Computer optional: Refer to the previous problem. Download the African buffalo BTB data set from the book website. Focus on the variable survival of those individuals who became infected with BTB in the anthelmintic-treated and control buffalo.

a. Draw a Kaplan–Meier curve to visualize survival of BTB-infected buffalo in the anthelmintic-treated and control buffalo. Include 95% confidence intervals for the probability of survival.

b. Estimate the hazard ratio of treated buffalo relative to untreated buffalo.

c. Carry out a formal test of the null hypothesis of no difference in survival curves of treated and untreated BTB-infected buffalo.

Data from previous problem

Infection by parasitic worms such as helminths can affect the immune response in ways that increase the susceptibility of hosts to infection by bacteria and viruses. Hence, treatment against helminths represents one way to combat microbial diseases. Ezenwa and Jolles (2015) investigated the effect of anthelmintic treatment on the acquisition of bovine tuberculosis (BTB) in a wild population of African buffalo and the effects on buffalo survival. The graph below shows Kaplan–Meier survival curves for the time to infection by BTB in treated and untreated (control) buffalo. Vertical ticks are censored observations. Confidence intervals for proportion uninfected are not shown, but they fully overlap between the two groups. The observed and expected number of infected individuals are shown below. Expected values are calculated under the null hypothesis of no difference in survival curves between groups.

Transcribed Image Text:

Treatment Anthelmintic Anthelmintic Control Control nn 100100 101101 Observed infected 3333 3636 Expected infected 32.8832.88 36.1236.12