Question

trail arm	number randomized	death
placebo	624	67
Cephalexin	615	49

A standard model specification is that the number of deaths in each arm may be regarded as an independent binomially distributed random variable:

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Answer #1

The likelihood function for π1,M2 is the following: y2 Then the likelihood ratio for θ is T1 ,T2 ER nax Now in order to find the maximum for numerator and denominator, we need to find the MLE for π, and (n, π2). Let π, and (π.π2) be the corresponding MLEs. Then log →dekh log π + (ni-vi ) log (1-π) +92 log π + (n2-ya) log (1-7)--0 TL Sirniarly for (πι, π2), we get (πι, π2) (n1, n2 ). În our case, π,-67624 ,加= 49/615 , π (67+49)/(624 + 615)-11671239. Hence our likelihood ratio obtained from the sample would be: A(0)-0.245 Now we know that-2 log λ(θ) ~ χ . Hence the p-value for the test is PG -2 log 0.245) = P(X < 2.813) = 0.91.

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Answer 1

The likelihood function for π1,M2 is the following: y2 Then the likelihood ratio for θ is T1 ,T2 ER nax Now in order to find the maximum for numerator and denominator, we need to find the MLE for π, and (n, π2). Let π, and (π.π2) be the corresponding MLEs. Then log →dekh log π + (ni-vi ) log (1-π) +92 log π + (n2-ya) log (1-7)--0 TL Sirniarly for (πι, π2), we get (πι, π2) (n1, n2 ). În our case, π,-67624 ,加= 49/615 , π (67+49)/(624 + 615)-11671239. Hence our likelihood ratio obtained from the sample would be: A(0)-0.245 Now we know that-2 log λ(θ) ~ χ . Hence the p-value for the test is PG -2 log 0.245) = P(X < 2.813) = 0.91.