The longitudinal studies of HPV infection are important for determining the covariates and outcomes associated with HPV persistence, which leads to the development of cancer. Traditionally, the rate of HPV clearance are usually compared in HIV-1-positive patient subgroups based on baseline CD4 counts (such as <200, 200–500, and >500 cells/mm3
) using Kaplan-Meier curves and Cox proportional hazards models 
. The new method developed in this study is based on the logistic-type model and allows for prediction of future HPV status, conditional on its current status and the measurements of factors that are potential predictors of an HPV clearance event; i.e., CD4 count was considered to be a main predictor with HIV-1 VL and HAART (with PI) as additional predictors. The model parameters were estimated by maximizing the likelihood function constructed as the product over transfers with known HPV statuses (measured every 6 months) and HIV-1-related covariates (measured every 3 months). Similar to Kong et al. 
, our methodology is based on conditional probabilities that take into account multiple correlations between individual outcomes measured longitudinally. However, the developed method extends the opportunities of approaches by Kong as well as several other researchers 
by reconstructing between-the-measurements HPV statuses (i.e., presence or absence of HPV infection). This approach allows for inclusion of the whole longitudinal dataset, thus increasing the accuracy of prediction of probability of HPV clearance without making multiple assumptions about how the time of incidence, clearance, and censoring events could be reconstructed (as it is required for Kaplan-Meier and Cox analyses). The shorter intervals accessible in our method allow for taking into account the dynamics of potential predictors, which could change quickly (such as CD4 count, HIV-1 VL, and HAART regimen). This model allows for calculating the clearance probability with subsequent confirmation in another 3 months—
—by transferring the probabilities such as
, thus corresponding to the routine definition of HPV clearance when the absence of HPV type-specific infection is required for two subsequent visits. Opposite to the Cox model, in which HRs are estimated for time-dependent covariates, the developed approach allows us to estimate the transition probability and evaluate its standard errors. Since the developed model provides the hazard function for probability of HPV infection clearance, the respective survival function and characteristics of time-to-clearance distribution also can be evaluated: e.g., time to clearance (in months) could be estimated as
, and a median of HPV clearance time as
. The approaches utilizing the generalized estimating equation (GEE)—they take into account the mutual correlations in clearance of different HPV types and modeling mixed effects, allowing individuals to have their own characteristics (i.e., distributed in a population)—could be used to further enrich the developed base model; Xue et al. 
recently reviewed the series of approaches that can be used for similar generalizations.
In both approaches, a transitional probability-based model and Cox regression model, CD4 count was a significant predictor of clearance of all phylogenetic HPV groups in HIV-1-infected adolescent females; also, certain effects of HAART (with PI) on clearance of HPV16/16-like and HPV18/18-like infections were observed. However, while in the Cox model, being HIV-1-infected had a minor effect only on HPV56/56-like clearance, in the transitional probability model, this factor was a significant predictor of clearance of HPV16/16-like, HPV56/56-like, and low-risk HPVs.
In immunodeficient patients, the mechanisms by which immune deficiency increases the risk of persistence of HPV infection are still poorly understood: some alterations in dendritic antigen-presenting cells, Langerhans cells, and macrophages function, as well as a deficient cytotoxic lymphocyte response to E6 and E7 proteins, might be the contributing factors 
. The results obtained from our study about the role of CD4 in HPV clearance corroborate previous reports from the REACH cohort, as well as several other studies on adult HIV-infected females 
. However, there is no agreement about the role CD4 play in clearance of individual types of HPVs; e.g., in several studies on both HIV-1-negative and HIV-1-positive females, it has been shown that HPV16 infection has a lower probability of clearance than other HPV types, possibly due to its greater ability to escape immunologic surveillance 
, while other studies did not demonstrate such a difference 
. In our study, a lower clearance probability was registered for the HPV16/16-like than for the 18/18-like group, while HPV16 had an equal-with-HPV18 chance to be cleared at both pathologic and normal CD4 counts. The observed heterogeneity of phylogenetic groups of HPV infection in terms of a probability of HPV clearance may depend not only on CD4 counts and other predictors measured at current time (such as HIV-1 VL and HAART with PI), but also from the history of HPV type-specific infection (e.g., from the time since HPV acquisition, which is an unobserved variable), depending on a prevalent or incident type-specific HPV infection. Further analysis could be performed using non-Markov approaches to model unobserved time since HPV acquisition.
