Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
The Effect of Cluster Size for Model Performance in High-Dimensional Longitudinal Studies: A Simulation Study
Yüksek Boyutlu Boylamsal Çalışmalarda Küme Büyüklüğünün Model Performansına Etkisi: Bir Simülasyon Çalışması
Merve TÜRKEGÜN ŞENGÜLa , Bahar TAŞDELENb , Saim YOLOĞLUc
aDepartment of Biostatistics and Medical Informatics, Alaaddin Keykubat University Faculty of Medicine, Antalya, Türkiye
bDepartment of Biostatistics and Medical Informatics, Mersin University Faculty of Medicine, Mersin, Türkiye
cDepartment of Biostatistics and Medical Informatics, İnönü University Faculty of Medicine, Malatya, Türkiye
Turkiye Klinikleri J Biostat. 2023;15(3):161-70
doi: 10.5336/biostatic.2023-98699
Article Language: EN
Full Text
ABSTRACT
 Objective: In order to prevent model estimation errors and deviations in high-dimensional longitudinal studies, risk models are established through penalized methods. The aim of this study is to examine the effect of small cluster effects on the generalized estimating equations (GEE) and penalized GEE (PGEE) model performances in high-dimensional longitudinal data. Material and Methods: A simulation study was designed to compare the GEE and PGEE model performances, Type I error rates, and power in two-period longitudinal data structures with different cluster sizes (n=20, 30, 50, 100, 200), different numbers of predictors (p=10, 20, 50) and different correlation levels between predictors (r=0.20, 0.50, 0.80). Results: It was observed that the GEE coefficient estimates were misleading and inconsistent, the Type I error rates were high, and the power of the test was weak at insufficient cluster sizes and high correlations between predictors. Even when the number of predictors and cluster size were in the balance (p=10, n=100, 200), Type I error rates were obtanied high for GEE. Increasing the cluster size was not enough to reduce the Type I error rate of GEE. The PGEE produced more successful results than GEE in all conditions. The power of PGEE increased to over 80% in all scenarios. Conclusion: The PGEE yielded more consistent results by controlling the relationships both within the cluster and between the predictors. In highdimensional longitudinal studies, it was observed that the use of PGEE is more effective than GEE.

Keywords: Generalized estimating equations; penalized generalized estimating equations; model selection; penalized methods; high dimensional longitudinal data
ÖZET
 Amaç: Yüksek boyutlu boylamsal çalışmalardaki model tahmin hatalarının ve sapmaların önüne geçebilmek amacıyla risk modelleri, cezalı yöntemler aracılığı ile oluşturulur. Bu çalışmada amaç; yüksek boyutlu boylamsal veride küçük küme büyüklüğünün etkisinin, genelleştirilmiş tahmin eşitlikleri [generalized estimating equations (GEE)] ve cezalı genelleştirilmiş tahmin eşitlikleri [penalized generalized estimating equations (PGEE)] model performansları üzerine etkisini incelemektir. Gereç ve Yöntemler: Farklı küme büyüklüklerine (n=20, 30, 50, 100, 200), farklı açıklayıcı değişken sayılarına (P=10, 20, 50) ve açıklayıcı değişkenler arasında farklı korelasyon düzeylerine sahip (r=0.20, 0.50 ve 0.80) iki periyotlu boylamsal veri yapılarında GEE ve PGEE model performanslarını, Tip I hata oranlarını ve testin gücünü karşılaştırmak amacıyla simülasyon çalışması kurgulanmıştır. Bulgular: Yetersiz küme büyüklüklerinde ve açıklayıcı değişkenler arasındaki yüksek korelasyonlarda, GEE katsayı tahminlerinin yanıltıcı ve tutarsız olduğu, Tip I hata oranlarının yüksek ve testin gücünün ise zayıf olduğu gözlemlenmiştir. Değişken sayısı ile küme büyüklüğünün dengede olduğu durumlarda dahi (P=10, n=100, 200) GEE için Tip I hata oranları yüksek elde edilmiştir. Küme büyüklüğünü artırmak GEE'nin Tip I hata oranını düşürmek için yeterli olmamıştır. PGEE ise her koşulda GEE'den daha başarılı sonuçlar üretmiştir. PGEE'nin gücü tüm senaryolarda %80'in üzerine çıkmıştır. Sonuç: PGEE küme içi ve kümeler arası ilişkileri kontrol altında tutarak GEE'ye göre daha geçerli sonuçlar üretmiştir. Yüksek boyutlu boylamsal çalışmalarda GEE yerine PGEE'nin kullanımın daha etkili olduğu gözlemlenmiştir.

Anahtar Kelimeler: Genelleştirilmiş tahmin eşitlikleri; cezalı genelleştirilmiş tahmin eşitlikleri, model seçimi; cezalı yöntemler; yüksek boyutlu boylamsal veri
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