11.8 Given the small data set:Sample 1:24; 30 ; 42 ; 15 þ; 40 þ; 42 þ
Sample 2:10; 26 ; 28 ; 30 ; 41 ; 12 þcompare them using both the log-rank and generalized Wilcoxon tests.
11.9 Pneumocystis cariniipneumonia (PCP) is the most common opportu-
nistic infection in HIV-infected patients and a life-threatening disease.
Many North Americans with AIDS have one or two episodes of PCP
during the course of their HIV infection. PCP is a consideration factor
in mortality, morbidity, and expense; and recurrences are common. In
the data set given in Table E11.9 at the end of this chapter, we have:
Treatments, coded as A and B
Patient characteristics: baseline CD4 count, gender (1, male; 0, fe-
male), race (1, white; 2, black; 3, other), weight (lb), homosexuality
(1, yes; 0, no)
PCP recurrence indicator (1, yes; 0, no), PDATE or time to recur-
rence (months)
DIE or survival indicator (1, yes; 0, no), DDATE or time to death (or
to date last seen for survivors; months)
Consider each of these endpoints: relapse (treating death as censor-
ing), death (treating relapse as censoring), and death or relapse (which-
ever comes first). For each endpoint:
(a)Estimate the survival function for homosexual white men.
(b)Estimate the survival functions for each treatment.
(c)Compare the two treatments; do they di¤er in the short and long
terms?
(d)Compare men and women.
(e)Taken collectively, do the covariates contribute significantly to
prediction of survival?
(f)Fit the multiple regression model to obtain estimates of individual
regression coe‰cients and their standard errors. Draw conclusions
concerning the conditional contribution of each factor.
(g)Within the context of the multiple regression model in part (b),
does treatment alter the e¤ect of CD4?
(h)Focus on treatment as the primary factor, taken collectively; was
this main e¤ect altered by any other covariates?
(i) Within the context of the multiple regression model in part (b), is
the e¤ect of CD4 linear?
(j)Do treatment and CD4, individually, fit the proportional hazards
model?
(Note: A Web-based electronic copy is available upon request.)428 ANALYSIS OF SURVIVAL DATA