Web - based Supplementary Materials for “ A joint model for multistate disease processes and random informative observation times , with applications to electronic medical records data ”

We use the abbreviation x1:k for x1, . . . , xk, o1:k for o1, . . . ok, h1:k for h1, . . . , hk. The sequence of DDO times up to observation time tk is denoted τ (1, k) = {ti : hi = 1, i = 1, . . . , k}. Forward functions are defined as αtk(u) = P [o1:k, τ (1, k),h1:k, Xk = u] and backward functions as βtk(u) = P[ok+1:n, τ (k + 1, n),hk+1:n|Xk = u]. The forward function is initialized with αt1(u) = P(O1 = o1, X1 = u,H1 = h1) = e(u, o1)νh1πx1(h1), and the recursion for k = 2, . . . , n− 1 is