Forecasting the impact of population ageing on tuberculosis incidence.

BACKGROUND: Tuberculosis (TB) disease reactivates from distant latent infection or recent (re)infection. Progression risks increase with age. Across the World Health Organisation Western Pacific region, many populations are ageing and have the highest per capita TB incidence rates in older age groups. However, methods for analysing age-specific TB incidence and forecasting epidemic trends while accounting for demographic change remain limited.
METHODS: We applied the Lee-Carter models, which were originally developed for mortality modelling, to model the temporal trends in age-specific TB incidence data from 2005 to 2018 in Taiwan. Females and males were modelled separately. We combined our demographic forecasts, and age-specific TB incidence forecasts to project TB incidence until 2035. We compared TB incidence projections with demography fixed in 2018 to projections accounting for demographic change.
RESULTS: Our models quantified increasing incidence rates with age and declining temporal trends. By 2035, the forecast suggests that the TB incidence rate in Taiwan will decrease by 54% (95% Prediction Interval (PI): 45%-59%) compared to 2015, while most age-specific incidence rates will reduce by more than 60%. In 2035, adults aged 65 and above will make up 78% of incident TB cases. Forecast TB incidence in 2035 accounting for demographic change will be 39% (95% PI: 36%-42%) higher than without population ageing.
CONCLUSIONS: Age-specific incidence forecasts coupled with demographic forecasts can inform the impact of population ageing on TB epidemics. The TB control programme in Taiwan should develop plans specific to older age groups and their care needs.

Introduction

In 2018, tuberculosis (TB) was still the top infectious killer in the world [1]. The End TB strategy aims at a 90% reduction in TB incidence rate by 2035 compared with 2015, but the current global rate of decline of around 2% per year is not on track to achieve this [2]. Latent TB infection risk accumulates over lifetimes while TB transmission is ongoing. The prevalence of latent TB infection is highest in older age groups [3], who not only have had the longest exposure, but were often exposed to higher TB transmission rates in the past. ageing, with associated higher rates of progression [4], thus acts as a demographic driver towards higher per capita TB incidence [5]. In the Western Pacific region, many countries have their highest per capita TB incidence rates among older age groups [1]. Among Western Pacific region countries, China, Hong Kong (China), Japan, Korean, Singapore, and Taiwan are facing both high TB burden and population ageing[6,7].

The age profile of future TB incidence is critical for forecasting public health needs and rational policy design [8]. First, older populations will have higher TB (and background) mortality rates [9,10], which implies added difficulty in meeting treatment success targets. Secondly, older adults have more comorbidities and more complex health care needs, which may lead to a longer care-seeking process and higher healthcare expenditure per case. For instance, patients with chronic lung diseases may have signs or symptoms overlapping with TB, making correctly diagnosing their TB slower and more costly [11]. Thirdly, the proportion of TB cases in older age groups should inform policy making, for example suggesting integrating TB care entry points into long-term care programmes, or through clinician training highlighting older people as a TB risk group with their own diagnostic and management challenges [11].

Quantitatively forecasting the TB incidence age profile needs combined models forecasting demographic change and statistical forecasts of age-specific TB incidence. However, a time series analysis producing age-specific forecasts of the TB incidence has not been published to our knowledge. Use of autoregressive integrated moving average models, often including the seasonality of TB incidence is more common [12], and comoving time series analysis has been applied [13] without age-specific information. Age-specific TB incidence modelling, including the use of age-period-cohort models, has been undertaken but without producing epidemic forecasts (e.g. Iqbal et al. [14] and Wu et al. [15]). Mechanistic mathematical modelling, with age structure, also has the potential to generate forecasts [5,16-18]. Indeed, Arregui et al. [18] developed forecasts for the effects of demographic change on TB epidemics, focussing on four relatively young countries; our interests are in developing statistically rigorous time-series approaches and in focusing on an example of a much older population.

In many settings, the demographic transition and population ageing are outpacing declines in TB incidence, so methods to understand and forecast the impact of changing demography on TB epidemics are needed. We, therefore, developed a statistical method capturing age-specific incidence trends and forecasting future epidemics while accounting for demographic change so more methods to understand and forecast the impact of changing demography on TB epidemics are needed.

Materials and methods

Setting and data sources

TB incidence in Taiwan has steadily declined from 64 confirmed TB cases per 100,000 in 2007 to 41 per 100,000 in 2017. Since 2005, the proportion of TB cases in Taiwan over 65 years of age has been over 50% and increasing. Between 2007 and 2017, the average age in Taiwan increased from 36 to 40, and the proportions of adults above 65 rose from 10% to 14% [7].

Notification data of culture-confirmed TB cases, excluding foreigners, were obtained from the Taiwan Center for Disease Control surveillance system. Counts were reported by age group, sex, month, and county. Ages were reported as (0–4, 5–9, …, 65–69, 70+) years. The demographic data were obtained from the Department of Statistics, the Ministry of the Interior, Taiwan. These data included the mid-year population estimators, deaths, migration in single-year ages, and fertility in five-year age groups (15–19, …, 45–49). We used data in 2005–2018 as a training set. The demographic data from 2005 to 2017 were collected for the population demographic modelling (a shorter period because of the release schedule). All the training data in this article were published by the Taiwan officials and free access on the internet; the usage is licensed by the Open Government Data License: [https://data.gov.tw/license].

Importantly, we assumed no case detection gaps existed during the time frame covered by this article. We, therefore, regard “TB notification” and “TB incidence” as synonymous with the number culture-confirmed tuberculosis cases notified during a specific period.

Age-specific incidence modelling and forecasting

We considered annual incidence rates by age and sex. The incidence rates by age groups and sex were calculated as the yearly notification counts divided by corresponding mid-year population estimates. Females and males were analysed separately with the same parameterisation. We modelled the incidence rates using Lee-Carter Models (LCMs) [19] formulated with age and time-varying terms. The LCMs were initially designed for mortality rate modelling, where they now predominate. Estimation, forecasting, bootstrapping methods for LCMs are well-developed.

