Using phase type distributions for modelling HIV disease progression

Abstract

Disease progression models are useful tools for gaining a systems' understanding of the transitions to disease states, and characterizing the relationship between disease progress and factors affecting it such as patients' profile, treatment and the HIV diagnosis stage. Patients are classified into four states (based on CD4+ T-lymphocyte count) and all the transitions are allowed. Examinations to identify disease progression of the patient are carried out routinely throughout the follow-up period. Therefore, the times spent at the various HIV infection stages are interval censored or right censored. This makes difficult to use simple statistical methods such as regression to model the disease progression and its relationship with the diagnosis stage. We present a novel, more intuitive and realistic approach based on phase type distributions to model progression of HIV infection and the effects and prognostic significance of HIV diagnosis stage. The approach is illustrated using a real database of total 2,092 HIV infected patients enrolled in the Italian public structures from January 1996 to January 2008. The approach can also be used to examine the effect of other covariates such as patient's profile

An Analytics‐Driven Approach for Optimal Individualized Diabetes Screening

“…Markov decision processes (MDPs) and POMDPs are the methodological tools of choice for sequential decision‐making problems in healthcare, especially for chronic diseases such as diabetes (e.g., Hoerger et al., 2004, Santoso and Mareels 2001, Shih et al., 2007), HIV/AIDS (e.g., Garg et al., 2012, Lee et al., 2014, Shechter et al., 2008), and cancer (e.g., Ahsen and Burnside 2018, Ayer et al., 2012, Chhatwal et al., 2010, Maillart et al., 2008, Nohdurft et al., 2017, Petousis et al., 2019, Zhang et al., 2012a). MDPs and POMDPs have also been employed to obtain optimal policies in other settings, such as to design therapeutic regimens for hypertension (Zargoush et al., 2018), develop personalized treatments (Ibrahim et al., 2016), and address emergency room congestion (Patrick 2011).…”

“…The model assumes that the Markov property (approximately) holds, that is, the transition to future health states can be approximated using only the current state and current actions. This assumption is quite popular in the healthcare operations literature that model disease progression (Ahsen and Burnside 2018, Garg et al., 2012, Hoerger et al., 2004, Lee et al., 2014, Santoso and Mareels 2001, Shechter et al., 2008, Shih et al., 2007).…”

Applications of phase type survival trees in HIV disease progression modelling

“…The analysis of healthcare systems is an important application area where PHD can be applied since in this area PHD is used to describe the time that patients stay in hospitals or to describe infection models, where in the latter PHD models the duration of different phases of an infection [6,9]. However, PHD models are very flexible and as a consequence huge effort to find the parameters is needed so that the resulting model approximates closely the required or observed behavior.…”

“…C-PHD is a special type of PHD where entry can only occur to the first state, i.e. a patient can only enter the system in the first state and only sequential transitions can take place, as shown in Figure 1 which was obtained from [9], with a transition rate λk from any state k to the next state k+1. A transition from any state k to the absorbing state n+1 is also possible with a transition rate µk where the absorbing state represents the death of a person [10].…”

“…In [9], the authors use PTSTs to evaluate the effect that the HIV diagnosis (HD) stage has, using the akaike information criterion (AIC). From this study, it was analysed that after clustering the data with respect to the HD stage there was a significant improvement in AIC and hence the HD stage affects the LOS that a patient spends in an HIV infection (HI) stage.…”