Question

3. Two drugs are compared to see which of them is more likely to produce unpleasant side effects. Each of 100 subjects is given the two drugs on different occasions. The results are tabulated below Nausea with drug B 38 10 No nausea with B Nausea with drug A No nausea with A 50 Let pij denote the probabilities that a patient has a response in the ijth cell. For instance p12 denotes the probability that a patient experiences nausea with drug A but does not experience nausea with drug B The question of interest is whether there is evidence of a real difference between the drugs. (a) The null hypothesis can be expressed as: The probability that a patient experiences nausea using drug A equals the probability that a patient experiences nausea using drug B. Express this hypothesis in terms of the p (b) Obtain the maximized log likelihood under the full model for the data that places no restrictions on the P . You can use any results that you know about likelihoods and MLEs for multinomial data c) Obtain the result of a likelihood ratio test of the hypothesis in (a). You can use any results that you know about likelihoods and MLEs for ltinomial data

Although the sample sizes are not large for some of the examples below, you can use chi-square ap- proximations to calculate p-values for the likelihood ratio tests.

Answer 1

Answer:

a)

Design is completely randomized since it focuses on only the treatment (two different drugs) effects making it a single-factor experiment. The allotment of subjects is randomized.

b)

Design is matched pairs because by choosing each pair having the same value of the PCF, the effect of PCF, if any, is the same for both members of the pair and hence can be considered as identical entities. Consequently, the difference in the response variable for each pair becomes the statistic of concern.

c)

Design does not fit into any of the listed designs.

Clearly Design 2 is the best of the lot in terms of experimental error minimization. It recognizes the existence of PCF and also takes due care of that. The effect of PCF, if any, is nullified by pairing. Random assignment minimizes bias.