For the log-transformed confidence interval for H(t), Us depends on which quantity(s)?

• A. The coefficient of variation of H(t) and the standard normal quantile
• B. H(t) itself
• C. S(t)
• D. d_j / r_j

Answer: (A)

The main idea is that when you form a confidence interval for H(t) on the log scale, you use a normal approximation for log H(t). The width of that interval on the log scale depends on how variable H(t) is relative to its size, i.e., the coefficient of variation of H(t), and on the chosen confidence level through the standard normal quantile. Concretely, the half-width on the log scale is z times the coefficient of variation of H(t). After back-transforming, the interval endpoints involve H(t) multiplied by an exponential of that same half-width, but the determination of the width itself relies only on the coefficient of variation and the normal quantile. So Us depends on cv(H(t)) and the standard normal quantile.

In contrast, the actual value of H(t) itself affects the center of the interval but not the width on the log scale; S(t) and d_j / r_j do not enter into this log-transformed width.