Effect sizes are estimated from several study designs when the subjects are individually sampled. When the samples are the aggregate cluster of individuals, the within cluster correlation must be accounted for to construct correct confidence intervals, and to conduct valid statistical inference. The purpose of this article is to propose and evaluate statistical procedures for the estimation of the variance of the estimated attributable risk in parallel groups of clusters, and in a design dividing each of k clusters into two segments creating multiple sub-clusters. The estimated variance is the first order approximation and is obtained by the delta method. We apply the methodology and propose a Wald type confidence interval on the difference between two correlated attributable risks. We also construct a test on the hypothesis of equality of two correlated attributable risks. We evaluate the power of the proposed test via Monte-Carlo simulations.
References
[1]
Richardson, J. (1996) Measures of Effect Size. Behavior Research Methods, Instruments and Computers, 28, 12-22. https://doi.org/10.3758/BF03203631
[2]
Levin, M.L. (1953) The Occurrence of Lung Cancer In Man. Acta Unio Internationalis Contra Cancrum, 9, 531-541.
[3]
Fleiss, J. (1982) Statistical Methods for Rates and Proportions. 2nd Edition, John Wiley, New York.
[4]
Fletcher, R.H., Fletcher, S.W. and Wagner, E.H. (1996) Clinical Epidemiology: The Essentials. Lippincott Williams & Wilkins, Philadelphia.
[5]
Gordis, L. (1996) Epidemiology. WB Saunders Co., Philadelphia.
[6]
Donner, A. and Klar, N. (2000) Design and Analysis of Cluster Randomized Trials in Health Research. Arnold, New York.
[7]
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models. 2nd Edition, Chapman & Hall/CRC.
[8]
Cox, D.R. and Snell, E.J. (1989) Analysis of Binary Data. 2nd Edition, CRC Press, Boca Raton, FL.
[9]
Walter, S.D. (1975) The Distribution of Levin’s Measure of Attributable Risk from Case-Control Studies. American Journal of Epidemiology, 106, 206.
[10]
Kendall, M. and Stuart, A. (1987) Advanced Theory of Statistics. Vol. 1, 5th Edition, Griffin, London.
[11]
Saudi Congenital Heart Disease Registry. http://rc.kfshrc.edu.sa/chd_program
[12]
Mitchell, S.C., Korones, S.B. and Berendes, H.W. (1971) Congenital Heart Disease, in 56,109 Births. Incidence and Natural History. Circulation, 43, 323-332.
https://doi.org/10.1161/01.CIR.43.3.323
[13]
Satoda, M., Pierpont, M.E., Diaz, G.A., Bornemeier, R.A. and Gelb, B.D. (1999) Char Syndrome, an Inherited Disorder with Patent Ductus Arteriosus, Maps to Chromosome 6p12-p21. Circulation, 99, 3036-3042.
https://doi.org/10.1161/01.CIR.99.23.3036
[14]
Satoda, M., Zhao, F., Diaz, G.A., Burn, J., Goodship, J., Davidson, H.R., Pierpont, M.E. and Gelb, B.D. (2000) Mutations in TFAP2B Cause Char Syndrome, a Familial Form of Patent Ductus Arteriosus. Nature Genetics, 25, 42-46.
https://doi.org/10.1038/75578
[15]
Khoury, S.A. and Massad, D. (1992) Consanguineous Marriages in Jordan. American Journal of Medical Genetics, 43, 769-775.
https://doi.org/10.1002/ajmg.1320430502
[16]
Jurdi, R. and Saxena, P.C. (2003) The Prevalence and Correlates of Consanguineous Marriages in Yemen: Similarities and Correlates with Other Arab Countries. Journal of Biosocial Sciences, 35, 1-13. https://doi.org/10.1017/S0021932003000014
[17]
El-Hazmi, M.A., Al-Swailem, A.R. and Warsey, A.S. (1995) Consanguinity among the Saudi Arabian Population. Journal of Medical Genetics, 32, 623-626.
https://doi.org/10.1136/jmg.32.8.623
[18]
Becker, S.M., Al Halees, Z., Molina, C. and Paterson, R.M. (2001) Consanguinity and Congenital Heart Disease in Saudi Arabia. American Journal of Medical Genetics Part A, 99, 8-13.
https://doi.org/10.1002/1096-8628(20010215)99:1<8::AID-AJMG1116>3.0.CO;2-U
[19]
El-Mouzan, M., Al-Salloum, A., Al-Herbish, A., Qurashi, M. and Al-Omar, A. (2008) Consanguinity and Major Genetic Disorders in Saudi Children: A Community-Based Cross-Sectional Study. Annals of Saudi Medicine, 28, 169-174.
https://doi.org/10.4103/0256-4947.51726
[20]
William, D.A. (1975) The Analysis of Binary Responses from Toxicological Experiments Involving Reproduction and Teratogenicity. Biometrics, 31, 949-952.
https://doi.org/10.2307/2529820
[21]
Weil, C.S. (1971) Selection of the Valid Number of Sampling Units and a Consideration of Their Combination in Toxicological Studies Involving Reproduction, Teratogenesis or Carcinogenesis. Food Cosmetics Toxicology, 8, 177-182.
[22]
Donner, A., Klar, N. and Zou, G. (2004) Methods for the Statistical Analysis of Binary Data in Split-Cluster Designs. Biometrics, 60, 919-925.
https://doi.org/10.1111/j.0006-341X.2004.00247.x
[23]
Miall, W.E. and Oldham, P.O. (1955) A Study of Arterial Blood Pressure and Its Inheritance in a Sample of the General Population. Clinical Science, 14, 459-487.
