Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Cepten Sağlık Harcamasının Tahmininde Copas Testi ve İstatistiksel Daraltıcı (Shrinkage) Modellerin Uygulanması
Usage of Copas Test and Shrinkage Models to Predict Out-of-Pocket Health Expenditures
Songül ÇINAROĞLUa
aHacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi, Sağlık Yönetimi Bölümü, Ankara, TÜRKİYE
Turkiye Klinikleri J Biostat. 2020;12(3):303-19
doi: 10.5336/biostatic.2020-75787
Article Language: TR
Full Text
ÖZET
 Amaç: Sağlık harcaması değişkeninin, normal dağılım özelliği göstermeyerek aşırı derecede sağa çarpık olması doğrusallıktan ayrılmayı beraberinde getirerek, regresyon modelini zayıflatmaktadır. Copas testi ile istatistiksel daraltıcı (Shrinkage) modellerin kullanılması yolu ile tahmin modeli performansının iyileştirilmesi mümkündür. Bu çalışmada, cepten sağlık harcamasını tahmin etmek amacıyla Copas testi ve istatistiksel daraltıcı modelleri uygulanarak model performansları karşılaştırılmıştır. Gereç ve Yöntemler: Türkiye İstatistik Kurumu 2012 yılı Hane halkı Bütçe Anketi verileri kullanılmıştır. Cepten sağlık harcamasının tahmininde ödeme gücü değişkeni ile hane reisinin cinsiyet, 65 yaş üzerinde olma, sağlık sigortası ve kır ya da kentte yerleşim durumu değişkenleri kullanılmıştır. Eğitim veri setinin orijinal veri setini %50-95 oranlarında temsil ettiği 10 farklı eğitim ve test veri setleri oluşturulmuş ve Copas testi kullanılarak, en iyi performans sergileyen veri seti seçilmiştir. En küçük kareler (EKK) regresyonu ile istatistiksel daraltıcı olarak da bilinen Lasso ve Ridge regresyon teknikleri uygulanmıştır. Bulgular: EKK modelinin en düşük ortalama karesel hataya sahip olduğu ve en iyi performansı sergilediği görülmüştür. Cepten sağlık harcamasını tahmin etmede en etkili değişken ödeme gücü olup, Lasso regresyonun, Ridge regresyona göre daha iyi tahmin gücüne sahip olduğu görülmüştür. Lasso regresyon için optimal büzülme parametre değerinin eğitim veri seti için λ=0,0158; test veri seti için ise λ=0,0630 olduğu bulunmuştur. Sonuç: Copas testinin sağlık harcaması gibi modellenmesi zor değişkenler için en iyi model performansının araştırılmasında yararlı bir teknik olduğu, EKK ve Lasso regresyonun iyi tahmin performansına sahip olduğu ve ödeme gücü değişkeninin modele en fazla katkı sağlayan değişken olduğu belirlenmiştir. Farklı regresyon modelleri kullanılarak yapılacak incelemeler ile çalışma bulgularının geliştirilmesi tavsiye edilmektedir.

Anahtar Kelimeler: Cepten sağlık harcaması; Copas testi; EKK regresyonu; Lasso regresyon; Ridge regresyon
ABSTRACT
 Objective: Not normal and extremely positively skewed distribution of health expenditures causes departure from normality and poor regression performance. It is possible to improve prediction performance with the usage of Copas test and Shrinkage models. In this study Copas test and Shrinkage models are used and compared to predict out-of-pocket health expenditures. Material and Methods: TurkStat Household Budget Survey for the year 2012 was used. Capacity to pay, which is a kind of adjusted income variable, gender of head of household, being older than 65 years old, health insurance and rural or urban settlement variables are used to predict households out-of-pocket health expenditures. Ten different training and test data sets were created, in which the training data set represented 50% to 95% of the original data set, and the data set with the best performance was selected by applying the Copas test. Least squares regression (LSR) and Lasso and Ridge regression techniques are applied which are also known as Shrinkage methods. Results: It is seen that LSC model had the lowest mean square error and had superior performance. The most effective variable in predicting out-of-pocket health expenditure is capacity to pay, and Lasso regression was found to have better predictive power than Ridge regression. It is seen that optimal Shrinkage parameter for Lasso regression for training data is λ=0.0158 and λ=0.0630 for test data. Conclusion: It has been determined that the Copas test is a useful technique in investigating the best model performance for variables that are difficult to model, such as health expenditure, LSC regression performs better than the Shrinkage models, and capacity to pay is the variable that contributes most into the model. It is recommended to develop study findings by examining different regression models.

Keywords: Out-of-pocket health expenditure; Copas test;LSR regression; Lasso regression;Ridge regression
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