Comparison of generalized estimating equations' performance in clustered Bbnary observations

Bu çalışmada, gruplandırılmış ikili gözlemler içeren veri setlerinin analizlerinde kullanılan genelleştirilmiş tahmin denklemlerinin (GTD) performansı, farklı grup ve birim sayısında grup içi korelasyon katsayısına (G‹KK) göre karşılaştırıldı Gereç ve Yöntem: Genelleştirilmiş tahmin denklemleri yönteminin performans karşılaştırmaları parametre tahminlerinin yanlılıkları kullanılarak farklı grup büyüklükleri, grup içi korelasyon katsayısı, grup sayısı ve her bir gruptaki gözlem sayısında simülasyon çalışmaları yapılarak gerçekleştirildi. Simülasyonlar Monte Carlo simülasyon yöntemi kullanılarak SAS 9.0 programı nda yapıldı. Analizlerde SAS GENMOD prosedürü kullanıldı. Bulgular: Grup içi korelasyon katsayısı düşük düzeylerde olduğunda (GİKK0.10), parametre tahminlerinin yüksek oranda yanlı olduğu bulundu. Toplam örnek büyüklüğü sabit kalmak koşuluyla; grup sayısı azalırken genel örnek büyüklüğü tüm gruplarda sabit olmasına raımen, gruplarda yer alan birim sayıları arttığında parametre tahminlerinin ve yanlılıklarının bu durumdan önemli düzeyde etkilenmediği, parametre tahminlerinde etkili olan faktörün yine GİKK olduğu gözlendi. Sonuç: Genelleştirilmiş tahmin denklemleri yöntemi popülasyon ortalamalı lojistik regresyon yaklaşımını kullandığından grup içindeki değişimleri ve ilişkiyi iyi düzeyde açıklayamamaktadır. Özellikle GİKK’si 0.10’dan büyük veri setleri için GTD yönteminin kullanılması oldukça sakıncalıdır.

Anahtar Kelimeler:

Monte Carlo metodu, Konu ile ilgili istatistikler, Kümeleme çözümlemesi

Genelleştirilmiş tahmin denklemlerinin performansının gruplandırılmış ikili gözlemlerde karşılaştırılması

The objective of this study is to compare the performance of generalized estimating equations (GEE) for analysis of clustered binary observations under varying group and observation numbers according to intraclass correlation coefficients (ICC). Materials and Methods: The comparison of GEE performance was made by using bias of parameter estimations through computer simulations under varying group sizes, ICC, number of clusters, and number of observations per cluster. Simulations were performed in SAS 9.0 by using Monte Carlo simulation method. Analyses were made with SAS GENMOD procedure. Results: When intraclass correlation coefficient was low (ICC<0.10), there was no significant difference in parameter estimation and their biases and it was observed that GEE gave reliable, consistent and unbiased estimations. However, when ICC increased (ICC>0.10), it was found that the parameter estimations were significantly biased. On the condition that total sample size is fixed; it was observed that, even though the general sample size was constant in all groups while the number of groups was decreasing, when the number of observations per cluster increased, parameter estimations and their biases weren’t affected significantly and the effective factor in parameter estimation was ICC. Conclusion: Because GEE method uses population averaged logistic regression approach, it cannot explain the changes and correlations in clusters completely. The use of GEE method is inconvenient particularly for data sets which have ICC greater than 0.10.

Keywords:

Monte Carlo Method, Statistics as Topic, Cluster Analysis,

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1. Giraudeau B, Mallet A, Chastang C. Case influence on the intraclass correlation coefficient estimate. Biometrics 1996;52:1492-7.
2. Kang W, Lee MS, Lee Y. HGLM versus conditional estimators for the analysis of clustered binary data. Stat Med 2005;24:741-52.
3. Morel JG, Neerchal NK. Clustered binary logistic regression in teratology data using a finite mixture distribution. Stat Med 1997;16:2843-53.
4. Murray DM, Alfano CM, Zbikowski SM, Padgett LS, Robinson LA, Klesges R. Intraclass correlation among measures related to cigarette use by adolescents: estimates from an urban and largely African American cohort. Addict Behav 2002;27:509-27.
5. Neuhaus JM. Estimation efficiency and tests of covariate effects with clustered binary data. Biometrics 1993;49:989-96.
6. Albert JM. Estimating efficacy in clinical trials with clustered binary responses. Stat Med 2002;21:649-61.
7. Reed JF 3rd. Adjusted chi-square statistics: application to clustered binary data in primary care. Ann Fam Med 2004;2:201-3.
8. Smeeth L, Ng ESW. Intraclass correlation coefficients for cluster randomized trials in primary care-data from the MRC trial of the assessment and management of older people in the community. Controlled Clinical Trials 2002;23:409-421.
9. Song JX, Ahn CW. An evaluation of methods for the stratified analysis of clustered binary data in community intervention trials. Stat Med 2003; 22:2205-16.
10. Murray DM, Short BJ. Intraclass correlation among measures related to tobacco use by adolescents: estimates, correlates, and applications in intervention studies. Addict Behav 1997;22:1-12.
11. Ananth CV, Platt RW, Savitz DA. Regression models for clustered binary responses: implications of ignoring the intracluster correlation in an analysis of perinatal mortality in twin gestations. Ann Epidemiol 2005;15:293-301.
12. Heo M, Leon AC. Comparison of statistical methods for analysis of clustered binary observations. Stat Med 2005;24:911-23.
13. Rieger RH, Weinberg CR. Analysis of clustered binary outcomes using within-cluster paired resampling. Biometrics 2002;58:332-41.
14. Ridout MS, Demetrio CGB, Firth D. Estimating intraclass correlation for binary data. Biometrics 1999; 55:137-48.
15. Tian L. Interval estimation and hypothesis testing of intraclass correlation coefficients: the generalized variable approach. Stat Med 2005;24:1745-53.
16. Zou GY, Donner A. Confidence interval estimation of the intraclass correlation coefficient for binary outcome data. Biometrics 2004;60:807-11.
17. Murray DM, Catellier DJ, Hannan PJ, Treuth MS, Stevens J, Schmitz KH, et al. School-level intraclass correlation for physical activity in adolescent girls. Med Sci Sports Exerc 2004;36:876-82.
18. Parker DR, Evangelou E, Eaton CB. Intraclass correlation coefficients for cluster randomized trials in primary care: the cholesterol education and research trial (CEART). Contemp Clin Trials 2005;26:260-7.
19. Molenberghs G, Ryan LM. An exponential family model for clustered multivariate binary data. Environmetrics 1999;10:279-300.
20. Hardin JW, Hilbe JM, (editors). Generalized estimating equations. New York: Chapman & Hall/CRC; 2003.
21. Hosmer DW. Lemeshow S, (editors). Applied logistic regression. New York: John Wiley & Sons, Inc.; 2000.
22. Patel JK, Kapadia CH, Owen DB, (editors). Handbook of statistical distributions. New York: Marcel Dekker Inc.; 1976.
23. Neuhaus JM. Assessing change with longitudinal and clustered binary data. Annu Rev Public Health 2001;22:115-28.