We performed a likelihood-based LCM estimation, and also the comparable Poisson regression [20]: , where E(.) is expectation function, year ∈ {2005,…,2018} is the calendar year, α is age effect term, κ is period effect term, and β is coefficients adjusting period effects for different age groups, and age ∈ {0−4,5−9,…,70+} represents the age categories. To maintain identifiability, we imposed the constraints Σκ = 0 and Σβ = 1. We followed the fitting procedure provided by Brouhns et al. [20] for likelihood maximisation.

Two nested Poisson models, one using an age-profile and a discrete period effect, i.e α + κ, and another using an age-profile and a linear effect, i.e. α + year × κ, were used as comparators. Akaike information criterion (AIC), Bayesian information criterion (BIC), and log-likelihood were considered as goodness of fit metrics. The definitions of these metrics were identical to the ordinary Poisson regression model [21]. See S1 Appendix for the details of the LCM specification in our approach.

For forecasting, inspired by the Lee-Carter demographic forecasting, we used Autoregressive Integrated Moving Average models with drift [22], constructed from the LCM period effects. In forecasting, the death and birth processes applied semiparametric bootstrap sampling [23].

Population modelling and forecasting

We constructed a synthetic population with birth, death and migration processes. The demographic methods adapted from those used in the Taiwan National Development Council’s population projection report [7]. The demography was modelled by single age (0–100 years old) and sex. Mortality forecasting used the Lee-Carter model [19] below 84 years of age; and we used the Coale-Kisker method [24] for those aged over 85 years in death rate modelling as it was found to have a better reliability for small sample sizes in inferring of death rates. The birth forecasting used the fertility rates of women in childbearing ages, from 15 to 49, with a modified LCM [25]. For consistency with incidence forecasting, semiparametric bootstrap sampling was used for deaths and births [23]. The Migration process was modelled by linear regression with age effects and a linear trend; the forecasting applied residual bootstrap sampling with the age-specific parameters seen in 2017. The forecasts were used for the next step by aggregating to the age groups as that of the incidence data. See S2 Appendix for the detailed methodology of the synthetic population.

Forecasting overall TB incidence

The TB incidence model and the demographic model were built independently. Forecasts of age-specific TB incidence were weighted by forecasted population demography to obtain forecasts of per capita TB incidence for the whole population. TB incidence was calculated as per 100,000 rates by given strata. TB incidence rate reductions were calculated with respect to the incidence in 2015 and presented as percentages. For simplicity, some results were presented with age groups of 0–14, 15–34, 35–64, and above 65. In forecasting, the 95% prediction intervals and mean values were computed from 10,000 bootstrap samples. Uncertainty was propagated from every submodel. To compare with the global reduction target of the End TB strategy [2], we forecasted the incidence until 2035. The milestones of 2020, 2030 and 2035 of the End TB strategy of percentage reductions in per capita TB incidence from 2015 were used as intermediate outcomes.

Incidence attributable to demographic change

We performed a scenario analysis to clarify the potential impact of demographic change. While forecasting the age-specific TB incidence to 2035, we kept the population size and age structure fixed as it was in 2018. This TB incidence was compared against values including projected changes in population structure by computing the fraction of total TB incidence attributable to demographic change in each year as (I1,−I0,)/I1,, where I1, and I0, are the incident cases with and without demographic change respectively and is the calendar year. This corresponds to the definition of population attributable fraction [26].

All the analyses were performed using R 3.5 [27] and analysed/visualised by R package StMoMo, TSA, ggplot2 [28-30]. All analysis code is available at [https://github.com/TimeWz667/AgeingTB].

Results

Incidence modelling

Fig 1 shows the estimators of the Lee-Carter models of the incidence data. The age effect estimators (α) suggested the baseline incidence rates increase with age. In both sexes, the higher levels in age groups older than fifteen years correspond to higher TB incidence rates. The point estimators of age-period adjustments (β) showed no specific trend. However, there are large uncertainties for all estimates pertaining to under 15-year age groups due to the small numbers of notifications observed. The period effect estimators (κ) had nearly constant slopes with calendar years. Fig 1 also demonstrates the forecasting of period effects with 95% prediction intervals: prediction intervals of both sexes grew at a constant rate with calendar time. Table 1 shows the goodness of fit of the LCMs, the nested age-period Poisson models, and age-trend Poisson models. In AIC, BIC and log-likelihood on the training data, the LCM result is preferred over the other two although it costs a higher degree of freedom. See S3 Appendix for the details of the goodness of fit, and residuals plots.

Fig 1

Lee-Carter model fitting and forecasting of the TB incidence.

(Data: 2005–2018, Forecasting: 2019–2035). 95% confidence intervals of estimators and prediction intervals of forecasts were calculated through bootstrapping with 10,000 sample size.

Table 1

Summary of model comparison.

	Age-Trend	Age-Period	Lee-Carter Model
Model family	Poisson Regression
Period effect	Linear	Discrete
No. observations	420
No. parameters	32	56	84
Log(Likelihood)	-1855	-1819	-1682
AIC	3773	3751	3531
BIC	3902	3977	3871

AIC: Akaike information criterion, BIC: Bayesian information criterion

Population forecasting

Fig 2 shows the demographic change from 2005 to 2035. In Fig 2A, the population will reach a maximum of 23.6 million in 2023, and will start shrinking to 23.2 million in 2035. The proportion of the population aged over 65 is increasing across the period and will reach 27% in 2035. The proportion of the population aged under 15 is declining to around 11%. Fig 2B compares the age structure of the Taiwanese population in 2018 and 2035, highlighting the population ageing.

Fig 2

Demographic change.

(Data: 2005–2017, Forecasting: 2018–2035).

