Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Modelling Right-Censored Data with Partially Linear Model and Feed Forward Neural Networks: A Methodological Study
Sağdan-Sansürlü Verilerin Kısmi Doğrusal Model ve İleri Beslemeli Yapay Sinir Ağları ile Modellenmesi: Metodolojik Bir Çalışma
Çağatay BALa, Ersin YILMAZa
aDepartment of Statistics, Muğla Sıtkı Koçman University Faculty of Art, Muğla, Türkiye
Turkiye Klinikleri J Biostat. 2022;14(2):90-102
doi: 10.5336/biostatic.2022-89354
Article Language: EN
Full Text
ABSTRACT
 Objective: Modeling right-censored data becomes a challenging task in survival analysis, due to having an incomplete data structure. When the response variable is rightcensored, classical estimation methods cannot be used directly. Therefore, the censorship problem should be solved before the modeling process. The purpose of this study is to solve the censorship problem with synthetic data transformation and to make a comparison between the partial linear model (PLM) and feed forward neural networks (FFNN), two popular modeling procedures in recent years, in terms of model residuals. Thus, it is to study the behavior of methods. Material and Methods: This paper aims to estimate the effects of explanatory variables on a right-censored response variable whose distribution is unknown by two different methods, PLM and FFNN based on the spline smoothing method. The spline smoothing method is a mathematical approximation method used in PLM estimation. FFNN is a machine learning method that has become very popular recently and produces satisfactory models. To overcome the censorship problem, the right-censored response variable for the two mentioned methods has been replaced with synthetic data. Synthetic data transformation is a widely used censorship resolution method that allows censorship presence to be included in the prediction process. Results: To achieve the aim of the study, both simulation and real data studies were carried out and the results were presented. Conclusion: Kidney weakness data is used as an example of real data. When the results are examined, it is seen that FFNN is superior to PLM in both numerical studies.

Keywords: Feed forward neural networks; smoothing spline; partially linear models; right-censored data
ÖZET
 Amaç: Eksik bir veri yapısına sahip olması nedeniyle sağdansansürlenmiş verilerin modellenmesi, sağkalım analizinde zor bir işlemdir. Yanıt değişkeni sağdan sansürlendiğinde, klasik tahmin yöntemleri doğrudan kullanılamaz. Bu nedenle modelleme sürecinden önce sansür problemi çözülmelidir. Bu çalışmanın amacı, sansür problemini sentetik veri dönüşüm ile çözerek literatürde son yıllarda popüler olarak kullanılan 2 modelleme prosedürü olan kısmi doğrusal model [partial linear model (PLM)] ve ileri beslemeli sinir ağları [feed forward neural networks (FFNN)] arasında model artıkları açısından bir karşılaştırma yapmak ve böylece yöntemlerin davranışlarını incelemektir. Gereç ve Yöntemler: Bu makale, açıklayıcı değişkenlerin, dağılımı bilinmeyen sağdan sansürlü bir yanıt değişkeni üzerindeki etkilerini, splayn düzleştirme yöntemine dayalı PLM ve FFNN olmak üzere 2 farklı yöntemle tahmin etmeyi amaçlar. Splayn düzleştirme yöntemi, PLM tahmininde kullanılan matematiksel yaklaştırma yöntemidir. FFNN ise son zamanlarda oldukça popülerleşen ve tatmin edici modeller üreten bir makine öğrenmesi yöntemidir. Sansür sorununun üstesinden gelmek için bahsedilen 2 yöntem için sağdan sansürlü yanıt değişkeni sentetik verilerle değiştirilmiştir. Sentetik veri dönüşümü, sansür varlığını tahmin sürecine dâhil edilmesini sağlayan yaygın kullanılan bir sansür çözüm yöntemidir. Bulgular: Çalışmanın amacına ulaşmak için hem simülasyon hem de gerçek veri çalışmaları yapılmış ve sonuçlar sunulmuştur. Sonuç: Gerçek veri örneği olarak böbrek zayıflığı verisi kullanılmıştır. Sonuçlar incelendiğinde, her iki sayısal çalışmada da FFNN'nin PLM'ye üstünlük sağladığı açıkça görülmektedir.

Anahtar Kelimeler: İleri beslemeli sinir ağları; splayn düzleştirme; kısmi doğrusal modeller; sağdan-sansürlü veri
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