

www.turkiyeklinikleri.com cannot reach to user’s identity, address, service providers or other information. The users may send this information to the website through forms if they would like to. However, www.turkiyeklinikleri.com may collect your hardware and software information. The information consists of your IP address, browser type, operating system, domain name, access time, and related websites. www.turkiyeklinikleri.com cannot sell the provided user information (your name, e-mail address, home and work address, phone number) to the third parties, publish it publicly, or keep it in the website. Gathered information has a directing feature to be a source for the website’s visitor profile, reporting and promotion of the services.

www.turkiyeklinikleri.com uses the taken information:

-To enhance, improve and maintain the quality of the website

-To generate visitor’s profile and statistical data

-To determine the tendency of the visitors on using our website

-To send print publications/correspondences

-To send press releases or notifications through e-mail

-To generate a list for an event or competition

By using www.turkiyeklinikleri.com you are considered to agree that;

-Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. cannot be hold responsible for any user’s illegal and immoral behavior,

-Terms of use may change from time to time,

-It is not responsible for other websites’ contents it cannot control or the harms they may cause although it uses the connection they provided.

Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. may block the website to users in the following events:

-Information with wrong, incomplete, deceiving or immoral expressions is recorded to the website,

-Proclamation, advertisement, announcement, libelous expressions are used against natural person or legal identity,

-During various attacks to the website,

-Disruption of the website because of a virus.

Written, visual and audible materials of the website, including the code and the software are under protection by legal legislation.

Without the written consent of Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. the information on the website cannot be downloaded, changed, reproduced, copied, republished, posted or distributed.

All rights of the software and the design of the website belong to Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc.

Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. will be pleased to hear your comments about our terms of use. Please share the subjects you think may enrich our website or if there is any problem regarding our website.

info@turkiyeklinikleri.com