As in Section 1.3, represent the observed failure times in a sample of size no from a homogeneous population with survivor function F{t). Suppose that dj items fail at tj and that n; items are at risk at tj.
the constrained estimate is not unique for t(b) Show that the log-likelihood ratio statistic for the hypothesis F(b) = c can be written
) Thomas and Grunkemeier (1975) show that the usual asymptotic properties apply and that -2R is asymptotically χ$ under the hypothesis. Use this result to establish a 95% confidence interval for F(b). Compare these results with those obtained in Section 1.3 for the carcinogenesis data (Table 1.1) with b = 150