Incidence forecasting and age structure

Fig 3 demonstrates the trends of the population TB incidence rate and TB incidence rates by age-group (<15, 15–34, 35–64, >65). The forecast in Fig 3A suggests that the TB incidence in 2035 will be 22 (95% Prediction Interval (PI): 19–25) per 100,000. The overall incidence reduction will reach 54% (95% PI: 45%-59%) in 2035, which is 37% short of the reduction in the End TB Strategy. Fig 3B shows the age-specific incidence rates will have 60% to 80% reductions from 2015 to 2035 apart from the 5–9 group. The rate reductions in most age groups will be higher than the forecast reduction of 44% in the whole population. Fig 3C shows the overall incidence rates by age group as a stacked histogram. The TB incidence rates from age groups below 65 will be gradually decreasing whereas the above 65 will nearly stay constant from 2018 to 2035. Fig 3D shows the proportion of TB incidence in each age group. The proportion among adults aged over 65 years will reach 68% (95% PI: 67%-69%) and 79% (95% PI: 78%-81%) in 2025 and 2035, respectively. In 2035, more than 97% of incident cases will occur among those aged 35 years or older, indeed the contribution from cases under 15 years is nearly invisible in Fig 3C and 3D.

Fig 3

TB incidence rate forecasting.

(A) Overall incidence rate per 100,000. In the forecasting, dashed line features the mean values and the shaded area is 95% prediction interval. (B) Incidence rate reductions by five-year age groups during 2015–2035 with 95% prediction interval. (C) Incidence rates attributed to age groups. (D) Proportions of age groups in Incidence cases.

Impact of demography on TB incidence

Fig 4 shows the forecast incidence rates with and without demographic change. In the scenario without demographic change, the forecast suggests that the incidence in 2035 will be around 13 per 100,000 compared to 23 with demographic change and the 90% reduction target of 4.5 per 100,000. The 95% prediction intervals for forecasts with demographic change continuously expand year by year, whereas without demographic change they converge to a constant width within five years. Table 2 shows the impact of demographic change. Up to 2020, TB incidence rates will have 23% and 27% reductions with and without demographic change respectively. Considering demographic change, the incidence rates are projected to reduce by 54% (95% PI: 45%-59%) from 2015 to 2035; without demographic change, the reduction will be 72% (95% PI: 67%-76%). In both scenarios, the trends of incidence rates showed diminishing reductions to the time scale. In both scenarios, the declines in incidence rates slowed over time. Comparing the forecasts with dynamic and fixed demography suggested that 39% (95% PI: 36%-42%) of incident TB cases in 2035 will be attributable to demographic change.

Fig 4

TB incidence with and without demographic change.

Ribbons show 95% prediction intervals.

Table 2

Summary of reductions in TB incidence with and without demographic change.

Year	Percentage reduction in per capita TB incidence from 2015:		Percentage of total TB incidence attributable to demographic change
	with demographic change	without demographic change after 2018
2020	23.1% (18.2%, 27.2%)	26.6% (22.2%, 30.8%)	4.6% (1.6%, 7.5%)
2025	35.2% (27.2%, 40.7%)	47.0% (41.0%, 52.2%)	18.3% (15.5%, 21.2%)
2030	45.0% (35.9%, 50.5%)	61.6% (56.0%, 66.4%)	30.0% (27.3%, 33.0%)
2035	53.7% (44.5%, 58.9%)	72.1% (67.1%, 76.1%)	38.8% (36.1%, 41.7%)

Discussion

A substantial proportion of tuberculosis (TB) incidence in Taiwan is among people aged over 65 years. Social and economic development typically bring reductions in TB incidence but also reduced birth and death rates and population ageing. This study provides a novel investigation into the potential impact on TB incidence from population ageing using statistical modelling and forecasting. Current trends of TB incidence decline and demographic change suggest TB incidence rates in Taiwan will decrease to 25 per 100,000 by 2035. This represents a 45% reduction since 2015, missing the End TB goal of 90% reductions in TB incidence rates. We have shown that higher age-specific incidence rates in older age groups can mean that population ageing acts against reductions in TB rates, with TB incidence in 2035 projected to be 39% higher than without demographic change.

Previous studies have employed statistical methods either to forecast TB incidence, [12,13,31,32] or to analyse patterns by age using age-period-cohort models, [14,15] but we are the first study to statistically forecast age-specific TB incidence. Some transmission modelling studies [16,18] have explored issues related to age-structure, and Arregui et al. [18] generated forecasts. However, the fitting in Arregui et al. was not likelihood-based and did not use age-specific TB data, and so could not evaluate age-specific goodness of fit for TB projections or compare alternative models with conventional metrics. We made novel use of Lee-Carter models (LCMs), [19,22] which employ an elegant low-dimensional decomposition of age-specific rates to model trends and overall shape. LCMs were originally introduced for mortality rate modelling and are now the dominant approach, but have been applied elsewhere. Within demography, Hyndman [25] and Rueda-Sabater and Alvarez-Esteban [33] used LCMs to forecast the fertility rates, and Cowen [34] fitted LCMs to abortion rates. Kainz et al. [35] modelled chronic kidney disease prevalence as rate data, and Yue et al. [36] modelled cancer incidence and mortality. However, we are the first to apply LCMs to TB, finding they fitted better than Poisson Age-Period models. Our approach offers a generalizable and easily-implemented method for forecasting age-specific TB incidence and the impact of demographic change on total TB incidence.

In our model fitting results, the age effects (α) demonstrated the TB incidence rates positively correlated with age in both females and males. The period effect estimators (κyear) were almost linear despite not assuming linearity in the LCM formulation. The declines may reflect improvements in infection control and case detection, and the declining latent TB prevalence in each age group. Improvements in infection control and case detection both reduce the force of infection that will induce further TB incidence. Latent TB prevalence depends on cumulative lifetime infection risks, and therefore on the history of active TB prevalence. As TB incidence has been declining, the latent TB prevalence in recent cohorts will be lower than in historical cohorts at the same age. Lastly, the age-period interaction terms (β) were used to demonstrate how the incidence rate reduced differently in each age group, although no overall pattern was identified. The variance of the estimators in young people was larger because the only around 1% of incident TB (< 100 cases every year in the recent decade) were from people below 15 years old.

