PLoS Negl Trop DisplosplosntdsPLOS Neglected Tropical Diseases19352735Public Library of ScienceSan Francisco, CA USAPNTDD180030510.1371/journal.pntd.0006531Research ArticleMedicine and health sciencesInfectious diseasesBacterial diseasesTrachomaMedicine and health sciencesOphthalmologyEye diseasesTrachomaMedicine and health sciencesTropical diseasesNeglected tropical diseasesTrachomaMedicine and health sciencesEpidemiologyMedicine and health sciencesEpidemiologyInfectious disease epidemiologyMedicine and health sciencesInfectious diseasesInfectious disease epidemiologyMedicine and health sciencesEpidemiologyDisease surveillanceInfectious disease surveillanceMedicine and health sciencesInfectious diseasesInfectious disease controlInfectious disease surveillanceMedicine and health sciencesPathology and laboratory medicineSerologyPeople and placesPopulation groupingsAge groupsBiology and life sciencesPopulation biologyPopulation dynamicsMedicine and health sciencesDiagnostic medicineOptimising sampling regimes and data collection to inform surveillance for trachoma controlSampling for trachoma surveillancehttp://orcid.org/0000000157475291PinsentAmyConceptualizationFormal analysisInvestigationMethodologyVisualizationWriting – original draftWriting – review & editing^{1}*HollingsworthT. DèirdreFunding acquisitionInvestigationMethodologySupervisionVisualizationWriting – original draftWriting – review & editing^{2}Department of Public Health and Preventative Medicine, Monash University, Melbourne, Victoria, AustraliaBig Data Institute, Li Ka Shing Centre for Health Informatics, University of Oxford, Oxford, United KingdomFrenchMichaelEditorRTI International, UNITED STATES
The authors have declared that no competing interests exist.
* Email: amy.pinsent@lshtm.ac.uk102018111020181210e0006531242201815520182018Pinsent, HollingsworthThis is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.The role of case proximity in transmission of visceral leishmaniasis in a highly endemic village in Bangladesh
It is estimated that 190 million individuals are at risk of blindness from trachoma, and that control by mass drug administration (MDA) is reducing this risk in many populations. Programs are monitored using prevalence of follicular trachoma disease (TF) in children. However, as programs progress to low prevalence there are challenges interpreting this indirect measure of infection. PCR and serosurveillance are being considered as complementary tools to monitor lowlevel transmission, but there are questions on how they can be most effectively used. We use a previouslypublished, mathematical model to explore the dynamic relationship between TF and PCR throughout a control program and a serocatalytic model to evaluate the utility of two crosssectional serosurveys for estimating seroconversion rates. The simulations show that whilst PCR is more sensitive than TF at detecting infection, the probability of detecting at least one positive individual declines during an MDA program more quickly for PCR than for TF (for the same sample size). Towards the end of a program there is a moderate chance of a random sample showing both low PCR prevalence and higher TF prevalence, which may contribute to the lack of correlation observed in epidemiological studies. We also show that conducting two crosssectional serosurveys 10 years apart can provide more precise and accurate estimation of epidemiological parameters than a single survey, supporting previous findings that whilst serology holds great promise, multiple crosssections from the same community are needed to generate the most valuable information about transmission. These results highlight that the quantitative dynamics of infection and disease should be included alongside the many logistical and practical factors to be considered in designing a monitoring and evaluation strategy at the operational research level, in order to help subsequently inform data collection for individual country programs. Whilst our simulations provide some insight, they also highlight that some level of longitudinal, individuallevel data on reinfection and disease may be needed to monitor elimination progress.
Author summary
Trachoma is a bacterial infection, which, with repeated infections over time, can lead to blindness. The WHO is aiming to eliminate trachoma as a public health problem by 2020, however at low prevalence levels the relationship between infection and disease prevalence is nonlinear, making the interpretation of data from the two diagnostic tests challenging. However, it is hard to know if this is an expected outcome or a biological inconsistency. Serosurveillance is being considered as an additional tool to understand transmission when infection and disease prevalence data provide different information. We highlight, through mathematical modelling, that a lack of strong correlation between infection and disease prevalence data at low levels of transmission seen in epidemiological data is not unexpected and demonstrate that multiple serosurveillance surveys should be conducted from at least 2 different age groups in order to accurately estimate epidemiological parameters that will help to monitor lowlevel transmission.
