Continuous-time, multi-state Markov models CDK inhibitors in clinical trials were applied to the status data on HPV detection, VL and CD4 cell count. The following four states

were defined for the VL model (Fig. 1a) to describe the high-risk HPV detection and clearance rates with time-varying VL: 1 = none of the high-risk HPV types (HPV negative) and HIV VL >400 copies/mL; 2 = at least one of the high-risk HPV types detected (HPV positive) and VL > 400 copies/mL; 3 = HPV negative and VL ≤ 400 copies/mL, and 4 = HPV positive and VL ≤ 400 copies/mL. A multi-state model describes a process where an individual is in one of the specified states at any time. An individual’s status at any time can be categorized as one of the four states above, and changes in the state can be followed. The choice of 400 copies/mL was based on the lower limit of quantification of the Roche assay at the time of A5029. To illustrate the assumed state structure, suppose a woman begins in state 1. She may acquire HPV without improvement of VL (transition to state

2), or she may remain HPV negative with improvement find more of VL (transition to state 3). State 4 may be reached from state 1 via state 2 (change in HPV status first) or state 3 (change in VL first), but not directly from state 1; that is, we assume that simultaneous changes in HPV status and VL do not occur biologically. (However, pheromone state 4 may be observed after state 1 in the previous visit.) From state 2, the woman may clear HPV and return to state 1, or she may retain HPV and transition to state 4 with decreased VL. From state 3, she may acquire HPV while

maintaining VL status (transition to state 4), or her VL may increase while she remains HPV negative (transition to state 1). From state 4, she may clear HPV and transition to state 3, or remain HPV positive while her VL increases (transition to state 2). She may also remain in any of the states for the remainder of the study. The analysis methods of Kalbfleisch and Lawless [12] were applied to account for the lack of exact times of HPV detection and clearance. The methods also account for differences in visit times, numbers of visits and initial states among the study participants. The transition rates, or cause-specific hazard rates, are denoted by λs in Figure 1. For instance, λ12 represents the hazard rate for acquiring HPV when VL remains >400 copies/mL and λ34 represents the rate when VL remains ≤400 copies/mL. For HPV clearance rates, λ21 represents the rate for clearing HPV when VL remains >400 copies/mL, and λ43 represents the rate for clearing HPV when VL remains ≤400 copies/mL. To describe the changes in HIV-related status, λ13 represents the rate from VL > 400 to ≤ 400 copies/mL without HPV, and λ24 that with HPV.