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16.12 The Clark et al. [1971] heart transplant data were collected as follows. People with (a) Is the survival of the nontransplanted patients a reasonable estimate of the non- failing hearts waited for a donor heart to become available; this usually occurred operative survival of candidates for heart transplant? Why or why not? within 90 days. However, some patients died before a donor heart became available. Figure 16.19 plots the survival curves of (1) those not transplanted (indicated by circles) (b) Would you be willing to conclude from the figure (assuming a statistically signif and (2) the transplant patients from time of surgery (indicated by the triangles). icant result) that 1960s heart transplant surgery prolonged life? Why or why not? (c) Consider a Cox model fitted with transplantation as a time-dependent covariate: 100 hi(t) = ho(t)exp(a+BxTRANSPLANT(1)) O = NON-TRANSPLANT PATIENT (2) 80 A . TRANSPLANT PATIENT (20) The estimate of B is 0.13, with a 95% confidence interval (-0.46, 0.72). (Verify this if you have access to suitable software.) What is the interpretation of this estimate? What would you conclude about whether 1960s-style heart transplant 60 surgery prolongs life? (d) A later, expanded version of the Stanford heart transplant data includes the age % SURVIVING 40 of the participant and the year of the transplant (from 1967 to 1973). Adding these variables gives the following coefficients: 20 Variable B SE(B) p-value 12 16 17 18 19 20 21 Transplant -0.030 0.318 0.92 TIME IN MONTHS Age 0.027 0.014 0.06 Clark at al. . Prognosis of Cardiac Transplant Candidates Year -0.179 0.070 0.01 Figure 16.19 Survival calculated by the life table method. Survival for transplanted patients is calculated from the time of operation; survival of nontransplanted patients is calculated from the time of selection for transplantation. What would you conclude from these results, and why