http://dx.doi.org/10.13039/100000865Bill and Melinda Gates FoundationHollingsworthT DèirdreAP gratefully acknowledges funding of the NTD Modelling Consortium by the Bill and Melinda Gates Foundation in partnership with the Task Force for Global Health. The views, opinions, assumptions or any other information set out in this article should not be attributed to Bill & Melinda Gates Foundation and The Task Force for Global Health or any person connected with them. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Data AvailabilityNo data was used in the study but the code is available as a supplementary file.Introduction
Trachoma is targeted for elimination as a public health problem by 2020 by the World Health Organization. At the global level there has been a high degree of programmatic success in terms of control [1], as the established intervention strategies have been highly effective in a large proportion of endemic districts. There do, however, remain a number of districts, primarily in Ethiopia, where disease and infection remain persistent and endemic, despite longterm intervention programmes [2, 3]. Irrespective of a district or region’s current elimination status robust surveillance systems must be able to effectively monitor overall programmatic success, confirm elimination as well as reemergence [4], however the appropriate choice of diagnostic and sampling strategy is unlikely to be uniform when trying to address each of the three aforementioned surveillance questions.
Currently polymerase chainreaction (PCR) testing of eyeswabs and clinical examination for inflammation are the most established diagnostic tools for monitoring trachoma surveillance within the key indicator group of 19 year olds [5], although the vast majority of programmatic decisions are currently made based only on TF prevalence. However, an increasing number of studies are looking to assess the value of ‘alternative indicators’ (serology and PCR for trachoma surveillance), as it has been suggested that other factors may cause TFlike symptoms making it difficult to ascertain at low TF prevalence levels whether what is being observed is truly TF. Current epidemiological data suggests that following a period of intervention within a community the relationship between PCR and TF prevalence within the community becomes nonlinear [6] and the results from the two diagnostics no longer correspond well with one another. Therefore it can be challenging and unclear how to interpret and explain such data in a programmatic setting [6].
As global prevalence of trachoma continues to decline it becomes increasingly challenging to identify and confirm TF cases and the cost of training graders becomes more expensive [7], therefore serosurveillance for trachoma is also currently being evaluated as more longterm tool to monitor lowlevel transmission and reemergence (in addition to PCR) [8, 9]. For serosurveillance to be informative for understanding reemergence it is first important to understand how serology relates to transmission intensity, and the duration of time which individuals in the population remain seropositive, in order for us to understand what future seroprevalence in the community will be postelimination.
As programs approach the elimination phase and nonlinearity in diagnostic outcomes become apparent or the utility of new surveillance tools needs to be evaluated, welldesigned operational research is required before country specific programme surveillance recommendations can be provided. In this study, we provide two suggestions on how future data for trachoma surveillance could be collected in order to help provide insights into the dynamics of disease as population prevalence declines to help guide monitoring and evaluation. Here we evaluate how the proportion of TF and PCR positive individuals changes over the course of an intervention period and during reemergence to assess if, or how, this impacts our probability of detecting infection or disease within a community. We assess whether these variations can be explained by the differences in the proportion of people in each state that would test positive with each of the different diagnostic tools. With our findings we suggest the types of data that could be collected to fully elucidate and understand the differences in prevalence patterns observed in these data. We then use simulated serological data to assess the identifiability of key epidemiological parameters from single and multiple crosssections sampling a range of different age groups. Through this we advise on the optimal range of age groups to sample from in order to estimate the seroconversion and seroreversion rates for the population and for the key indicator group of 19 year olds.
Materials and methodsSimulating prevalence of PCR and TF
We simulated prevalence data within a single community of 3,000 individuals (1/3rd of which were assumed to be aged 19 years, denoted N_{1}) [10, 11] to assess the probability of identifying TF and PCR positive individuals. To simulate data we used an agestructured ordinary differential equation (ODE) transmission model. We used a previously validated model structure that was identified as the most parsimonious and appropriate model when fitting to a single crosssection of agespecific PCR and TF prevalence data [12]. We used the framework of the classic SEIR model structure, with slightly different notation to indicate the different infection states for trachoma Fig 1. Individuals were susceptible to infection in the (S) state, exposed and incubating in the (E) state, who would test PCR positive, infected and infectious (ID) with detectable TF and who would also test PCR positive and those who remained diseased but were no longer infectious to others (D) (TF positive only), individuals in the D state were susceptible to reinfection with a reduced probability. Those who were reinfected then returned to the AI state (both PCR and TF positive) [12]. For each endemicity we simulated 3 annual rounds of MDA with azithromycin distributed to the whole community, assuming 80% coverage and a treatment efficacy of 85% [13].
