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Assuming I am running an experiment in mice with a drug treatment at different doses I have been originally thinking that a Dunnett's Test is the right analysis to perform: compare each group against the non-treatment control. However, it was mentioned here and in Harvey Motulsky's book Intuitive Biostatistics, that the fact that I have a clear order in the expected response should further narrow and drive the analysis.

I have been looking into statistical tests with a single ordinal independent variable and found the Cochran-Armitage test for trend in the DescTools R package see pdf here.

Description: Perform a Cochran Armitage test for trend in binomial proportions across the levels of a single variable. This test is appropriate only when one variable has two levels and the other variable is ordinal. The two-level variable represents the response, and the other represents an explanatory variable with ordered levels. The null hypothesis is the hypothesis of no trend, which means that the binomial proportion is the same for all levels of the explanatory variable.

I have three questions:

  1. For the case I describe here, is this a valid analysis (increasing drug dose is ordinal variable and 'difference in in comparison to control' is the two-level response)?
  2. Since I would expect my drug to decrease tumor growth (and I have no expectation or interest in an increase) would I chose "decreasing" rather than the default "two.sided"?
  3. Are there other tests that similarly account for comparisons of a single ordinal (or numerical variable) with an expected trend?
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