data analysis for a partial two-by-two factorial design

Question

I need to analyze data generated from a partial two-by-two factorial design: two levels for drug A (yes, no), two levels for drug B (yes, no); however, data points are available only for three groups, no drugA/no drugB, yes drugA/no drugB, yes drugA/yes drug B, omitting the fourth group of no drugA/yes drugB. I think we can not investigate interaction between drug A and drug B, can I still run model using R as usual: response variable = drug A + drug B? if yes, how to explain coefficients for drug A and drug B?

Thank you very much!

Yuan Chun Ding

Answer 1

You would not be able to assess the effect on "response" from drug A alone but you would be able to assess the incremental effect of drug A+drug B (versus no drug) when compared to drug B alone (versus no drug). (So you would have half of an assessment of an "interaction".) Any further commentary would require that you better describe your data situation. Do you have measurements taken before and after drug or placebo were administered? Were these measurements perhaps taken in replicates? What is known about the reliability of the measurements of "response"?

As far as coding a model, I don't think you would use:

response variable = drug A + drug B

Rather I think you would form three categories for a single variable: baseline: 'no drugA/no drugB', DrugA_alone: 'yes drugA/no drugB', and combA_B: 'yes drugA/yes drug B'