10.1371/journal.pntd.0006531.g001A schematic of the model structure.
Individuals in the S state were susceptible to infection, those in the I state were exposed to infection and would test only PCR positive, those in the ID state were both PCR and TF positive, and those in the D state were diseased and TF only positive, but could be reinfected at a reduced rate Γ.
The baseline values of the model parameters are presented in Table 1. The code for the model is available as a supplementary file.
10.1371/journal.pntd.0006531.t001State variables, parameters definitions and values used in the model.
Name
Definition
Value
Units
Source
S_{i}
Susceptible individuals

Number
I_{i}
Infected but not infectious individuals (PCR +ve)

Number
ID_{i}
Infected and infectious individuals (PCR and TF+ve)

Number
D_{i}
Diseased and not infectious individuals (TF+ve)

Number
β
Transmission rate parameter
0.00655405
Proportion
N_{infs}
Maximum number of infections before immunity saturates
100
Number
[14]
ϵ
Degree of random mixing in the population
0.5
Proportion
[14]
c
Coverage
80%
Proportion
e
Treatment efficacy
85%
Proportion
[13]
λ_{a}
Age specific force of infection
day^{−1}
σ
Rate at which infected individuals become infectious
1/14
day^{−1}
[15]
ρ_{1}
Minimum rate of recovery from active disease after 1^{st} infection
1/300
day^{−1}
[12, 14, 15]
ρ_{100}
Maximum rate of recovery from active disease after 100^{th} infection
1/7
day^{−1}
[12, 14, 15]
ω_{1}
Minimum rate of recovery from infection after 1^{st} infection
1/200
day^{−1}
[12, 14, 15]
ω_{100}
Maximum rate of recovery from infection after 100^{th} infection
1/77
day^{−1}
[12, 14, 15]
α
Infectivity of an individual proportional to their bacterial load
0.114
Proportion
[12, 14, 15]
θ
Rate of change of the recovery from disease rate per infection
0.3
Proportion
[14, 15]
ϕ
Rate of change of the recovery from infection rate per infection
0.45
Proportion
[15]
Γ
Susceptibility to reinfection in the disease state
0.5
Proportion
[12, 16]
Testing for infection and disease
We used the transmission model to generate prevalence data at different sampling intervals to obtain the proportion of individuals PCR and TF positive at any point in time. The first scenario considered that the sampling was conducted at 6 monthly intervals over the course of 3 annual treatment rounds and we evaluated the probability (P_{i}) of detecting at least 1 TF and/or PCR positive individual. The sample size used at each sampling time point was fixed across the 3 year period. The probability of identifying a PCR positive individual in a given sample collected at time i was the proportion of the population who we would expect to be PCR positive:
PiPCR=Ei+AIiN1ϕ
Where ϕ is the sensitivity of the assay. The probability of detecting at least one PCR positive individual was given by:
1(1PiPCR)Nsample
where N_{sample} was the sample size, which was used, unless otherwise stated, 50 children [11].
Only AI and D state individuals test positive for TF therefore the probability of detecting a TF positive individual was:
PiTF=Ai+DiN1ψ
where ψ is the sensitivity of the diagnostic test for TF [17]. We note that sensitivity is a difficult parameter to quantify, particularly for TF, additionally it may reduce as local and global prevalence declines. The probability of detecting a single positive individual was similar to the expression for PCR above (Eq 2).
For the second scenario we simulated the model to endemic equilibrium for a range of TF prevalence levels (between 6% and 50%) and assessed after 3 rounds of annual MDA what the probability of detecting at least 1 PCR and TF positive individual was at the end of the intervention period only. For the final time point we also simulated sampling N_{sample} individuals from a population of individuals with this prevalence of PCR or TF, to demonstrate the range of possible outcomes which one would expect if the dynamics followed the transmission model (i.e. some correlation between PCR and TF positivity) to evaluate the range of outcomes that occur by chance.
Lastly, we assessed the probability of detecting at least 1 positive individual in a situation where infection and disease were reemerging within the community two years postintervention.
Estimating epidemiological parameters from crosssectional serology data
It has been reported that when only one seroprevalence crosssection is available it can be challenging to estimates key parameters such as the seroconversion rate (λ) and the seroreversion rate (ρ) simultaneously [18]. This is because with only one crosssection is not always possible to distinguish between a scenario where people seroconvert and serorevert quickly vs one where they seroconvert and serorevert slowly, as both scenarios can provide comparable fits to a single crosssectional dataset. As such, it is typically more preferable to have more than one crosssection from the sample population in order to distinguish between these two competing hypotheses.