For Taiwan and many other high-income settings, TB notifications are thought to parallel TB incidence with only a small gap. Taiwan lacks survey data (e.g. capture-recapture studies) to directly inform on the magnitude of this gap. In settings where this gap is larger and changing over time, interpretation of TB notification data is more problematic, and notifications may not be a good proxy for incidence. Even in a declining TB epidemic with evolving case-mix, it is possible that case detection may change differently over time in different age-groups; we have not attempted to include such effects. Taiwan does not have United Nations Population Division demographic forecasts, hence our bespoke demographic modelling. For most nations, these forecasts could be used ‘off the shelf’. We have presented results on percentage reductions in both per capita TB incidence rates and in total TB incidence (e.g. Table 2), which are similar because of Taiwan’s small projected population change over the period considered; this may not be true in all settings.

The decline in TB incidence in Taiwan probably has multiple contributory causes, including improvements in TB control, socio-economic development, and the reductions in the prevalence of latent TB as a result of declining transmission. For an infectious disease like TB, reduced transmission can amplify and sustain over time changes in underlying causative factors, complicating their analysis. The low TB rates in children aged under fifteen may reflect low exposure to TB in this group or potentially lower rates of case detection. Our assessment of the impact of population ageing on TB incidence and case-mix has particular current relevance to many WHO Western Pacific region countries [1] and will be relevant to many more countries and regions in the future. Our analysis could provide a template for analysts who wish to explore issues related to future TB incidence and demography where age-specific data are available.

Our analysis accounted for cohort propagation of latent tuberculosis infection (LTBI) in a phenomenological way. LTBI represents accumulated lifetime risk of infection by exposure to active tuberculosis disease. Older individuals in most settings have higher LTBI prevalence due both to longer cumulative exposure and (in declining epidemics) exposure to a higher mean infection rate over their lifetime. The ageing through of these LTBI positive cohorts thus generates a secular time trend in reactivation disease rates at a particular age. Our approach does not explicitly model LTBI prevalence, because this would introduce additional parameters and, without LTBI data, identifiability issues. However, LTBI cohort effects are accounted for in our current approach indirectly by modelling the secular trends in age-specific incidence rates.

Another limitation of our approach is that it would fail to account for non-linear threshold behaviour, such as during outbreaks. However, in many high-income settings (including Taiwan), the steadily declining tuberculosis incidence implies the net reproduction number is below one.

Extending the model by adding exogenous variables is possible. Our analysis did not address the impact of other variables for simplicity and clarity. Important predictors could include socioeconomic status and comorbidities such as diabetes mellitus [37]. However, projections would require additional time-series analysis to forecast these explanatory variables. It is worth noting that according to Taiwan CDC surveillance, in 2005, 0.72% of TB cases in Taiwan were coded as HIV; neglecting HIV is unlikely to have impacted our results.

Older age as a risk factor for TB disease has perhaps been under-explored since age is not a modifiable risk factor, and since in most current high-burden settings populations and the typical age of TB cases are fairly young. Our result that population ageing will act to slow declines in TB incidence tallies with that of Arregui et al [18], obtained for different settings using very different methods, and quantifies the magnitude of this effect. However, the importance of older age groups to TB control is already evident in many Asian populations, [16] and this will be an increasingly widespread facet of global TB control if reductions in incidence continue and accelerate in the future. Older populations will also have their own particular challenges in terms of access, diagnosis and comorbidities complicating their care. Public health planning to develop adapted strategies for care and control to meet these changing population needs is essential.

In conclusion, the Lee-Carter model provides a tool to project age-specific tuberculosis incidence and hence forecast overall TB incidence while accounting for demographic change. In Taiwan, population ageing may slow the decline of TB incidence by 39% over the period 2015–2035. TB care and control programmes will increasingly need to address the needs of older adults, who will comprise a growing majority of the TB epidemic.

Specification of the Lee-Carter approach.

(PDF)

Click here for additional data file.

Synthetic population, modelling details.

(PDF)

Click here for additional data file.

Residual analysis and the goodness of fit.

(PDF)

Click here for additional data file.

24 Jul 2019

PONE-D-19-18299

Forecasting the impact of population ageing on tuberculosis incidence

PLOS ONE

Dear Mr. Ku,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

We would appreciate receiving your revised manuscript by Sep 07 2019 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. This file should be uploaded as separate file and labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

We look forward to receiving your revised manuscript.

Kind regards,

Michele Tizzoni

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1) Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

http://www.journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and http://www.journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2) Please add the following to your COI statement: "Peter J. Dodd is also a PLOS ONE handling editor for this collection."

Please confirm that this does not alter your adherence to all PLOS ONE policies on sharing data and materials, by including the following statement: "This does not alter our adherence to  PLOS ONE policies on sharing data and materials.” (as detailed online in our guide for authors http://journals.plos.org/plosone/s/competing-interests).

If there are restrictions on sharing of data and/or materials, please state these. Please note that we cannot proceed with consideration of your article until this information has been declared.

Please include your updated Competing Interests statement in your cover letter; we will change the online submission form on your behalf.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors estimate future trends in the age-specific tuberculosis (TB) incidence in Taiwan until 2035, by applying statistical models (called Lee-Carter models) to time series of incidence data from 2007-2017 and accounting for sex, age, and year-specific effects. The estimated age-specific incidences are then applied to the projected demographic age structure to derive total incidence trends. Overall, the idea is simple and the considerations on demographic changes are important for projections of TB incidence in countries with declining transmission and undergoing a demographic transition, therefore the paper deserves consideration.

My main criticism is that Lee-Carter models were, according to the authors, previously applied in demography and non-communicable diseases epidemiology. However, because the incidence of infectious diseases is critically dependent on the current prevalence of infections, highly non-linear effects in temporal trends take an important role (e.g. threshold effects in the reproductive number) which may make these models highly inaccurate for projecting disease incidence. If transmission dynamics are very far from the epidemic threshold and therefore the large majority of TB cases are due to reactivations, these effects can likely be neglected. Previous studies from US (a low incidence country) showed that only 30% of cases are recently transmitted (Guzzetta et al., JTB 2011), and the large burden of reactivated disease results in a poor performance of TB control strategies applied in the state (Guzzetta et al., JTB 2013). Considering that the average incidence of TB in the US is around 5 per 100k, one might expect a larger contribution of recently transmitted cases in Taiwan, given the average current incidence of about 8 times the US one.

