Comparison of Piecewise Regression and Polynomial Regression Analyses in Health and Simulation Data Sets

Amaç: Bir veya daha fazla parçanın kırılma noktalarında birleştirildiği parçalı regresyon, istatistiksel bir teknik olarak yaygın bir şekilde kullanılmaktadır. Bu çalışmada hem simülasyon verisi hem de gerçek veri setleri kullanılarak tek değişkenli polinom regresyon analizi ile karesel ve kübik parçalı regresyon analizlerinin karşılaştırılması hedeflendi. Materyal-Metot: Çalışmanın uygulama basamağında R yazılım programı kullanılarak simülasyon uygulaması için algoritmalar yazıldı. Polinom ve sürekli parçalı regresyon analiz yöntemlerinin karşılaştırılması n=100 birimlik veri setleri için 1000 tekrarlı simülasyon ile gerçekleştirildi. Ayrıca Türkiye’de 2010 yılındaki tüberküloz vaka sayılarını içeren tüberküloz veri seti ile Türkiye’deki 1973-2010 yılları arasındaki kızamık vaka sayılarını içeren kızamık veri setleri kullanılarak oluşturulan polinom ve parçalı regresyon modellerinin tahmin performansları; , HKO, ABK ve BBK değerlerine göre karşılaştırıldı. Bulgular: Tüm polinom ve parçalı regresyon modellerinin , HKO, ABK ve BBK değerleri bakımından performansları istatistiksel olarak birbirinden farklı bulundu (p<0.001). Parçalı regresyon modellerinin değerlerinin polinom regresyon modellerine göre daha yüksek; HKO, ABK ve BBK değerlerinin ise daha düşük olduğu gözlendi. Gerçek veri setleri ile yapılan uygulamalarda en uygun dönüm noktalarına göre oluşturulan tüm parçalı regresyon modellerinin değerlerinin polinom regresyonlardan daha yüksek; HKO, ABK ve BBK değerlerinin ise daha düşük olduğu belirlendi Oluşturulan parçalı regresyon modellerinin veri setlerini polinom regresyonlara göre daha iyi tahmin ettiği belirlendi. Sonuç: Sağlık alanında yapılan çalışmaların çoğunda polinom regresyon yöntemlerinin tercih edilmesine rağmen bu çalışma ile en uygun dönüm noktalı parçalı regresyonlarla veri analizinin istatistiksel açıdan üstünlük sağladığı uygulamalarla ortaya konmuştur.

Anahtar Kelimeler:

Parçalı Regresyon, Simülasyon, Tüberküloz, Kızamık, Polinom Regresyon

Comparison of Piecewise Regression and Polynomial Regression Analyses in Health and Simulation Data Sets

Objective: Piecewise regression, which one or more pieces are combined in breakpoints, is widely used as a statistical technique. It was aimed to compare piecewise regression analyses and polynomial regression analysis using both simulated data and real data sets.Material-Method: In the application step of the study, algorithms were created by using R software for simulation practice. Polynomial and piecewise regression analysis methods were compared using data sets with n=100 units and 1000 times running simulation. In addition, estimation performances of piecewise and polynomial regression built by using the data sets which contained in the number of tuberculosis cases according to age in 2010 year and the number of measles cases from 1993 to 2015 years in Turkey were compared.Results: It was found that there was a significant difference between all of the polynomial and piecewise regression models (p<0.001). The values of piecewise regression models were higher than polynomial regression models; MSE, AIC and BIC values were observed to be lower. According to the result of both simulation and real data set applications, piecewise regression models which were generated according to optimal knots were found to have better estimation performance than polynomial regression models according to , MSE, AIC and BIC criteria. Conclusions: This study revealed that data analysis with piecewise regressions having optimal knots provided statistically superiority, although polynomial regression methods are preferred in the field of health studies mostly.

Keywords:

Piecewise Regression, Simulation, Tuberculosis, Measles, Polynomial Regression,

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