We simulated seroprevalence data for individuals aged 160 years within a community exposed to trachoma. We simulated 2 crosssectional surveys, one pre and one postintervention where in the post intervention data we assumed an 80% reduction in transmission occurred 10 years ago. We assumed that no individuals in the population were seropositive as a result of exposure to any other pathogens, only trachoma. We fitted serocatalytic models to data from both crosssections simultaneously and also to each crosssection individually to assess how the precision and accuracy of the estimates was impacted by fitting to 1 vs 2 crosssections. When fitting the 2 crosssections together and the postintervention only crosssection we estimated 4 parameters the: seroconversion rate (λ), seroreversion rate (ρ), the proportional drop in transmission (γ) and the time at which the drop in transmission occurred (T_{c}).
Seronegative individuals become seropositive at a rate λ and seropositive individuals become seronegative at a rate ρ [19]. Thus the proportion of seropositive individuals within the crosssection collected is determined by the following:
dPdt=λ(t)(1P)ρP
Where in a model that assumes a change in transmission at an instantaneous point in time λ is defined as follows:
λ(t)={λ0t<Tcλc≥Tc
For the preintervention dataset we only estimated 2 parameters λ and ρ. We also estimated epidemiological parameters from data collected from only 19 year olds (the key indicator group for surveillance), from both crosssections simultaneously and individually. We then assessed how sampling an additional age group as well the current indicator group impacted the accuracy and precision of parameter estimation. We henceforth define accuracy in terms of parameter estimation as how close the paramater estimate was to the true simulated value, and precision as the narrowness of the credible intervals (CrI) for the estimate of any given parameter.
ResultsProbability of detecting PCR and TF positives during an intervention period with a fixed sample size
We considered a community with a true endemic disease prevalence of 20% (16% infection prevalence). Following a single round of treatment, the prevalence of PCR detectable infection dropped much more quickly than the prevalence of TF (Fig 2a). Thus, declines in TF prevalence lagged behind the changes observed for PCR. This was consistent for all three rounds of MDA (Fig 2a). Consequently, true TF prevalence was consistently higher than true PCR prevalence within the period evaluated.
10.1371/journal.pntd.0006531.g002Changes in the prevalence and detectability of PCR (red) and TF (blue) positive individuals over an intervention period.
a) prevalence of infection and disease prevalence change during an intervention within the community, points on the x axis labelled with an S indicate that a sample was taken at that point, and those labelled with a T indicate when treatment occurred. b) the proportion of individuals present in each diagnostic state at each sampling point during the intervention period: pink—PCR positive only, purple—PCR and TF positive, blue—TF positive only and c) indicates the probability of detecting at least 1 positive individual when taking 50 samples by PCR (red) and TF (blue) eye examination, dots represent the median prevalence point from 100 binomial samples for PCR and TF at each sampling point, the intervals represent the lower and upper interquartile range of prevalence.
The proportion of individuals that were prevalent by any diagnostic test (Fig 2b) prior to MDA commencing showed that 6% of exposed individuals would have tested PCRonly positive, 67% would have tested PCR and TF positive, while 27% would have tested TFonly positive (Fig 2b). Once the intervention had begun the ratio of individuals in different infection and disease states altered (Fig 2b). As the intervention period progressed the proportion of individuals that tested PCRonly positive fell from 6% to 3.5%, while the proportion of individuals that tested both PCR and TF positive declined substantially from 67% to 41%. By contrast the proportion of TFonly positive people increased markedly from 27% to 55% (Fig 2b). The large decline in the overall proportion of people PCR positive helps to explain the marked reduction in the probability of detection for PCR positive individuals (Fig 2c) and the slower decline in the probability of detection of TF positive individuals (Fig 2c). As such, the opportunity to identify individuals who were both TF and PCR positive was most likely to occur when the ratio of PCR to TF positive individuals were similar in the population, which was most likely to occur at endemic equilibrium.
Once sampling time point 5 was reached we saw a slight indication that reemergence may be occurring (Fig 2a). For sampling point S_{5} in comparison to sampling point S_{4} there was a marked increase in the proportion of individuals that tested PCR and TF positive (41% to 63%, Fig 2b) and a decrease in the proportion of individuals that tested TFonly positive (55% to 30%, Fig 2b)—these differences were reflected in the increase in probability of detection for PCR, but only a minor increase in the probability of detection of TF positives (Fig 2c).
