Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Evaluating the Performances of ROC Curve Estimation Methods for Different Distributions and Different Kernel Functions
Farklı Dağılımlar ve Farklı Çekirdek Fonksiyonları için ROC Eğrisi Tahmin Yöntemlerinin Performanslarının İncelenmesi
Deniz SIĞIRLIa
aDepartment of Biostatistics, Bursa Uludağ University Faculty of Medicine, Bursa, TURKEY
Turkiye Klinikleri J Biostat. 2021;13(3):225-35
doi: 10.5336/biostatic.2021-85803
Article Language: EN
Full Text
ABSTRACT
 Objective: Receiver operating characteristic (ROC) curve is a statistical method used to examine the actual effectiveness of a diagnostic test or a biomarker in a comprehensive and reliable way. Several methods have been proposed to estimate ROC curve properly. The aim of the present study is to compare recent ROC curve estimation methods for different distribution and sample sizes. Material and Methods: Log-concave density and smooth log-concave density estimate based ROC curve estimation, kernel based ROC curve estimation with Gaussian, Epanechnikov, rectangular, triangular kernels, and binormal ROC estimation methods were compared for different simulation scenarios. Results: The ROC curve estimation methods based on kernel estimates gave their best performances when the biomarker values of non-diseased group are normal but the biomarker values of the diseased group are right-skewed, with a notable difference from other methods. Epanechnikov and rectangular kernel methods yielded better performance than other kernel methods in small sample sizes; but this difference disappeared as the sample size increased. The methods based on kernel or log-concave density estimate gave their worst results for the simulation scenario where the data were nonnormal but symmetric. Conclusion: The performances of the other methods examined in the study exceeded the performance of the binormal method in highly skewed data in both groups and when the distribution of diseased and non-diseased populations were right-skewed and normal, respectively.

Keywords: Diagnostic test; receiver operating characteristic curve; kernel density estimation; log-concave density estimation
ÖZET
 Amaç: Alıcı işletim karakteristiği [receiver operating characteristic (ROC)] eğrisi, bir tanı testinin veya bir biyobelirtecin gerçek etkinliğini kapsamlı ve güvenilir bir şekilde incelemek için kullanılan istatistiksel bir yöntemdir. ROC eğrisini doğru bir şekilde tahmin etmek için çeşitli yöntemler önerilmiştir. Bu çalışmanın amacı, farklı dağılım ve örneklem büyüklükleri için güncel ROC eğrisi tahmin yöntemlerini karşılaştırmaktır. Gereç ve Yöntemler: Log-konkav yoğunluk ve düzgün log-konkav yoğunluk tahmini tabanlı ROC eğrisi tahmin yöntemi, Gaussian, Epanechnikov, dikdörtgen, üçgen kernel fonksiyonu kullanan kernel tabanlı ROC eğrisi tahmin yöntemleri ve binormal ROC eğrisi tahmin yöntemleri farklı simülasyon senaryoları kullanılarak karşılaştırılmıştır. Bulgular: Kernel tahmincilerine dayanan ROC eğrisi tahmin yöntemleri, sağlıklı grubun biyobelirteç değerlerinin normal dağılım, hasta grubun biyobelirteç değerlerinin sağa çarpık dağılım gösterdiği durumda, diğer yöntemlerden büyük farkla en iyi performansı göstermiştir. Epanechnikov vedikdörtgen kernel yöntemleri, diğer kernel yöntemlerinden küçük örneklemlerde daha iyi performans göstermekle birlikte aralarındaki fark, örneklem büyüklüğündeki artışla ortadan kalkmıştır. Kernel ve log-konkav yoğunluk tahminine dayalı yöntemler, verinin normal olmadığı fakat simetrik olduğu durumda en kötü sonucu vermişlerdir. Sonuç: Çalışmada incelenen yöntemlerin performansları, her iki grupta yüksek oranda çarpık veriler olması durumunda ve hasta ve sağlıklı popülasyonların dağılımları sırasıyla sağa çarpık dağılım ve normal dağılım olduğunda, binormal yöntemin performansını geçmiştir.

Anahtar Kelimeler: Tanı testi; alıcı işlem karakteristik eğrisi; kernel yoğunluk tahmini; log-konkav yoğunluk tahmini
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