Exact Cochran-Armitage trend tests: comparisons under different models

Authors: Tang, Man-Lai¹; Keung Tony Ng, Hon²; Guo, Jianhua³; Chan, Wai⁴; Ping-Shing Chan, Ben⁵

Source: Journal of Statistical Computation and Simulation, Volume 76, Number 10, October 2006 , pp. 847-859(13)

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Abstract:

Exact methods for small-sample dose-response analyses with binary outcome have been rapidly developed in recent years. For exact conditional approach, nuisance parameters ( e.g . the intercept) are eliminated by conditioning on their reduced sufficient statistics ( e.g . marginal row totals for the intercept under the logit link). For exact unconditional approach, nuisance parameters, on the other hand, are eliminated by using the `worst-case' scenario. For instance, the p -value is the tail probability maximized overall possible values for the nuisance parameters. The performance of exact conditional and unconditional approaches on more general models including logit, probit, one-hit, and extreme-value are investigated here. Comparisons are conducted using the well-known Cochran-Armitage (C-A) trend test under different model specifications. Our simple empirical studies clearly show that the exact conditional approach is generally inferior to the exact unconditional approach with respect to actual significance level and exact power. When sample sizes are small or control group response probabilities are extreme ( i.e . close to 0 or 1), the exact conditional C-A trend test could be significantly conservative and less powerful than the exact unconditional C-A trend test even under the popular logit model. For moderate sample size, we also observe substantial exact power loss for the exact conditional approach under models other than logit model. We demonstrate our findings with a real data set from a toxicological study.

Keywords: Dose-response data; Exact conditional approach; Exact unconditional approach; Trend test

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10629360600569519

Affiliations: 1: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong 2: Department of Statistical Science, Southern Methodist University, Dallas, TX, USA 3: Department of Statistics, School of Mathematics and Statistics, Northeast Normal University, Chang Chun, 130024, China 4: Department of Psychology 5: Department of Statistics, The Chinese University of Hong Kong, Hong Kong

Publication date: 2006-10-01

Exact Cochran-Armitage trend tests: comparisons under different models

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