When sampling 50 individuals at each time point, we found that with the exception of time point S_{4} the expected median prevalence was consistently higher for TF than PCR (Fig 2c), however the variance in the expected TF prevalence was larger than for PCR. Additionally, the lack of overlap in the prevalence estimates over the intervention period suggested that at multiple times during the intervention period it is possible that people will test positive with one diagnostic but not the other (Fig 2c). This coupled with a marked reduction in the probability of detection as prevalence declines suggests nonlinearity in the results from different diagnostics is not unexpected.
Probability of detecting PCR and TF positives during reemergence with a fixed sample size
Following 2 years of MDA cessation in the community we considered the dynamics of detection during a potential resurgence (Fig 3a). As reemergence continued the rate at which TF prevalence increased was faster than that of PCR prevalence, this was because only few people test PCRonly positive, but there was an increase in the number of people who test positive PCR and TF as well as TF positive only. This was likely to be because when prevalence begins to increase gradually the rate of reinfection in the TF only state is low, due to an initial low force of infection in the community. Assessing the proportion of individuals by diagnostic state when reemergence first began, 5.5% of exposed individuals would have only tested PCR positive, 67% would have tested PCR and TF positive, while 27% would have tested TF positive only (Fig 3b). As reemergence continued to occur across the first 4 sampling time intervals the proportion of TF only positive individuals was consistently higher than PCR and TF positive individuals, at sampling time point 4, 41% of individuals tested PCR and TF positive, while 55% of individuals were TF positive only. In contrast, at sampling time point 5 the ratio of individuals in different diagnostic states was more comparable to that seen in the community prior to MDA being implemented (Fig 2b) where 63% of individuals tested PCR and TF positive and 30% of individuals were only TF positive (Fig 2b). As reemergence continued the probability of detection with both diagnostics increased, the probability of detection increased at a similar rate as time progressed for both tests (Fig 3c), in contrast to the results seen when prevalence was declining during the MDA programme where the probability of detecting PCR positive individuals declined much more rapidly than TF positive individuals (Fig 2c). The variance in the estimated PCR and TF prevalences were slightly higher for PCR detectable infection, whilst the variance in the estimated prevalence of TF and PCR overlapped at some sampling time points, this was not consistent for all sampling points. Highlighting that in a low prevalence reemergence setting it’s possible we would find individuals PCR and or TF positive (Fig 3c).
10.1371/journal.pntd.0006531.g003Changes in the prevalence and detectability of PCR (red) and TF (blue) positive individuals if reemergence was occurring 18 months after the last round of MDA.
a) prevalence of infection and disease prevalence change during reemergence within the community, points on the x axis labelled with an S indicate that a sample was taken at that point, and those labelled with a T indicate when treatment occurred. b) the proportion of individuals present in each diagnostic state at each sampling point during the intervention period: pink—PCR positive only, purple—PCR and TF positive, blue—TF positive only and c) indicates the probability of detecting at least 1 positive individual when taking 50 samples by PCR (red) and TF (blue) eye examination, dots represent the median prevalence point from 100 binomial samples for PCR and TF at each sampling point, the intervals indicate the lower and upper interquartile range of prevalence.
Ratios of different diagnostic states across a range of TF prevalence levels
In the preMDA setting at higher levels of TF prevalence the overall proportion of PCR and TF positive individuals was much higher than at lower levels of endemic prevalence. When TF prevalence was 50%, 74.5% of infected individuals were PCR and TF positive, but when TF prevalence was 10%, 64% of individuals were TF and PCR positive (Fig 4a). Here the proportion of TFonly positive individuals increased from 20%, to 32% when endemic prevalence was 50%, in comparison to 10% (Fig 4a). Whilst when TF prevalence was 30% the ratio of individuals in each diagnostic state was more comparable to when TF prevalence was 50%: (6.8%, 70%, 22%) (Fig 4a). At high levels of endemic prevalence we would expect the greatest proportion of individuals in the population to be both TF and PCR positive because individuals in the TF only state will be continuously reinfected. However, at lower levels of prevalence the rates of reinfection are not as high, resulting in a higher proportion of TFonly positive individuals.
10.1371/journal.pntd.0006531.g004Changes in the proportion of individuals positive in each diagnostic state, pre and post MDA for different initial endemic levels of TF prevalence.
