A New Approach to Estimating Trends in Chlamydia Incidence
A New Approach to Estimating Trends in Chlamydia Incidence
We estimated chlamydia incidence in the Australian population from 2001 to 2013 using a Bayesian statistical method based on a decision-pathway model.
The decision-pathway of this approach is a probabilistic tree to represent the branches along which people in the population can end in each calendar year as either acquiring or not acquiring chlamydia infection, developing symptoms, being tested and treated and being notified as a case. Stratified by age and sex, each individual in the population has an assigned probability of each step along the branch over the course of each year (figure 1). For some branches, the model parameters (probabilities) are strongly constrained a priori from estimates in the literature, while other parameters must be informed by fitting the model to the surveillance data of numbers of people tested and numbers diagnosed with chlamydia.
(Enlarge Image)
Figure 1.
Pathways of chlamydia infection to be notified to the National Notifiable Diseases Surveillance System. Each parameter represents the (annualised) probability of progressing over a particular step. The light grey branches/boxes represent drop-outs from the notification count, but those reaching the testing phase will (if correctly reported) nevertheless contribute to the total test count.
To follow the effects of an evolving disease burden and changes in public awareness of, and access to, relevant public health programmes, we allowed the annual infection and asymptomatic screening probabilities to vary yearly by age group and sex using a flexible, stepwise Gaussian process model, while all other input parameters were fixed in time.
Following a standard Bayesian approach, we adopted independent beta distributions for priors on the time-independent probability parameters; the two shape variables of each beta distribution were chosen so that the beta prior was closest (using the Kullback–Leibler divergence) to a triangular distribution for the corresponding parameter, which requires only an initial estimate of the minimum, mode and maximum for its characterisation (sourced directly from peer-reviewed literature or obtained from expert opinion). To best facilitate the calibration without sacrificing model flexibility, we adopted multivariate Gaussian priors on (the logistic transforms of) the time-dependent parameters, using the Matérn covariance function to favour small changes over consecutive years and across adjacent age cohorts (with independence between the sexes). Online supplementary table S1 http://sti.bmj.com/content/91/7/513/suppl/DC1 summarises the values chosen to specify the priors on the time-dependent and time-independent parameters.
The two main data sources used to calibrate the model were:
In addition, annual population census estimates published by the Australian Bureau of Statistics (ABS) were used for sex and age group population sizes.
A sequential Monte Carlo (SMC) approximate Bayesian computation (SMC-ABC) procedure was used to identify the optimal fit of parameters, infer annual incidence and gauge uncertainties when comparing the model with observed notifications and testing surveillance data. The model simulations were matched to (i) the annual notification counts reported and (ii) the annual test counts reported by Medicare for 2001–2005 and 2008–2013. The ABC algorithm allows for rigorous statistical inference from complex systems for which the true likelihood function may be computationally intractable but simulation from the model is comparatively cheap (see online supplementary material http://sti.bmj.com/content/91/7/513/suppl/DC1 for details).
Model outcomes were compared with independent empirical epidemiological measures. Chlamydia prevalence among 16–29-year-olds was measured in 2011 by the Australian Chlamydia Control Effectiveness Pilot (ACCEPt)—a randomised controlled trial of a chlamydia testing intervention in 150 general practice clinics. Since ACCEPt was conducted among sexually active 16–29-year-olds, prevalence estimates from the study were scaled down to account for the prevalence of sexual activity in these age groups (the Australian study of health and relationships found that 66%, 89% and 95% of men and 56%, 90% and 97% of women aged 15–19, 20–24 and 25–29 years, respectively, have been sexually active). The model outcomes were also compared with a study which measured incidence and prevalence among a cohort of young women (see Discussion section).
Methods
We estimated chlamydia incidence in the Australian population from 2001 to 2013 using a Bayesian statistical method based on a decision-pathway model.
