Discrete-time observations of Streptococcus pneumoniae colonisation analysis and design under continuous-time Markov models

by Juha Mehtälä

Institution: University of Helsinki
Department: Department of Mathematics and Statistics; Department of Vaccination and Immune Protection, National Institute for Health and Welfare
Year: 2015
Keywords: tilastotiede
Record ID: 1132217
Full text PDF: http://hdl.handle.net/10138/154701


Continuous-time Markov processes with a finite state space can be used to model countless real world phenomena. Therefore, researchers often encounter the problem of estimating the transition rates that govern the dynamics of such processes. Ideally, the estimation of transition rates would be based on observed transition times between the states in the model, i.e., on continuous-time observation of the process. However, in many practical applications only the current status of the process can be observed on a pre-defined set of time points (discrete-time observations). The estimation of transition rates is considerably more challenging when based on discrete-time data as compared to continuous observation. The difficulty arises from missing data due to the unknown evolution of the process between the actual observation times. To be able to estimate the rates reliably, additional constraints on how they vary in time will usually be necessary. A real world application considered in this thesis involves the asymptomatic carriage state (colonisation) with the bacterium \textit{Streptococcus pneumoniae} (the pneumococcus). The pneumococcus has over 90 strains and for understanding the dynamics of the pneumococcus among humans it is important to understand within-host competition between these strains. Research questions regarding competition in this thesis are: does colonisation by one serotype protect from acquisition of other serotypes and is clearance affected by concurrent colonisation by other serotypes? A question regarding the implication of competition to pneumococcal dynamics after vaccination is also of interest. In addition, vaccine protection may be heterogeneous across individuals, leading to a question about how well such vaccine protection can be estimated from discrete-time data. When only discrete-time observations are available, the decision when to measure the current status of the process is particularly important. With measurements that are temporally apart from each other, information about the state of the process at one point does not give information about the state at the other points. When measurements are very close to each other, knowing the state at one point bears information about the state at other, temporally close points. This thesis addresses the estimation of transition rates based on repeated observations of the current status of an underlying continuous-time Markov process. Applications to actual data concern the process of pneumococcal colonisation. Optimal study designs are considered for improved future studies of similar type, applications including but not limited to pneumococcal colonisation studies. Pneumokokki on bakteeri joka elää oireettomana ja suhteellisen yleisenä ihmisen nenänielussa. Joskus tällainen nenänielun kantajuus etenee taudiksi, kun pneumokokki leviää esimerkiksi korvaan tai keuhkoihin. Sekä kantajuus että tauti ovat erityisen yleisiä lapsilla ja tässä ryhmässä pneumokki onkin vakava terveydellinen taakka maailmanlaajuisesti. Pneumokki ei ole yksi…