On the left is the proportion of individuals positive in each diagnostic state prior to MDA occurring: pink—PCR positive only, purple—PCR and TF positive, blue—TF positive only, each x axis label indicates what the initial endemic prevalence was in the community prior to intervention. On the right is the proportion of individuals in each diagnostic state following 3 annual rounds of MDA for each initial level of endemic prevalence (as shown on the x label), again pink—PCR positive only, purple—PCR and TF positive, blue—TF positive only. At high levels of initial endemic prevalence we see the highest proportion of individuals test both PCR and TF positive as a result of rapid rates of reinfection within the community, while at lower levels of prevalence a high proportion of TF only individuals were present due to lower rates of reinfection. Changes in the proportion of individuals positive in each diagnostic state were more apparent for initial endemic prevalence’s lower than 25%.
Across all TF prevalence levels postMDA a comparable ratio of individuals in each diagnostic state to the preMDA levels was observed, although for a number of initial prevalence levels the proportion of PCR only positive individuals was slightly higher than at endemic equilibrium. For example, the proportion of PCR positives only increased from 7.6% to 9.7% (Fig 4b). For lower levels of endemic prevalence postMDA we observed a slight decrease in the proportion of individuals PCR and TF positive, and a small increase in the proportion of individuals who would test only TF positive—for an endemic TF prevalence of 10% the proportion of individuals TF and PCR positive dropped from 64% to 54.5% and the proportion of TF only positive individuals increased from 31% to 38% (Fig 4b).
Our simulations have suggested that the expected proportion of individuals detectable as both PCR and TF positive declines as the overall prevalence in the community declines, typically as prevalence declines a higher proportion of individuals become TFonly positive. Additionally, the probability of detecting an individual as PCR positive during an intervention period declines much more quickly than for TF, this difference in the probability of detection may also help to explain disparities in the reported prevalence of infection and disease as transmission declines when surveys are conducted. To understand more clearly what is happening when we observe nonlinearity in prevalence in 19 year olds by PCR and TF surveillance we would need individual level data on PCR and TF prevalence, this would enable us to see whether the proportion of PCR and TF positives in the data is comparable to the ratios that the model predicts.
Assessing TF prevalence vs PCR prevalence across the different levels of endemicity
At both high and low levels of transmission the simulations above suggest that the true underlying PCR and TF prevalence levels do correlate with one another. At high levels of infection and transmission PCR and TF prevalence correlate with one another due to rapid rates of reinfection occurring, ensuring that PCR and TF prevalence correlate well with one another. As prevalence declines although the true underlying prevalence’s may correlate at low prevalence sampling noise can play an important role, leading to some samples being collected in which TF prevalence is much higher than PCR prevalence (Fig 5). For these simulations, both TF and PCR sensitivity mean that prevalence is usually underestimated (the coloured dots are down and to the left of the black dot indicating true prevalence). If sensitivity declines as prevalence continues to fall, then this discrepancy will be larger.
10.1371/journal.pntd.0006531.g005PCR and TF prevalence postMDA for different initial endemicities (black dots), and for 10,000 different samples of 200 individuals (coloured dots) from a population with a true prevalence indicated by the black dots, for each of the different endemicity levels.Estimating epidemiological parameters from serological data
Fitting a 2 parameter model to preintervention crosssectional data the median estimates of λ and ρ were lower than the true values of the simulated data: 0.04 and 0.02 vs 0.10 and 0.05, however the credible intervals included the true value (Fig 6). Fitting the postintervention dataset in isolation the estimate of λ was close to the true value (0.13 vs 0.10), however the credible intervals were much wider than when the two crosssections were fitted simultaneously. The median estimate of γ was lower than the true value, with much wider credible intervals in comparison to when 2 crosssections were fitted together (Fig 6). Estimates of the ρ and T_{c} were similar to the true values, however the precision of the estimates were less than when 2cross sections were fitted simultaneously (Fig 6).
10.1371/journal.pntd.0006531.g006The estimated value for each serocatalytic model parameter using different simulated datasets.
For each parameter the true value is indicated in black (x label 1), fitting to allage data for both crosssections simultaneously is highlighted in red. Allage preintervention only data (green, 2 parameters estimated), allage post intervention data only (blue), 19 year old data—2 crosssections (cyan), 19 year old data preintervention data (pink), 19 year old data postintervention (purple), 19 and 1020 year olds pre and postintervention (orange), 19 and 2030 year olds pre and postintervention (light blue), 19 and 3040 year olds pre and postintervention (yellow), 19 and 4050 year olds pre and postintervention (sky blue), 19 and 5060 year olds pre and postintervention (rust).