Model
The decision-pathway of this approach is a probabilistic tree to represent the branches along which people in the population can end in each calendar year as either acquiring or not acquiring chlamydia infection, developing symptoms, being tested and treated and being notified as a case. Stratified by age and sex, each individual in the population has an assigned probability of each step along the branch over the course of each year (figure 1). For some branches, the model parameters (probabilities) are strongly constrained a priori from estimates in the literature, while other parameters must be informed by fitting the model to the surveillance data of numbers of people tested and numbers diagnosed with chlamydia.
(Enlarge Image)
Figure 1.
Pathways of chlamydia infection to be notified to the National Notifiable Diseases Surveillance System. Each parameter represents the (annualised) probability of progressing over a particular step. The light grey branches/boxes represent drop-outs from the notification count, but those reaching the testing phase will (if correctly reported) nevertheless contribute to the total test count.
To follow the effects of an evolving disease burden and changes in public awareness of, and access to, relevant public health programmes, we allowed the annual infection and asymptomatic screening probabilities to vary yearly by age group and sex using a flexible, stepwise Gaussian process model, while all other input parameters were fixed in time.
Priors
Following a standard Bayesian approach, we adopted independent beta distributions for priors on the time-independent probability parameters; the two shape variables of each beta distribution were chosen so that the beta prior was closest (using the Kullback–Leibler divergence) to a triangular distribution for the corresponding parameter, which requires only an initial estimate of the minimum, mode and maximum for its characterisation (sourced directly from peer-reviewed literature or obtained from expert opinion). To best facilitate the calibration without sacrificing model flexibility, we adopted multivariate Gaussian priors on (the logistic transforms of) the time-dependent parameters, using the Matérn covariance function to favour small changes over consecutive years and across adjacent age cohorts (with independence between the sexes). Online supplementary table S1 http://sti.bmj.com/content/91/7/513/suppl/DC1 summarises the values chosen to specify the priors on the time-dependent and time-independent parameters.
Calibration Data Sources
The two main data sources used to calibrate the model were:
National notification data (numbers of reported diagnoses per year) published by the Australian National Notifiable Diseases Surveillance System (NNDSS) and
National testing data collected by Medicare (the Australian universal health insurance scheme that rebates tests conducted by the majority of health providers). They include unique codes for a chlamydia test. However, tests conducted in public hospitals and most sexual health services are excluded, as these are funded separately and are not centrally collated. Medicare data on chlamydia tests were not available from November 2005 to April 2007 because the unique codes for identifying a chlamydia test were temporarily removed and any chlamydia tests conducted were recorded using a non-specific code that included tests for other genital organisms. Although tests conducted in public hospitals and most sexual health services are excluded, 82% of all chlamydia tests were conducted at GP clinics.
In addition, annual population census estimates published by the Australian Bureau of Statistics (ABS) were used for sex and age group population sizes.
Model Calibration Methods
A sequential Monte Carlo (SMC) approximate Bayesian computation (SMC-ABC) procedure was used to identify the optimal fit of parameters, infer annual incidence and gauge uncertainties when comparing the model with observed notifications and testing surveillance data. The model simulations were matched to (i) the annual notification counts reported and (ii) the annual test counts reported by Medicare for 2001–2005 and 2008–2013. The ABC algorithm allows for rigorous statistical inference from complex systems for which the true likelihood function may be computationally intractable but simulation from the model is comparatively cheap (see online supplementary material http://sti.bmj.com/content/91/7/513/suppl/DC1 for details).
Model Validation
Model outcomes were compared with independent empirical epidemiological measures. Chlamydia prevalence among 16–29-year-olds was measured in 2011 by the Australian Chlamydia Control Effectiveness Pilot (ACCEPt)—a randomised controlled trial of a chlamydia testing intervention in 150 general practice clinics. Since ACCEPt was conducted among sexually active 16–29-year-olds, prevalence estimates from the study were scaled down to account for the prevalence of sexual activity in these age groups (the Australian study of health and relationships found that 66%, 89% and 95% of men and 56%, 90% and 97% of women aged 15–19, 20–24 and 25–29 years, respectively, have been sexually active). The model outcomes were also compared with a study which measured incidence and prevalence among a cohort of young women (see Discussion section).
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