One misconception that some students initially have about survival analysis methods is that they can be applied only to survival data that contain some censored observations. While survival analysis methods are appropriate for incomplete data, they are also perfectly acceptable for noncensored survival data. Earlier we noted that the empirical survival function and Kaplan- Meier estimator are identical when there are no censored event times. The data set Fruitfly, introduced by Partridge and Farquhar and further analyzed by Hanley and Hanley and Shapiro, 20 was originally analyzed for the purpose of investigating the relationship between increased sexual activity of male fruitflies and longevity of life (in days) using regression and analysis of covariance techniques. However, survival analysis methods can also be used to study the life durations of male and female fruit flies. Brief descriptions of the variables are provided below:
Partners: number of companions (0, 1, or 8)
Type: type of companion (0 = newly pregnant female, 1 = virgin female, 9 = not applicable (when Partners = 0))
Longevity: lifespan, in days (This is the time- to- event variable.)
Thorax: length of thorax in mm
Sleep: percentage of each day spent sleeping
Censor: censoring status (This variable takes only value 1, since the data are all complete. A censoring status variable is necessary for software implementation.)
a. Construct the Kaplan- Meier curve with a confidence interval for the Fruitfly data and describe the survival pattern for the fruitflies over time. Use Longevity as the time-to-event variable.
b. Construct the Kaplan- Meier curves for the lifetimes of the fruitflies by number of partners, using Partners as the grouping variable. Briefly comment on the observed relationship between survival and number of female partners.
c. Perform the log- rank and Wilcoxon tests. Report the test statistics and p- values for both tests. State the conclusions for both tests. If the tests yield different conclusions, briefly explain why.