Fitting 2 crosssections to data from only 19 year olds (300 samples) the median estimated λ was similar to the true estimate (0.12 vs 0.10), T_{c} was also estimated relatively accurately. The estimate of γ was much lower than the true value 0.09 (CrI: 0.010.28), but the credible intervals did include the true value. The estimate of ρ was higher than the true value (0.09 vs 0.05), but the wider credible intervals still included the true value.
Fitting to preintervention period data from 19 year olds, estimates of λ and ρ were much lower than the true values and the credible intervals did not include the true values, estimates were also much lower than when a single cross section for the full dataset was fitted to, suggesting that fitting to a small crosssection of the population is not sufficient to accurately estimate these parameters. For the postintervention data in 19 year olds λ was overestimated and the credible interval range was large, much wider than when the full single cross section was evaluated. Estimates of ρ were similar when 19s were evaluated as when the full crosssection was, however this is likely to have traded off with the estimate of ρ. The median estimate of gamma was below the true value but similar to when all data was fitted to for the single postintervention dataset, whilst T_{c} was above the true value. Therefore overall for the preintervention data estimates of λ and ρ were markedly different to the full dataset and when the two crosssection were fitted together. For the postintervention data estimates of ρ and T_{c} were similar to when the single full cross section was fitted to and not too dissimilar from when 2 crosssections were fitted together. However the estimate of λ was much higher in 19s in comparison to the full single cross section and gamma was similar to when both crosssections were fitted together, but lower than when all the data was evaluated.
When we fitted only 19 year olds the precision and accuracy of the estimated parameters was lower than when the allage data was fitted to, therefore we evaluated whether sampling an additional age group outside of the current indicator group containing the same total number of samples could help improve the precision and accuracy of the parameter estimates. When including an additional age group outside of the current indicator group, for λ the precision and accuracy of the estimate when 2030 year olds were also sampled was much improved, and the median estimate of 0.095 was very close to the true value of 0.10. The precision of the estimated value of γ was generally poorer than when only 19s were evaluated, however when a second group was also fitted to the accuracy of the estimate to the true value was much better than when only 19s were fitted to. Including age ranges above 30 years slightly reduced the precision of the estimate in comparison to when 1020 or 2030 year olds were included. Incorporating an additional age group up to 50 years of age helped improve the precision and accuracy of the estimated value of ρ, highlighting the value of sampling outside of the current indicator group for more precise parameter estimates. The most precise and accurate estimates of ρ were obtained when individuals 2030 years were in the sample as well. T_{c} was also most accurately and precisely estimated when 2030 year olds were included in the sample.
Discussion
Inconsistencies in the observations from PCR and TF samples can make interpretation of trachoma surveillance data challenging [6]. The similarity observed between PCR and TF prevalence that breaks down as prevalence declines is currently not well understood or fully explained. In this article we have presented a possible explanation as to how these observations in surveillance data may be occurring. Through evaluating the proportion of individuals that would be present in each diagnostic state in the community with a dynamic model we have shown that as prevalence declines within a community the proportion of individuals PCR only or PCR and TF positive declines and a higher proportion of the PCR or TF positive population are only TF positive. These changes in the proportion of people that would test positive in each diagnostic state impact the diagnostic test results, making the proportion of TF and PCR positives less similar. The dynamics of transmission also mean that as prevalence declines the probability of detecting at least 1 positive individual by PCR with a fixed sample size declines much more rapidly than with TF (assuming a fixed sensitivity of the diagnostic over time). We note that an individualbased modelling approach would be needed to fully explain the observations seen in surveillance data. Importantly, individuallevel diagnostic data from low prevalence settings would help us to understand whether the proportions of PCR and TF positives align with those predicted by the model. Individual level data is essential for testing the assumptions in this model and providing guidance on sampling strategies for PCR use in routine surveillance.
For serosurveillance we have shown that much more accurate and precise parameter estimates can be inferred when 2 crosssections are fitted to in comparison to 1. Particularly for the preintervention crosssection, we clearly saw how estimates of λ and ρ could be traded off with one another causing imprecise estimation [18]. When only fitting to data from 19 year olds the accuracy and precision of the parameter estimation was reduced in comparison to fitting to the allage data. However, through the inclusion of one additional agegroup we were able to improve the precision and accuracy of all parameter estimates when fitting 2 crosssections simultaneously. In this situation it appeared that the inclusion of 2030 year olds as well as 19 year olds had the most substantial impact on improving parameter estimation precision and accuracy. Therefore in terms of helping to quantify epidemiological parameters more accurately in the future we would suggest that at least 2 crosssections be collected from the same community and that an agegroup outside of the 19 year old group also be sampled. This will ensure that both ρ and the force of infection (determined by λ) are estimated more accurately and with less uncertainty.
