The Cochran–Armitage (CA) test is commonly used in both epidemiology and genetics to test for linear trend in two-way tables with a binary outcome. There has been increasing interest in the power and size of the test and in determination of sample size, especially when there is potential misclassification in the ‘exposure’ category. This article provides a unified approach to determination of the power function over different sampling strategies (fixed overall sample size or fixed marginal sample sizes) and allowing for misclassification in one or both variables. The misclassification may be either differential or non-differential. In addition to the standard CA test, results are also given which provide some insight into the performance of the modified CA test, which utilizes a standard error obtained without invoking the null hypothesis. Even without misclassification, some new expressions are also obtained for determining power with a fixed overall sample size. Numerical illustrations are presented with an emphasis on the more commonly occurring problem of misclassification in the exposure category.
HiganoCSCormanJMSmithDC. Phase 1/2 dose-escalation study of a GM-CSFsecreting, allogeneic, cellular immunotherapy for metastatic hormone-refractory prostate cancer. Cancer2008; 113: 975–984.
5.
MarcusE-LMenczelJ. Higher prevalence of osteoporosis among female Holocaust survivors. Osteoporos Int2007; 18: 1501–1506.
6.
IndredavikBRohwederGNaalsundELydersenS. Medical complications in a comprehensive stroke unit and an early supported discharge service. Stroke2008; 39(2): 414–420.
7.
BrysonJCoeGSwamiN. Administrative outcomes five years after opening an acute palliative care unit at a comprehensive cancer center. J Palliat Med2010; 13(5): 559–565.
8.
ElferinkMAvan SteenbergenLNKrijnenP. On behalf of the Working Group Output of the Netherlands Cancer Registry. Marked improvements in survival of patients with rectal cancer in the Netherlands following changes in therapy, 1989-2006. Eur J Cancer2010; 46(8): 1421–1429.
9.
DavidsonSWuXLiuY. Association of ERAP1, but Not IL23R, with ankylosing spondylitis in a han chinese population. Arthritis and Rheumatism2009; 60: 3263–3268.
10.
CotteSVon AhsenNKruseN. ABC-transporter gene-polymorphisms are potential pharmacogenetic markers for mitoxantrone response in multiple sclerosis. Brain2009; 132: 2517–2530.
11.
ChanJOhWXieW. Plasma selenium, manganese superoxide dismutase, and intermediate- or high-risk prostate cancer. J Clin Oncol2009; 27: 3577–3583.
12.
AgrestiA. Categorical data analysis, 2nd ed. New York: John Wiley, 2002.
13.
FreidlinBZhengGLiZGastwirthJL. Trend tests for case-control studies of genetic markers: power, sample size and robustness. Hum Heredity2002; 53: 146–152.
14.
ChapmanDGNamJM. Asymptotic power of chi square tests for linear trends in proportions. Biometrics1968; 24(2): 315–327.
15.
SlagerSLSchaidDJ. Case-control studies of genetic markers: power and sample size approximations for Armitages test for trend. Hum Heredity2001; 52: 149–153.
16.
GuedjMDella-ChiesaEPicardFNuelG. Computing power in case-control association studies nthrough the use of quadratic approximations: application to meta-statistics. Ann Hum Geneti2006; 71: 262–270.
17.
ZhengGGastwirthJ. On estimation of the variance in Cochran–Armitage trend tests for genetic association using case-control studies. Stat Med2006; 25: 3150–3159.
18.
AhnKHaynesCKimSt WFleurRGordonDFinchS. The effects of SNP genotyping errors on the power of the cochran–armitage linear trend test for case/control association studies. Ann Hum Genet2006; 71: 249–261.
19.
AhnKGordonDFinchS. Increase of rejection rate in case-control studies with the differential genotyping error rates. Stat Appl Genet Mol Biol2009; 8(1): Article 25.
20.
MarquardVBeckmannLHeidIMLaminaCChang-ClaudeJ. Impact of genotyping errors on the type I error rate and the power of haplotype-based association methods. BMC Genet2000; 10: 3–3.
21.
YamadaTKinukawaNNakamuraTNoseY. Simulation program for power and sample size determination in logistic analysis of single nucleotide polymorphisms when the response variable is subject to misclassification. Compu Methods Programs Biomed2009; 96(1): 42–48.
22.
FreudenheimJLJohnsonNEWardropRL. Nutrient misclassification: bias in the odds ratio and loss of power in the Mantel test for trend. Inte J Epidemiol1989; 18: 232–238.
23.
BrennerH. Notes on the assessment of trend in the presence of nondifferential exposure misclassification. Epidemiology1992; 5: 420–427.
24.
LevoisMSwitzerP. Differential exposure misclassification in case-control studies of environmental tobacco smoke and lung cancer. J Clin Epidemiol1998; 51: 37–54.
25.
DelpizzoVSalzbergMR. Relative-risk-estimate bias and loss of power in the Mantel test for trend resulting from the use of magnetic-field point-in-time (“spot”) measurements in epidemiological studies based on an ordinal exposure scale. Bioelectromagnetics1992; 13(5): 363–378.
26.
WilliamsP. Trend tests for counts and proportions. Encyclopedia of Biostatistics, New York: John Wiley, 2005.
27.
ArmitagePBerryG. Statistical methods in medical research, 3rd ed. Boston, MA: Blackwell, 1994.
28.
SasieniPD. From genotypes to genes: doubling the sample size. Biometrics1997; 53: 1253–1261.
29.
GustafsonPLeND. Comparing the effects of continuous and discrete covariate mismeasurement, with emphasis on the dichotomization of mismeasured predictors. Biometrics2002; 58: 878–887.
30.
KuhaJSkinnerCPalmgrenJMisclassification errors. In: ArmitagePColtonT (eds). Encyclopedia of biostatistics2009; Vol. 4, Chichester: John Wiley and Sons, pp. 2615–2621.
ZhangGTianX. The impact of diagnostic error on testing genetic association in case-control studies. Stat Med2005; 24: 869–882.
33.
GraybillFA. Theory and application of the general linear model, Scituate, MA: Duxbury, 1976.
34.
GordonDHaynesCYangYKramerPFinchS. Linear trend tests for case-control genetic association that incorporate random phenotype and genotype misclassification error. Genet Epidemiol2009; 31: 853–870.
35.
BorchersBBrownMMcLellanBBekmetjevATintleyN. Incorporating duplicate genotype data into linear trend tests of genetic association: methods and cost-effectiveness. Stat Appl Genet Mol Biol2009; 8(1): Article 24.