Thus, the authors should:

- provide a demonstration that the method works when parametrizing the model with a subset of data, e.g. the first 5 years of the time series, and projecting the final 5 years against actual observations (this would not be final proof, because short term projections are highly correlated to the current status, but would at least show that the model works in a very easy case);

- discuss the proportion of reactivated vs. recently transmitted TB in Taiwan or countries with similar epidemiology/geographic settings, in light of the above criticism;

- acknowledge the overall limitation of using Lee-Carter models in a context of highly non-linear time trends.

Other comments:

- a minimum description of how Lee-Carter models work mathematically should be provided, at least in the Supplementary Materials; a Coale-Kisker method is mentioned at l. 147, but no specification of why a different method is used for the age class above 85 years old, nor a description of how the method differs from the Lee-Carter one;

- the definition of the likelihood formula used to calculate AIC and BIC should be made explicit;

- do the authors have specific reasons for considering sex-specific incidence separately? Are differences in results significant? Fig. 1 could show estimates for the two sexes in the same graph, in order to allow an easier comparability;

- l. 59: the burden of TB in the mentioned countries cannot be considered "high" from a global point of view. They are perhaps higher than most industrialized countries, but certainly very low compared to the 22 high-burden countries representing 83% of the overall TB burden. Also, "Korean" should be South Korea;

- l. 189: "excepting the reference group aged 0-4": what is the exception? Uncertainties seem large for this age group as well;

- l. 190: "constant trends with calendar years": the trend is linear, perhaps the authors mean that the effect (slope) is constant;

- l. 219, "which is 37% short of the 90%": using percentages as differences may be very confusing, I recommend dropping the 37% figure;

- sentence at lines 246-247 is not clear;

- when mentioning co-morbidities in the discussion (l.328 and 329), HIV should also be mentioned and average prevalences/trends in Taiwan of the two main comorbidities should be provided, to give a general idea on how much neglecting them can impact results;

- I suggest to move the final paragraph of the discussion to somewhere in the beginning: as it is, it has a very anticlimactic effect.

Reviewer #2: This work presents a series of analyses based on statistical modelling to describe the interplay between population's ageing and TB incidence rates -both aggregated and age-specific- in Taiwan. Based on Lee-Carter models, authors analyse age-specific time series between 2005 and 2018 regarding both TB incidence and population structures, and extrapolate to produce forecasts of both aggregated and age-specific TB incidence rates that run until 2035.

The paper is written in a clear and concise manner, and the general research question -what can be expected from the effects of populations' aging on global TB burden levels- is timely and of utmost importance. Statistical modelling methods are sound and described in a (perhaps too much) succinct way. Results -the main observation that contemplating populations' ageing translate into more pessimistic forecasts for TB incidence in Taiwan for the next years- are robust, and in line with previous literature, which is, however, scarce, as authors point out. Conclusions are backed up by the analyses done, and the limitations of the statistical approach are framed in a way that is essentially adequate.

I have therefore no major objections for the publication of this manuscript, and congratulate the authors for their important work. I have, though, the following minor comments/questions, which should be successfully addressed before I can finally recommend the article for publication in this journal:

1. I think that the description of the methods should probably be more exhaustive and explicit, given the specialised character of the statistical modelling framework used in this study, which the interdisciplinary audience of PLoS One might not be necessarily familiar with. Other aspects that might better be explained to a higher level of detail are how the age-specific and aggregated TB incidence rates are built, and rescaled from the demographic and migration forecasts, how does the bootstrap work and how (explicitly) does the uncertainty to TB rates propagates from the different sub-models.

2. At several points of the manuscript, we read the following statements:

line 74: "time series analysis producing age-specific forecasts of the TB incidence has not been published to our knowledge."

line 83: "However, age-specific forecasting and the impact of demographic change have yet to be analysed."

line 281: "Some transmission modelling studies [16,18] have explored issues related to age-structure, but without forecasts or formal assessment of fit."

line 335: "Our result that population ageing will act to slow declines in TB incidence does not seem to have been previously noted."

Which are not totally true. As a matter of fact, reference [18] is a study where authors report the impact of populations' ageing on TB incidence forecasts using transmission modelling. In [18], incidence rate forecasts, both aggregated and age-specific, are indeed reported for different countries, as well as fit evaluations of incidence and mortality rates between 2000 and 2015, upon model calibration. Importantly, the main conclusion of that work -that populations' ageing appears to be directly proportional to an increase in model-based TB burden forecasts with respect to simpler estimations that neglect demographic evolution- is exactly the same of the work here presented for the case of Taiwan, despite the type of models used in that work being radically different from what is presented here. Therefore, the aforementioned statements should be modified, and the findings presented in this work should be put in context to the conceptually similar results reported for other countries in [18].

3. In their analyses, authors assume, as they explicitly acknowledge, the equivalence between TB cases notifications and incidence for the sake of the results they reports. Is not there available data about case notification rates that could be integrated into the models? If not, this possibility should at least be discussed. Even if working with just notification data might be reasonable in the case of contemporary Taiwan; the changes in the population structure that authors forecast in the years to come, along with the eventual added difficulties to detect and register active TB cases in the oldest population strata (which authors also discuss in the introduction) might translate into the growth of a reservoir of undetected/unregistered active TB among eldest age-groups. This plausible scenario might bias the quantitative conclusions of this work, and it should probably be discussed when exposing the limitations of working on notification data alone.

-3. In line 224, we read: "age groups below 65 will be gradually decreasing whereas the above 65 will nearly stay constant from 2018 to 2035"

It took me some time to understand that the age-specific incidence is proportional to the area under the curves, but not to the lines (i.e. that the histograms are stacked), this probably should be stated more clearly. Also, and more important, in figures 3C-3D, four shades are included in the legend, but only three can be appreciated in the figures.

4. The text is very well written, I only found the following couple of typos:

Line 195: "although it cost a higher degree of freedom" should read "it costs"

Line 262: "Table 2. Summary of reductions in TB incidence reductions with and without

263 demographic change" (remove the second "reductions"?)