For a number of NTDs the issue of systematic noncompliance/adherence to treatment has been reported and the potential issues it may present to elimination evaluated, ie. Treatment coverage within the community is not random. However, for the purposes of this study when modelling treatment we have assumed coverage is random. If individuals in the community systematically miss treatment then they may remain a reservoir source of infection, helping to ensure ongoing transmission. However, for trachoma in particular little to no epidemiological data has been presented to suggest that systematic noncompliance is occurring during MDA rounds, and generally the coverage level is reported to be at least at the target level of 80%, as such, currently no data are available to indicate to what extent systematic noncompliance may be occurring. Despite our assumption of random coverage we do not expect a large impact at these coverage levels for the qualitative conclusions, unless it is quite extreme. However, if those being treated are the same as those being tested, and there were a group who were consistently not treated or measured, that would be more of a problem for the discussion posed here. Also, at these coverage levels, systematic noncompliance becomes a particular issue when nonadherence to treatment is correlated with infection risk, ie if those more at risk of infection continually miss treatment then they are more likely to remain a reservoir source of infection in the community. If this is the case in the communities we have evaluated, we would be more likely to see faster rates of reemergence of infection but the qualitative observations and diagnostic outcomes reported in the study would be unlikely to change.
The are a number of limitations to the study. Firstly, for both diagnostic tests we assumed 100% specificity [17], if this assumption were relaxed we would expect an increase in the proportion of overall positives, leading to a possible overestimate of the prevalence, and thus increasing the probability of detection with each diagnostic. However, despite modelling a slightly higher proportion of positives in the population in comparison to what may be true we would not expect the qualitative form of the relationships observed to be altered. Secondly it is possible that the sensitivity and specificity of the PCR and TF diagnostics may alter over time as prevalence declines [6], whereas we have only considered a single fixed value. Again, it is likely that this assumption would not alter the qualitative relationships observed here, but potentially the magnitude. As prevalence declines it becomes more challenging to detect both infection and disease, therefore we would expect the true probability of detection to potentially be even lower. Furthermore we would expect the noise around the low prevalence estimates to increase substantially [20]. Thirdly, in the serosurveillance work, we chose to illustrate the importance of a second crosssection over only one, with an assumed reduction in transmission compared with 10 years previously, as we felt this was a case which would illustrate the point most effectively. However, as we approach an era of elimination for trachoma it is becoming increasingly unlikely that the opportunity will arise to conduct 2 surveys 10 years apart in time, therefore the question becomes how frequently should surveys be conducted in order to help accurately estimate the seroreversion rate. This crucially depends on the rate of antibody decay, which is not yet known. However with exploratory simulation it may be possible to get a better idea on how frequently surveys should be conducted in order to estimate this. Lastly, in settings where urogenital infection is high such as the South Pacific [21], individuals may also test seropositive to antitrachoma antigens as a result of exposure to urogenital chlamydia. This can complicate the estimation of the seroreversion and conversion rates for exposure due to trachoma, and would potentially need to be accounted for if serosurveillance data was being collected in individuals past the age of sexual debut in populations with a high incidence of urogenital chlamydia infection.
PCR and serosurveillance are important potential tools for trachoma surveillance, which may offer additional opportunities for understanding transmission dynamics as incidence declines. This paper highlights some of the links between these dynamics and potential survey design. However, there are, of course, many logistical constraints which would need to be considered before they were implemented widely in routine surveillance. From this study we highlight 2 key recommendations for future data collection for trachoma surveillance, in order to understand lowlevel transmission dynamics in greater detail as population prevalence declines. Firstly, individuallevel diagnostic data from low prevalence settings would help us to understand whether the proportions of PCR and TF positives align with those predicted by the model. Secondly, we clearly highlight that for serosurveillance more accurate and precise parameter estimates can be inferred when 2 crosssections are fitted to in comparison to 1. We would therefore recommend at least 2 crosssectional serological surveys being conducted several years apart in order to improve the estimation of epidemiological parameters from serological data.
Supporting informationCode for the mathematical model in R.
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