THE COCHRAN-ARMITAGE TEST TO ESTIMATE THE SAMPLE SIZE FOR TREND OF PROPORTIONS FOR BIOLOGICAL DATA

Abstract

The biological activity of a substance can be investigated through a series of experiments done with the increased or decreased dosage of it. One of the purposes of such studies is to determine the trend of responses based on dosage. In studies carried out for this purpose, appropriate sample size has an indisputable influence on the reliability of the decisions to be made at the end of the study. There are various statistical methods for determining the trend of proportions. One of them is the Cochran-Armitage test. In a categorical data analysis, the trend between two variables with k categories can be determined through the Cochran-Armitage test. This study aims to explore the sample size calculation method developed by Nam J. (1987) for the Cochran-Armitage test. The power of the test was investigated in different numbers of categories and in different sample sizes for each category when the least biologically significant differences changed as Type I error was taken as 0.05. To this end, the study examined the results obtained by making 10000 repetitions for each case through the Monte Carlo simulation method. When the least biologically significant differences change at the end of simulation studies, the power of test highly varies in different combinations. When the number of categories is 2, determination of trend requires working with very large samples. When the number of categories is 3 or 4, the desired power can be obtained with smaller samples compared to the case where the number of categories is 2. When the number of categories is over 4, a substantial increase is needed in sample size to obtain the desired power. Change in marginal frequencies does not have much influence on sample size.

Keywords

• cochran-armitage,exact test,sample size,trend of proportions,type I error rate

References

1. Ahn, K., C. Haynes, W. Kim, R. St. Fleur, D. Gordon, and S. J. Finch. 2007. The effects of SNP genotyping errors on the power of the cochran-armitage linear trend test for case/control association studies. Annals of Human Genetics, 71(2):249–261. http://doi.org/10.1111/j.1469- 1809.2006.00318.x
2. Akgun, I., M. Tosun, K. Haliloglu, M. Aydin. 2011. Development of autotetraploid perennial rye (Secale montanum Guss.) and selection for seed set, Turk J Field Crops, 16(1): 23-28.
3. Armitage P. 1955. Tests for linear trends in proportions and frequencies. Biometrics; 11:375–386.
4. Banks, K. E., D. H. Hunter and D. J. Wachal. 2005. Diazinon in surface waters before and after a federally-mandated ban. Science of the Total Environment, 350(1-3):86–93. http://doi.org/10.1016/j.scitotenv.2005.01.017
5. Chapman D.G. and J. Nam. 1968. Asymptotic power of chisquare tests for linear trends in proportions. Biometrics; 24:317–327.
6. CochranW.G. 1954. Some methods for strengthening common the tests. Biometrics; 10:417–451.
7. Cuming Semizer D., F. Altan, H. Akdemir, M. Tosun, A. Gurel and B. Tanyolac. 2015. Qtl analysis of fiber color and fiber quality in naturally green colored cotton (Gossypium hirsutum L.), Turk J Field Crops, 20(1), 49-58
8. Hintze, J. PASS 11. [Chapter 255 Cochran-Armitage Test for Trend in Proportions] Kaysville, Utah, USA: NCSS, LLC; 2011:2-5: 595:1-7

9. Kang, S. H., and J. W. Lee. 2007. The size of the CochranArmitage trend test in 2 ?? C contingency tables. Journal of Statistical Planning and Inference, 137(6):1851–1861. http://doi.org/10.1016/j.jspi.2006.03.009
10. Lachin, J. M. 2011. Power and sample size evaluation for the Cochran-Mantel-Haenszel mean score (Wilcoxon rank sum) test and the Cochran-Armitage test for trend. Statistics in Medicine, 30(25):3057–3066.http://doi.org/10.1002/sim.4330
11. Mehta, C. R., N. R.Patel, P. Senchaudhuri and N. Dec. 2007. Exact Power and Sample-Size Computations for the Cochran-Armitage Trend Test SHORTER COMMUNICATIONS EDITOR : Exact Power and SampleSize Computations for the Cochran-Armitage Trend Test, 54(4):1615–1621.
12. Mortazavian S. M. M. and S. Azizi-Nia. 2014. Nonparametric Stability Analysis In Multi-Environment Trial Of Canola, Turk J Field Crops, 19(1):108-117
13. Nam J. A. 1987. Simple approximation for calculating sample sizes for detecting linear trend in proportions. Biometrics; 43:701–705.
14. Shen, H., Y. Hu, Y. Chen and T. Tung. 2014. Prevalence and Associated Metabolic Factors of Gallstone Disease in the Elderly Agricultural and Fishing Population of Taiwan.
15. Slager S.L. and D.J. Schaid. 2001. Case-Control Studies Of Genetic Markers: Power And Sample Size Approximation For Armitage’s Test Of Trend. Human Heredity; 52:149– 153. DOI: 10.1159/000053370.
16. Tekindal M.A., H. Bayrak, B. Ozkaya, Y. Yavuz. 2014. Secondorder response surface method: factorial experiments an alternative method in the field of agronomy, Turk J Field Crops, 19(1):35-45
17. Yol E., F. Seymus and B. Uzun. 2013. Genetic Control Of Purple Plant Color In Sesame, Turk J Field Crops, 18(2), 229-232
18. Zheng, G., and J.L. Gastwirth. 2006. On estimation of the variance in Cochran-Armitage trend tests for genetic association using case-control studies. Statistics in Medicine, 25(18):3150–3159. http://doi.org/10.1002/sim.2250