Exact Cochran–Armitage trend tests: comparisons under different models

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

Acknowledgement

An earlier version of this paper has greatly benefited from constructive comments of a referee and Associate Editor. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CUHK4371/04M).