Bayesian Semiparametric Regression Analysis of Interval-Censored Data with Monotone Splines - Interval-Censored-Time-to-Event Data: Methods and Applications - page 152

interior knots m plus the degree d (Ramsay, 1988). Figure 6.1 plots the mono-
tone spline basis functions with four interior knots f0:2; 0:4; 0:6; 0:8g within
interval [0; 1] for dierent degree values. The calculation of these basis func-
tions are simple, and an R function is available upon request from the authors
of this chapter.
FIGURE 6.1: Examples of monotone spline basis functions with different
degree values. Interior knots are f0:2; 0:4; 0:6; 0:8g.
We use the exact expression (6.5) to model the cumulative baseline haz-
ard function 0 (t) under the PH model. To model the unknown function (t)
in models (6.3) and (6.4), we add an intercept 0 because there is no con-
straint on (L) for any small positive value L and (0) = 1. In specifying
the monotone splines, we recommend to use 2 or 3 for the degree to pro-
vide adequate smoothness. In terms of knots placement, one can use random
knots placement, that is, treat the number and positions of knots as random.
However, using a random knots placement leads to great computation bur-
den in deciding to add or drop a knot, or change a knot position, and for
recalculating and evaluating the basis functions whenever a change occurs. In