On the power of the Cochran–Armitage test for trend in the presence of misclassification

Abstract

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.

Keywords

Case–control genotype error linear trend Mantel test random sample stratified

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References

Cochran

. Some methods for strengthening the common chi-square tests. Biometrics 1954; 10: 417–451.

Armitage

. Tests for linear trends in proportions and frequencies. Biometrics 1955; 11: 375–386.

Robaux

Blunt

Viel

. Tramadol added to 1.5 analgesia dose-dependently. Anesth Analg 2004; 98(4): 1172–1177.

Higano

Corman

Smith

. Phase 1/2 dose-escalation study of a GM-CSFsecreting, allogeneic, cellular immunotherapy for metastatic hormone-refractory prostate cancer. Cancer 2008; 113: 975–984.

Marcus

E-L

Menczel

. Higher prevalence of osteoporosis among female Holocaust survivors. Osteoporos Int 2007; 18: 1501–1506.

Indredavik

Rohweder

Naalsund

Lydersen

. Medical complications in a comprehensive stroke unit and an early supported discharge service. Stroke 2008; 39(2): 414–420.

Bryson

Coe

Swami

. Administrative outcomes five years after opening an acute palliative care unit at a comprehensive cancer center. J Palliat Med 2010; 13(5): 559–565.

Elferink

van Steenbergen

Krijnen

. 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 Cancer 2010; 46(8): 1421–1429.

Davidson

Liu

. Association of ERAP1, but Not IL23R, with ankylosing spondylitis in a han chinese population. Arthritis and Rheumatism 2009; 60: 3263–3268.

10.

Cotte

Von Ahsen

Kruse

. ABC-transporter gene-polymorphisms are potential pharmacogenetic markers for mitoxantrone response in multiple sclerosis. Brain 2009; 132: 2517–2530.

11.

Chan

Xie

. Plasma selenium, manganese superoxide dismutase, and intermediate- or high-risk prostate cancer. J Clin Oncol 2009; 27: 3577–3583.

12.

Agresti

. Categorical data analysis, 2nd ed. New York: John Wiley, 2002.

13.

Freidlin

Zheng

Gastwirth

. Trend tests for case-control studies of genetic markers: power, sample size and robustness. Hum Heredity 2002; 53: 146–152.

14.

Chapman

Nam

. Asymptotic power of chi square tests for linear trends in proportions. Biometrics 1968; 24(2): 315–327.

15.

Slager

Schaid

. Case-control studies of genetic markers: power and sample size approximations for Armitages test for trend. Hum Heredity 2001; 52: 149–153.

16.

Guedj

Della-Chiesa

Picard

Nuel

. Computing power in case-control association studies nthrough the use of quadratic approximations: application to meta-statistics. Ann Hum Geneti 2006; 71: 262–270.

17.

Zheng

Gastwirth

. On estimation of the variance in Cochran–Armitage trend tests for genetic association using case-control studies. Stat Med 2006; 25: 3150–3159.

18.

Ahn

Haynes

Kim

St W

Fleur

Gordon

Finch

. The effects of SNP genotyping errors on the power of the cochran–armitage linear trend test for case/control association studies. Ann Hum Genet 2006; 71: 249–261.

19.

Ahn

Gordon

Finch

. Increase of rejection rate in case-control studies with the differential genotyping error rates. Stat Appl Genet Mol Biol 2009; 8(1): Article 25.

20.

Marquard

Beckmann

Heid

Lamina

Chang-Claude

. Impact of genotyping errors on the type I error rate and the power of haplotype-based association methods. BMC Genet 2000; 10: 3–3.

21.

Yamada

Kinukawa

Nakamura

Nose

. 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 Biomed 2009; 96(1): 42–48.

22.

Freudenheim

Johnson

Wardrop

. Nutrient misclassification: bias in the odds ratio and loss of power in the Mantel test for trend. Inte J Epidemiol 1989; 18: 232–238.

23.

Brenner

. Notes on the assessment of trend in the presence of nondifferential exposure misclassification. Epidemiology 1992; 5: 420–427.

24.

Levois

Switzer

. Differential exposure misclassification in case-control studies of environmental tobacco smoke and lung cancer. J Clin Epidemiol 1998; 51: 37–54.

25.

Delpizzo

Salzberg

. 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. Bioelectromagnetics 1992; 13(5): 363–378.

26.

Williams

. Trend tests for counts and proportions. Encyclopedia of Biostatistics, New York: John Wiley, 2005.

27.

Armitage

Berry

. Statistical methods in medical research, 3rd ed. Boston, MA: Blackwell, 1994.

28.

Sasieni

. From genotypes to genes: doubling the sample size. Biometrics 1997; 53: 1253–1261.

29.

Gustafson

. Comparing the effects of continuous and discrete covariate mismeasurement, with emphasis on the dichotomization of mismeasured predictors. Biometrics 2002; 58: 878–887.

30.

Kuha

Skinner

Palmgren

Misclassification errors. In: Armitage

Colton

(eds). Encyclopedia of biostatistics 2009; Vol. 4, Chichester: John Wiley and Sons, pp. 2615–2621.

31.

Buonaccorsi

. Measurement Error: models, methods and applications, London: Chapman & Hall, 2010.

32.

Zhang

Tian

. The impact of diagnostic error on testing genetic association in case-control studies. Stat Med 2005; 24: 869–882.

33.

Graybill

. Theory and application of the general linear model, Scituate, MA: Duxbury, 1976.

34.

Gordon

Haynes

Yang

Kramer

Finch

. Linear trend tests for case-control genetic association that incorporate random phenotype and genotype misclassification error. Genet Epidemiol 2009; 31: 853–870.

35.

Borchers

Brown

McLellan

Bekmetjev

Tintley

. Incorporating duplicate genotype data into linear trend tests of genetic association: methods and cost-effectiveness. Stat Appl Genet Mol Biol 2009; 8(1): Article 24.

36.

Johnson

Kotz

. Discrete distribution, Boston, MA: Houghton-Miflin, 1969.