Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
A New Perspective for Area Under the Curve in Decision Making with Extra Safety Threshold Value: A Simulation Study
Ekstra Güvenlik Eşik Değeri ile Karar Vermede Eğri Altında Kalan Alan İçin Yeni Bir Bakış Açısı: Bir Simülasyon Çalışması
Selma GÜRLERa, Özlem EGE ORUÇa, Dinçer GÖKSÜLÜKb, Aslı SUNERc
aDepartment of Statistics, Dokuz Eylül University Faculty of Science, İzmir, Türkiye
bDepartment of Biostatistics, Erciyes University Faculty of Medicine, Kayseri, Türkiye
cDepartment of Bioistatistics and Medical Informatics, Ege University Faculty of Medicine, İzmir, Türkiye
Turkiye Klinikleri J Biostat. 2022;14(3):137-46
doi: 10.5336/biostatic.2022-89951
Article Language: EN
Full Text
ABSTRACT
Objective: In studies conducted to detect a disease, making a false negative decision in cases such as detecting a deadly disease (Case I), or making a false positive decision in cases where diseases with high treatment costs (Case II) can lead to dangerous results. In this study, a new definition of the area under the curve (AUC) is proposed using a safety threshold value t for the diagnostic test to provide flexible decisions in critical cases. The alternative cut-off point for test diagnosis is evaluated by a simulation study in terms of sensitivity/specificity and relative efficiency. Materials and Methods: A simulation study was performed using different AUC values to obtain the cut-off point c shifted towards c-t for Case I and c+t for Case II. The normal distribution is used for the diseased (X) and non-diseased (Y) data. When obtaining the shift amount t, the gamma probability, which is the desired percentage of increase or decrease in the sensitivity/specificity value, is taken into account. Results: The results of our study showed that the relative efficiency is not significantly affected by working with the safety threshold t value when the test is less accurate and has a low AUC value. Conclusion: In this study, alternative cut-off points are obtained using the shift amount t determined by a predefined gamma probability. It is suggested that in critical situations, using the extra safety threshold t, determining the actual disease margin and safety standards for subjects can provide a more tolerant decision, especially in tests with low discrimination power.

Keywords: Area under curve; cut-off-value; sensitivity; Youden Index; maximum efficiency
ÖZET
Amaç: Bir hastalığı saptamak için yapılan çalışmalarda, ölümcül bir hastalığın saptanması gibi durumlarda yanlış negatif karar verilmesi (Durum I), veya tedavi maliyetinin yüksek olduğu hastalıklarda yanlış pozitif karar verilmesi (Durum II) tehlikeli sonuçlara yol açabilir. Bu çalışmada, kritik durumlarda esnek karar sağlamak için tanı testi için bir güvenlik eşik değeri t kullanılarak eğri altındaki alanın (AUC) yeni bir tanımı önerilmiştir. Test tanısı için alternatif kesme noktası, duyarlılık/özgüllük ve göreli etkinlik açısından bir simülasyon çalışması ile değerlendirilmiştir. Gereçler ve Yöntemler: Durum I için c-t'ye ve Durum II için c+t'ye kaydırılan kesme noktası c'yi elde etmek için farklı AUC değerleri kullanılarak bir simülasyon çalışması yapılmıştır. Hasta (X) ve hastalıklı olmayan (Y) için normal dağılım kullanılmıştır. Kaydırma miktarı t elde edilirken, duyarlılık/özgüllük değerinde yüzde olarak istenen artış veya azalış miktarı olan gama olasılığı dikkate alınır. Bulgular: Çalışmamızın sonuçları, testin daha az doğru ve düşük AUC değerine sahip olduğu durumlarda, güvenlik eşiği t değeriyle çalışmanın göreli etkinliğinin önemli ölçüde etkilenmediğini göstermiştir. Sonuç: Bu çalışmada, önceden tanımlanmış bir gama olasılığı ile belirlenen kaydırma miktarı t kullanılarak alternatif kesme noktaları elde edilmiştir. Kritik durumlarda, ekstra güvenlik eşiği t kullanılarak, denekler için gerçek hastalık sınırı ve güvenlik standartlarının belirlenmesi, özellikle ayırt etme gücü düşük testlerde daha toleranslı bir karar sağlayabileceği önerilmektedir.

Anahtar Kelimeler: Eğri altında kalan alan; kesme noktası; duyarlılık; Youden Indeks; maximum etkinlik
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