Question

Please answer all parts. I am sorry image is upside down

betic patients? Simulated rosiglitazone 1.70 Heart transplants. The Stanford University Heart Transplant Study ws pach patient conducted to t Study w determine whether an experimental heart transplant program increased entering the program was designated an official heart transplant candidate, mean gravely ill and would most likely benefit from a new heart. Some patients go some did not. The variable transplant indicates which group the patients were treatment group got a transplant and those in the control group did not. Another survived was used to indicate whether or not the patient was alive at the ena the 34 patients in the control group, 30 died. Of the 69 people in the treatment group lifespan.that he ing that he was t a transp a transplant andd tients in the able called of the study. Of vari 74 45 died. control treatment alive 1500 1000 dead control treatment (a) Based on the mosaic plot, is survival independent of whether or not the patient got a trans- plant? Explain your reasoning (See the next page for additional parts to this question.) 74B. Turnbull et al. "Survivorship of Heart Transplant Data". In: Journal of the A Association 69 (1974), pp. 74-80.

Answer 1

a) No. The treatment group has much higher survival rate.

b) On average, it increases length of survival, but by how much is highly variable.

c) Proportion who died by treatment:

control = 30/34 = 88.2%;

treatment = 45/69 = 65.2%

d)

(i) Null hypotheses H0: We start with a null hypothesis that represents the status quo.

Alternative hypotheses Ha: We also have an alternative hypothesis that represents our research question.

(ii) We write alive on 28 cards representing patients who were alive at the end of the study, and dead on 75 cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size 69 representing treatment, and another group of size 34 representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment - control) and record this value. We repeat this 100 times to build a distribution centered at 45/69−30/34=−0.230179. If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative.

(iii) Based on the 100 simulations, we can conclude as follows:

We conclude that the study results do provide strong evidence against the NULL hypothesis. That is, we do have sufficiently strong evidence to conclude the heart transplant was a success since the difference in between the 100 simulations is centered near zero.

We conclude that the evidence is sufficiently strong to reject H0 and assert that there was a success survival rate due to heart transplant. When we conduct formal studies, usually we reject the notion that we just happened to observe a rare event 0.50 So in this case, we reject the independence model in favor of the alternative. That is, we are concluding the data provide strong evidence of survival due to hearth transplant.