HIV infection, independent of CD4 count, has also been suggested to be a predictor of persistence of HPV infection in HIV-1-positive women. This may imply an alternate mechanism besides CD4, e.g., via alteration of the cytokine response to HPV infection in the cervical mucus 
. In our study, being HIV-1-positive affected the probability of clearance of HPV16/16-like, 18/18-like, and low-risk HPVs. In the REACH cohort–based study by Moscicki et al. 
, when only subjects with normal CD4 counts (i.e., ≥500 cells/mm3
) were considered, the multivariable regression showed high significance of HIV status as an independent predictor of HPV clearance event (HR
Currently, prognostic importance of high HIV-1 VL for HPV clearance is not clear, but it likely increases the risk of persistence of HPV infection at low CD4 cell counts 
. In our study, HIV-1 VL could affect the clearance of low-risk HPVs and certain oncogenic HPVs (e.g., HPV58 and HPV59). The apparent impact of HAART on HPV incidence, clearance, and persistence also is not clear 
. In our study, when HAART was analyzed taking into account its PI component, a significant effect was observed for HPV16, and minor effects were observed for HPV16/16-like, HPV18/18-like, and HPV59. In vitro studies have shown that specific PIs inhibit the ability of HPV16 E6 to degrade p53 and selectively kill E-6-dependent cervical carcinoma cells 
. Previous crossover analyses in REACH suggested no significant effect of HAART on HPV clearance 
; however, the effect of PI was not examined, as it is incorporated in this new method. These results require further investigation with longer follow up and more detailed analysis of HAART/PI history and dose/exposure.
The observation on C. trachomatis
increasing probability of clearance of low-risk HPV falls in with the results from animal studies about potential role of interferon-γ as local “protector” against other (i.e., non-Chlamydia
) infections 
. Oncogenic HPV types could be strong enough to avoid this mechanism; recently, it has been speculated that C. trachomatis
could have effect on oncogenic HPV types 
The results of this study have several limitations. While the prevalence and incidence of HPV infections among HIV-1-positive adolescents in the REACH study is high 
, some of the associations may have been limited by the relatively smaller sample size of HIV-1-negative individuals along with the lower HPV infection rate. Due to the populations served at the REACH recruitment sites, young African-American women were a significant proportion of the population; therefore, the results may not be fully generalized to other populations. Also, the interrelations described in this study were obtained on a cohort of young adolescent girls with relatively short histories of HIV-1 infections, who are generally healthy and whose immune response to the infection may differ from older women; for example, it has been shown in several studies that older age was associated with higher risk of HPV persistence in both HIV-infected and HIV-uninfected women 
. Regarding the approach, the simple version of the model was intentionally chosen as a base model, resulting in some limitations; e.g., there was no distinction between the effects of incident infection and re-infection, no correlations between clearance of distinct HPV types in one individual were modeled, and the time after the incidence was not explicitly represented. Due to the two-step design of the study, some variables which were statistically insignificant were not included into the second step of the analysis thus potentially compromising the robustness of the model. Nevertheless, the limitations can be overcome by the extensions of the proposed approach using approaches specifically developed for analyses of HPV clearance 
and those that were successfully used in other related research areas, e.g., g-formula 
or a (binomial) stochastic process model 
In summary, our new model estimates a probability for HPV clearance of type-specific HPV groups at a 3-month period by coordinating uneven time scales of measurements on biannual HPV status and other quarterly HIV-1-related clinical data and risk factors.