, Contract HD33345; Washington University in St Louis, CTU Grant AI69495; Beth Israel Medical

Center, CTU Grant AI46370; Vanderbilt University, CTU Grant AI69439; University of Hawaii at Manoa, CTU Grant AI34853; University of Maryland selleck kinase inhibitor Medical Center, Division of Pediatric Immunology & Rheumatology; Mt. Sinai Hospital Medical Center, Women’s & Children’s HIV Program, Los Angeles County/University of Southern California Pediatric AIDS Clinical Trials Unit/Maternal-Child-Adolescent HIV Center, NICHD Contract HD33345, Westat Subcontract Grant 7735-S042 and GCRC Grant RR000043; University of Washington, CTU Grants AI27664 and AI69434; University of North Carolina at Chapel Hill, CTU Grant AI69423-01, CFAR Grant AI50410 and GCRC Grant RR00046; University of Florida/Jacksonville, NIHCD Contract HD33345. Let p jk(s,t) represent the probability that an individual in state j at time s is in state k at

time t, where j,k = 1,2,3,4 and s ≤ t. As the process is assumed to be time-homogeneous, p jk(s,t) = p jk(0,t – s). The intensity function for transition from state j to state k, or cause-specific hazard at time t, Venetoclax research buy is denoted by λij and defined as Let P(s,t) and Λ denote the 4 × 4 matrices of transition probabilities and intensities, respectively, where Bay 11-7085 the jth diagonal element (λjj) is the negative of the rate of leaving state j: The relationship between the transition probabilities and the transition rates is given by The time that the process stays in a state before

making a transition to a different state is exponentially distributed, with the mean sojourn time in state j given by –1/λjj. The transition intensity matrix for the model in Figure 1 is given by (1) where λ12 = θ1, λ13 = θ2, λ21 = θ3, λ24 = θ4, λ31 = θ5, λ34 = θ6, λ42 = θ7 and λ43 = θ8. The likelihood function for θ = (θ1, … ,θ8) is given by where the Markov process is observed intermittently at times , i = 1, … , n individuals, each with m i observations. Kalbfleisch and Lawless provide a scoring procedure to obtain the maximum likelihood estimate (MLE) for θ and an estimate of its asymptotic covariance matrix.