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

19 Aug 2019

Reviewer #1: The authors estimate future trends in the age-specific tuberculosis (TB) incidence in Taiwan until 2035, by applying statistical models (called Lee-Carter models) to time series of incidence data from 2007-2017 and accounting for sex, age, and year-specific effects. The estimated age-specific incidences are then applied to the projected demographic age structure to derive total incidence trends. Overall, the idea is simple and the considerations on demographic changes are important for projections of TB incidence in countries with declining transmission and undergoing a demographic transition, therefore the paper deserves consideration.

My main criticism is that Lee-Carter models were, according to the authors, previously applied in demography and non-communicable diseases epidemiology. However, because the incidence of infectious diseases is critically dependent on the current prevalence of infections, highly non-linear effects in temporal trends take an important role (e.g. threshold effects in the reproductive number) which may make these models highly inaccurate for projecting disease incidence. If transmission dynamics are very far from the epidemic threshold and therefore the large majority of TB cases are due to reactivations, these effects can likely be neglected. Previous studies from US (a low incidence country) showed that only 30% of cases are recently transmitted (Guzzetta et al., JTB 2011), and the large burden of reactivated disease results in a poor performance of TB control strategies applied in the state (Guzzetta et al., JTB 2013). Considering that the average incidence of TB in the US is around 5 per 100k, one might expect a larger contribution of recently transmitted cases in Taiwan, given the average current incidence of about 8 times the US one.

-------------------------------

Thanks for this point. It is indeed a limitation that this projection method would not take into account threshold effects. We agree that the proportion of incidence due to reactivation is a valuable metric, but note that it is not logically connected with threshold behaviour (eg a high prevalence setting with declining incidence could have a majority of incidence from recent transmission but will, by definition, have a net reproduction number below one). We have added the following text to the limitations Discussion:

“Another limitation of our approach is that it would fail to account for non-linear threshold behaviour, such as during outbreaks. However, in many high-income settings (including Taiwan), the steadily declining tuberculosis incidence implies the net reproduction number is below one.”

Also we have added a paragraph in the discussion to emphasise the explanation of our model fitting results.

“In our model fitting results, the age effects demonstrated the TB incidence rates positively correlated with age in both females and males. The period effect estimators were almost linear despite not assuming linearity in the LCM formulation. The declines may reflect improvements in infection control and case detection, and the declining latent TB prevalence in each age group. Improvements in infection control and case detection both reduce the force of infection that will induce further TB incidence. For latent TB, which is accumulated during one's lifetime and depends on historical TB prevalent TB in history, different cohorts will have different prevalence. As TB incidence has been declining, the latent TB prevalence in recent cohorts will be lower than in historical cohorts at the same age. Lastly, the age-period interaction terms were used to demonstrate how the incidence rate reduced differently in each age group, although no overall pattern was identified. The variance of the estimators in young people was larger because the only around 1% of incident TB (< 100 cases every year in the recent decade) were from people below 15 years old.

”

-------------------------------

Thus, the authors should:

- provide a demonstration that the method works when parametrizing the model with a subset of data, e.g. the first 5 years of the time series, and projecting the final 5 years against actual observations (this would not be final proof, because short term projections are highly correlated to the current status, but would at least show that the model works in a very easy case);

-------------------------------

We have added a validation figure in S3 appendix to demonstrate the goodness of fit

-------------------------------

- discuss the proportion of reactivated vs. recently transmitted TB in Taiwan or countries with similar epidemiology/geographic settings, in light of the above criticism;

-------------------------------

Please see above. We have added a sentence pointing out the limitation that this method would not correctly predict threshold behaviour, and noting that for the settings where this method is most applicable, and the questions we investigate of most interest, incidence has been declining for a decade or more suggesting that the net reproduction number is safely below one.

We would expect our method to apply in high-burden settings with declining epidemics also, which might still have the majority of incidence due to recent transmission but still have R<1. But for these settings, the equivalence of notifications and incidence is not usually a safe assumption.

For your interest, estimates from our unpublished tuberculosis transmission modelling in Taiwan suggest around 50% of cases are recently transmitted in 2018 and will be down to 30% in 2035 .

-------------------------------

- acknowledge the overall limitation of using Lee-Carter models in a context of highly non-linear time trends.

-------------------------------

We have added the limitation of not being able to predict non-linear threshold behaviour in the Discussion (see above) - thanks for pointing this out. However, we would like to emphasize that the LCM we use is not restricted to linear trends in time (if that is what was meant). We have clarified this as part of our more detailed description of the LCM approach by adding an appendix file, S1 Appendix, with details of the LCM specification.

-------------------------------

Other comments:

- a minimum description of how Lee-Carter models work mathematically should be provided, at least in the Supplementary Materials; a Coale-Kisker method is mentioned at l. 147, but no specification of why a different method is used for the age class above 85 years old, nor a description of how the method differs from the Lee-Carter one;

-------------------------------

Thanks for the suggestion to describe LCMs in more detail. Reviewer 2 also suggested this and we agree. We have added a supplementary, S2 Appendix, to list the implementation details of our synthetic population modelling.

Thanks also for highlighting the unjustified detail around motivating the Coale-Kisker method in our demographic model. We have added:

“we used the Coale-Kisker method [24] for those aged over 85 years in death rate modelling as it was found to have a better reliability for small sample sizes in inferring of death rates. ”

-------------------------------

- the definition of the likelihood formula used to calculate AIC and BIC should be made explicit;

-------------------------------

Thanks. We have added the definitions as in S1 Appendix.

-------------------------------

- do the authors have specific reasons for considering sex-specific incidence separately? Are differences in results significant? Fig. 1 could show estimates for the two sexes in the same graph, in order to allow an easier comparability;

-------------------------------

Thanks for the question. The motivation for modelling sex-specific incidence was primarily because in Taiwan, as in most settings, the majority of incidence is in men. The reasons for this are complex and incompletely understood (see eg Horton et al). We didn’t want to assume that the trends would be the same in each sex and so modelled them separately.

-------------------------------

- l. 59: the burden of TB in the mentioned countries cannot be considered "high" from a global point of view. They are perhaps higher than most industrialized countries, but certainly very low compared to the 22 high-burden countries representing 83% of the overall TB burden. Also, "Korean" should be South Korea;

-------------------------------

Thanks, a very reasonable point. We have changed “high TB burden” to “TB burdens of substantial public significance”. We have changed “Korean” to “South Korea”.

