In a randomized one-year trial of 100 elm trees with Dutch Elm Disease, 50 are slated to receive only a fungicide treatment (we will call this Group A), and the other 50 are slated to receive the fungicide treatment and an additional insecticide treatment six months later (we will call this Group B). Assume that the insecticide treatment is ineffective in curing Dutch Elm Disease, so on average, the same proportion of trees in each group will die of the disease. In Group B, 5 of the 50 trees die in the six-month period leading up to the insecticide treatment. Of the 45 trees left, 5 die in the six months following the insecticide treatment. Since we know the insecticide treatment is ineffective, the trees in Group A will, on average, suffer the same fate as those in Group B, with 5 trees dying in the first six months and another 5 dying in the second six months.

a. For Group A, what is the rate of death due to Dutch Elm Disease? 

b. If we limit the analysis in Group B to only those trees which received the insecticide treatment, what is the rate of death due to Dutch Elm Disease?

c. What do your answers to parts a and b suggest regarding the reduction in deaths from Dutch Elm Disease due to the addition of the insecticide treatment?
d. Knowing what you do about the effectiveness of the insecticide treatment, what is the problem with this analysis? How would applying the intention-to-treat method verify your answer?