Generalized Linear Stochastic Process with Applications to Infectious Diseases
Date Issued
2014
Date
2014
Author(s)
Hsu, Chen-Yang
Abstract
Background
Modelling the transmission of infectious disease for acute infectious disease and the subsequent progression to the manifestation of disease for chronic infectious disease is fraught with a series of thorny issues. Correlated property and unobserved heterogeneity are implicated in the transmission of infectious disease. The progression from susceptible to latent infection and clinical disease regarding chronic infectious disease has involved with multi-state transition and hence the multiple categorical outcomes. The joint effect of covariates further complicated these issues. It is of great interest to provide a unified but preliminary framework to solve these problems. The generalized stochastic process provides a feasible statistical tool to reduce the dimension on modelling such a correlated sequence and also accommodate above statistical issues.
Methods and applications
Methods
A two-state Markov model with discrete time was first developed to model the observed binary sequences. Based on the Markov model, a subject remaining in the state of susceptible before he/she first enters the state of infective is expressed as a geometric form and negative binomial form as expressed in the conventional chain binomial model. The proposed two-state Markov model was then extended to multistate discrete-time Markov model. The generalized stochastic model in continuous time was also developed by using the general form for the specification of the intensity matrix with Kolmogorov differential equation. A variety of distributions including exponential distribution for the homogenous rate of transition and the Weibull and the lognormal distribution for the non-homogenous rate on disease progression were applied. The developed methodology also incorporated the effect of covariates using appropriate link function and that of measurement error
Applications
The proposed generalized liner stochastic model with two-state Markov underpinning was first applied to data on surveillance of influenza incorporating the effect of age, sex, and vaccination status making allowance for the correlated structure by using random intercept and random slope parameters.
To evaluate the transition between susceptible, LTBI, and tuberculosis (TB) the generalized stochastic process was extended to three states. Continuous-time Markov models with homogenous and non-homogenous rates of transition were specified by using a variety of distributions including exponential, Weibull, and lognormal distributions. The joint effects of covariates and measurement error were also evaluated.
Results
Regarding the application of generalized linear stochastic model with two-state Markov underpinning on surveillance data of influenza in Taiwan, vaccination showed a significant protective effect in hierarchical models with random slope (OR: 0.50, 95% CI: 0.32-0.75, Reed-Frost model). The variation of vaccination across household was quantified by using random effect parameter estimated as 1.11 to 1.23.
The application of three-state Markov model to data on contact tracing project of tuberculosis in ChangHua shows consistent result of applying both continuous time and discrete time frame. The comparison between models in continuous time shows the superiority of using the non-homogenous rate of disease progression for both infection rate and conversion rate using the Weibull- lognormal distribution. By using the three-state Markov model with the Weibull distribution for annual risk for TB infection (ARTI) and the lognormal distribution for the conversion from LTBI to TB, we found hazard for ARTI is not constant and decrease with follow-up time and the highest hazard rate was noted in age group 45-64. The hazard for annual conversion rate form LTBI to TB was higher in subjects older than 65 years and shows a steep increase with time, probably due to re-activation, and becomes plateau after around 5 years for the eldest group, and show a linear increase for the young age group aged 30-64 years. The false-positive and false-negative rates in terms of disease evolution were around 5%-10% and 55%, respectively.
Conclusion
The proposed generalized linear stochastic process with the Markov underpinning demonstrated the capability of accommodating correlated data on surveillance of influenza and also multi-state disease process of chronic infectious disease such as TB. This unified framework on generalized stochastic process is very powerful for the elucidation of transmission mode for acute infectious disease but also the quantification of the rate of progression from latent infection to the manifestation of disease for chronic infectious disease. Both are of utmost important to give a clue to the containment of various types of infectious disease.
Subjects
傳染病
廣義線性模式
隨機過程
多階段馬可夫模式
流行性感冒
結核病
SDGs
Type
thesis
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