For information, WHO have discontinued use of their 22 high burden country (HBC) list; their new 30 HBC tuberculosis incidence list includes China due to its large absolute incidence.

-------------------------------

- l. 189: "excepting the reference group aged 0-4": what is the exception? Uncertainties seem large for this age group as well;

-------------------------------

Thanks, the statement was a mistake. To fix this, we have removed the clause “excepting the reference group aged 0-4”; the sentence is still true. The uncertainties in children were due to the low number of notifications observed; we have added “due to small numbers.” in lieu of the previous clause.

-------------------------------

- l. 190: "constant trends with calendar years": the trend is linear, perhaps the authors mean that the effect (slope) is constant;

-------------------------------

Fixed

-------------------------------

- l. 219, "which is 37% short of the 90%": using percentages as differences may be very confusing, I recommend dropping the 37% figure;

-------------------------------

We take your point. We decided to drop the 90% so as to still include our numerical result here, ie:

“which is 37% short of the reduction in the End TB Strategy.”

-------------------------------

- sentence at lines 246-247 is not clear;

-------------------------------

Thanks for catching this. We have revised to:

“In both scenarios, the declines in incidence rates slowed over time. Comparing the forecasts with dynamic and fixed demography suggested that 39% (95% PI: 36%-42%) of incident TB cases in 2035 will be attributable to demographic change.”

-------------------------------

- when mentioning co-morbidities in the discussion (l.328 and 329), HIV should also be mentioned and average prevalences/trends in Taiwan of the two main comorbidities should be provided, to give a general idea on how much neglecting them can impact results;

-------------------------------

Thanks. We have added:

“It is worth noting that according to Taiwan CDC surveillance, in 2005, 0.72% of TB cases in Taiwan were coded as HIV; neglecting HIV is unlikely to have impacted our results.”

-------------------------------

- I suggest to move the final paragraph of the discussion to somewhere in the beginning: as it is, it has a very anticlimactic effect.

-------------------------------

Apologies. We were intending the last paragraph to be a ‘Conclusions’ as is commonly found in the biomedical literature, and may be sought for by readers with this background. To flag this more explicitly, we have changed this paragraph to begin “In conclusion,”, but left it where it was.

-------------------------------

Reviewer #2: This work presents a series of analyses based on statistical modelling to describe the interplay between population's ageing and TB incidence rates -both aggregated and age-specific- in Taiwan. Based on Lee-Carter models, authors analyse age-specific time series between 2005 and 2018 regarding both TB incidence and population structures, and extrapolate to produce forecasts of both aggregated and age-specific TB incidence rates that run until 2035.

The paper is written in a clear and concise manner, and the general research question -what can be expected from the effects of populations' aging on global TB burden levels- is timely and of utmost importance. Statistical modelling methods are sound and described in a (perhaps too much) succinct way. Results -the main observation that contemplating populations' ageing translate into more pessimistic forecasts for TB incidence in Taiwan for the next years- are robust, and in line with previous literature, which is, however, scarce, as authors point out. Conclusions are backed up by the analyses done, and the limitations of the statistical approach are framed in a way that is essentially adequate.

I have therefore no major objections for the publication of this manuscript, and congratulate the authors for their important work.

-------------------------------

Thank you for your kind comments.

-------------------------------

I have, though, the following minor comments/questions, which should be successfully addressed before I can finally recommend the article for publication in this journal:

1. I think that the description of the methods should probably be more exhaustive and explicit, given the specialised character of the statistical modelling framework used in this study, which the interdisciplinary audience of PLoS One might not be necessarily familiar with. Other aspects that might better be explained to a higher level of detail are how the age-specific and aggregated TB incidence rates are built, and rescaled from the demographic and migration forecasts, how does the bootstrap work and how (explicitly) does the uncertainty to TB rates propagates from the different sub-models.

-------------------------------

Thanks for this comment. Reviewer 1 also requested additional detail in the methodology (especially around LCMs). In response to their comments and yours, we have made the following changes:

Additional detail around LCM specification in S1 Appendix, including modelling fitting procedure, likelihood function, deviance residuals, bootstrap procedure, and propagation of uncertainty. The implementation can also be found in the code base we mentioned.

We hope these changes have improved the text without introducing too much detail for the typical reader. We note that additional detail is available in the supplementary appendix and that code for the analyses is fully open source and available as described.

-------------------------------

2. At several points of the manuscript, we read the following statements:

line 74: "time series analysis producing age-specific forecasts of the TB incidence has not been published to our knowledge."

line 83: "However, age-specific forecasting and the impact of demographic change have yet to be analysed."

line 281: "Some transmission modelling studies [16,18] have explored issues related to age-structure, but without forecasts or formal assessment of fit."

line 335: "Our result that population ageing will act to slow declines in TB incidence does not seem to have been previously noted."

Which are not totally true. As a matter of fact, reference [18] is a study where authors report the impact of populations' ageing on TB incidence forecasts using transmission modelling. In [18], incidence rate forecasts, both aggregated and age-specific, are indeed reported for different countries, as well as fit evaluations of incidence and mortality rates between 2000 and 2015, upon model calibration. Importantly, the main conclusion of that work -that populations' ageing appears to be directly proportional to an increase in model-based TB burden forecasts with respect to simpler estimations that neglect demographic evolution- is exactly the same of the work here presented for the case of Taiwan, despite the type of models used in that work being radically different from what is presented here. Therefore, the aforementioned statements should be modified, and the findings presented in this work should be put in context to the conceptually similar results reported for other countries in [18].

-------------------------------

Many apologies. On re-reading we do indeed do a disservice to reference 18 (this was a late addition in redrafting, as our systematic review of relevant literature focussed on statistical models).

In response to this:-

We have changed the last sentence of the Introduction paragraph (previously ending with the sentence you note as line 83) to:

“Indeed, Arregui et al. [18] developed forecasts for the effects of demographic change on TB epidemics, focussing on four relatively young countries; our interests are in developing statistically rigorous time-series approaches and in focusing on an example of a much older population.”

