Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Odds Oranı için Logit Güven Aralıkları: Bir Benzetim Çalışması
Logit Confidence Intervals for Odds Ratio: A Simulation Study
İsmet DOĞAN a, Nurhan DOĞAN a
aAfyonkarahisar Sağlık Bilimleri Üniversitesi Tıp Fakültesi, Biyoistatistik ve Tıbbi Bilişim ABD, Afyonkarahisar, Türkiye
Turkiye Klinikleri J Biostat. 2023;15(1):67-78
doi: 10.5336/biostatic.2022-91725
Article Language: TR
Full Text
ÖZET
 Amaç: Bu makalenin amacı, odds oranı için hesaplanan Woolf logit, Gart düzeltilmiş logit ve Agresti bağımsız-düzleştirilmiş logit güven aralıklarını farklı örneklem büyüklükleri için karşılaştırmaktır. Gereç ve Yöntemler: Çalışmada Phyton-random kütüphanesi kullanılarak 10≤n≤1000 aralığında yer alan 35 farklı n değeri için veri türetilmiştir. Verilerin türetilmesinde önce n 11,n 12,n 21 ve n 22 ile gösterilen frekanslardan hangisine değer atanacağı sonra da ilgili frekans değeri belirlenmiştir. n=10 için 286, n=15 için 815 ve n≥20 için 1000'er farklı veri seti çalışmada kullanılmıştır. Ancak odds oranları ile güven aralığı hesaplamalarında n 11,n 12,n 21 ve n 22 frekanslarından herhangi birinin sıfır olması durumunda hesaplama yapılamadığı için simülasyon sayıları her bir örneklem büyüklüğü ve yöntem için farklılık göstermiştir. Bulgular: n 11,n 12,n 21 ve n 22 frekanslarından herhangi birinin değerinin diğerlerine göre aşırı derecede farklılaşması odds oranının değerini önemli derecede etkilemekte, güven aralığını ise büyütmektedir. Odds değerleri ve güven aralığı açısından bakıldığında yöntemlerden elde edilen değerler Agresti≥Gart≥Woolf şeklinde sıralanmaktadır. Özellikle n≥150 olması durumunda her üç yöntemden elde edilen güven aralıkları istatistiksel olarak anlamlı hale getirmektedir. Sonuç: Çalışmada dikkate alınan güven aralıkları ile ilgili yöntemlerden hiçbirinin en iyi yöntem olarak belirtilemeyeceği, bu yöntemlerden yararlanılarak elde edilen güven aralıklarının çok geniş ve nokta tahminleri konusunda simetrik olmadıkları belirlenmiştir. Çalışmada dikkate alınan tüm örneklem büyüklükleri için Woolf yöntemi, hesaplanan odds oranının istatistiksel olarak anlamlı olup olmaması, güven aralığının büyüklüğü ve alt sınır<odds oranı<üst sınır kriterleri dikkate alındığında diğer iki yönteme göre daha iyi performans göstermiştir. Ancak n 11,n 12,n 21 ve n 22 frekanslarından herhangi birinin sıfır olması durumunda Woolf yönteminden elde edilecek güven aralığının anlamsız olduğu göz ardı edilmemelidir.

Anahtar Kelimeler: Odds oranı; Woolf logit güven aralığı; Gart düzeltilmiş logit güven aralığı; Agresti bağımsız-düzeltilmiş logit güven aralığı; iki sonuçlu veri
ABSTRACT
 Objective: The aim of this article is to compare the Woolf logit, Gart adjusted logit and Agresti independent-smoothed logit confidence intervals calculated for odds ratio for different sample sizes. Material and Methods: In the study, data were derived for 35 different n values in the range of 10≤n≤1000 using the Phyton random library. In the derivation of the data, first which of the frequencies indicated by n 11,n 12,n 21 and n 22 will be assigned a value, then the relevant frequency value is determined. 286 different data sets for n=10, 815 for n=15 and 1000 different data sets for n≥20 were used in the study. However, in the calculations of odds ratios and confidence intervals, if any of the n 11, n 12, n 21 and n 22 frequencies is zero, the calculation cannot be made, so the simulation numbers are different for each sample size and method. Results: Excessive variation in the value of any of the n 11,n 12, n 21 and n 22 frequencies from the others significantly affects the value of the OR and enlarges the confidence interval. In terms of odds values and confidence intervals, the values obtained from the methods are listed as Agresti≥Gart≥Woolf. Especially in the case of n≥150, the confidence intervals obtained from all three methods make it statistically significant. Conclusion: It has been determined that none of the methods related to the confidence intervals considered in the study can be specified as the best method, and the confidence intervals obtained by using these methods are very wide and not symmetrical in point estimations. For all sample sizes considered in the study, Woolf's method performed better than the other two methods, considering whether the calculated odds ratio was statistically significant, the size of the confidence interval, and the lower limit<odds ratio<upper limit criteria. However, if any of the n 11,n 12,n 21 and n 22 frequencies is zero, it should not be ignored that the confidence interval to be obtained from the Woolf method is meaningless.

Keywords: Odds ratio; Woolf logit interval; Gart adjusted logit interval; Agresti independence-smoothed logit interval; binary data
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