(We have left the sentence starting this paragraph - you reference as line 74 - as it was, since we believe this is correct.)

We have also changed a sentence in the last paragraph of the Introduction (by adding more):

“...so more methods to understand and forecast the impact of changing demography on TB epidemics are needed.”

We have changed the sentence you refer to at line 281 to:

“...Some transmission modelling studies [16,18] have explored issues related to age-structure, and Arregui et al [18] generated forecasts. However, the fitting in Arregui et al was not likelihood-based and did not use age-specific TB data, and so could not evaluate age-specific goodness of fit for TB projections or compare alternative models with conventional metrics.”

We have changed the sentence you refer to at line 335 to:

“...Our result that population ageing will act to slow declines in TB incidence tallies with that of Arregui et al [18], obtained for different settings using very different methods, and quantifies the magnitude of this effect...”

-------------------------------

3. In their analyses, authors assume, as they explicitly acknowledge, the equivalence between TB cases notifications and incidence for the sake of the results they reports. Is not there available data about case notification rates that could be integrated into the models? If not, this possibility should at least be discussed. Even if working with just notification data might be reasonable in the case of contemporary Taiwan; the changes in the population structure that authors forecast in the years to come, along with the eventual added difficulties to detect and register active TB cases in the oldest population strata (which authors also discuss in the introduction) might translate into the growth of a reservoir of undetected/unregistered active TB among eldest age-groups. This plausible scenario might bias the quantitative conclusions of this work, and it should probably be discussed when exposing the limitations of working on notification data alone.

-------------------------------

Unfortunately, there is no data in Taiwan to directly inform on the gap between notifications and incidence. This is a general problem for tuberculosis. Measuring tuberculosis incidence in the general population is not feasible and has never been done at a nationally representative level. Nationally representative tuberculosis prevalence surveys provide an unbiased measure of disease burden (though typically with around a 20% error margin), but the relationship between tuberculosis prevalence and incidence is uncertain and not constant across settings. Inventory studies are useful, especially for quantifying the contribution of under-reporting (as opposed to under-diagnosis) to the gap between notifications and incidence, and where three independent records are available they can be specialized to capture-recapture studies that inform on the whole notification-incidence gap (under additional assumptions). Unfortunately, a tuberculosis prevalence survey in Taiwan is unlikely to be pursued (eg they fail to meet the burden threshold above which WHO suggest such a survey would be useful and would need a huge sample size), and the universal insurance system means that the conditions for a capture-recapture study are unlikely to be met.

In the absence of these types of survey data, the recourse is typically to expert opinion on the case-detection ratio or a standard assumption about the notification-indence gap. The above hierarchy of approaches is broadly the approach followed by WHO in estimating tuberculosis incidence for member states (of which Taiwan is not one). Your suggestion that changing demography and increasingly rare cases may undermine experience in detecting tuberculosis in some groups, reversing improvements in case-detection is an interesting one, which although it has been made elsewhere, lacks data to strongly support it.

Obviously this is a complex topic. We have tried to capture the key points you are suggesting briefly in the relevant paragraph of the Discussion by adding (the underlined text):

“...only a small gap. Taiwan lacks survey data (eg capture-recapture studies) to directly inform on the magnitude of this gap. In settings where this gap is larger and changing over time, interpretation of TB notification data is more problematic and notifications may not be a good proxy for incidence. Even in a declining TB epidemic with evolving case-mix, it is possible that case detection may change differently over time in different age-groups; we have not attempted to include such effects. Taiwan does not...”

-------------------------------

-3. In line 224, we read: "age groups below 65 will be gradually decreasing whereas the above 65 will nearly stay constant from 2018 to 2035"

It took me some time to understand that the age-specific incidence is proportional to the area under the curves, but not to the lines (i.e. that the histograms are stacked), this probably should be stated more clearly. Also, and more important, in figures 3C-3D, four shades are included in the legend, but only three can be appreciated in the figures.

-------------------------------

Thanks for noting these potential sources of confusion. To help readers interpret the meaning of the histogram correctly, we have changed the sentence around line 224 introducing Fig 3C to read:

“Fig 3C shows the overall incidence rates by age group as a stacked histogram.”

To avoid confusion if readers can’t make out the color for the youngest age group, we have changed the last sentence of this section to read:

“In 2035, more than 97% of incident cases will occur among those aged 35 years or older, indeed the contribution from cases under 15 years is nearly invisible in Figures 3C and 3D.”

-------------------------------

4. The text is very well written, I only found the following couple of typos:

Line 195: "although it cost a higher degree of freedom" should read "it costs"

Line 262: "Table 2. Summary of reductions in TB incidence reductions with and without

263 demographic change" (remove the second "reductions"?)

-------------------------------

Thanks for spotting these typos. We have corrected the errors.

-------------------------------

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

11 Sep 2019

[EXSCINDED]

Forecasting the impact of population ageing on tuberculosis incidence

PONE-D-19-18299R1

Dear Dr. Ku,

We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.

Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.

Shortly after the formal acceptance letter is sent, an invoice for payment will follow. To ensure an efficient production and billing process, please log into Editorial Manager at https://www.editorialmanager.com/pone/, click the "Update My Information" link at the top of the page, and update your user information. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, you must inform our press team as soon as possible and no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

With kind regards,

Michele Tizzoni

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: (No Response)

Reviewer #2: The authors have been responsive to my previous comments; I have just caught a couple of confusing sentences which would need some rewording:

-1. In the main text, lines 311-312: "For latent TB, which is accumulated during one's lifetime and depends on historical TB prevalent TB in history"

-In supplementary appendix S1, the first paragraph of section 1.4 contains a number of grammar errors, please revise.

Being these details the only issues I found, I am therefore happy to recommend the work for publication in PLoS One.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

16 Sep 2019

PONE-D-19-18299R1

Forecasting the impact of population ageing on tuberculosis incidence

Dear Dr. Ku:

I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

For any other questions or concerns, please email plosone@plos.org.

Thank you for submitting your work to PLOS ONE.

With kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Michele Tizzoni

Academic Editor

PLOS ONE