a Communicable Disease Control, Prevention and Eradication, World Health Organization, 1211 Geneva 27, Switzerland.
b National TB Control Centre, Department of Diseases Control, Ministry of Health, Chao Yang District, Beijing 100025, China.
c CSIR, PO Box 91230, Auckland Park, Johannesburg, South Africa.
Reprint requests to: Dr C. Dye, Communicable Disease Control, Prevention and Eradication, World Health Organization, 1211 Geneva 27, Switzerland. E-mail: dyec{at}who.ch
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Abstract |
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Method We developed a mathematical model that makes use of routinely-collected data to calculate the number of deaths directly prevented by TB treatment (i.e. excluding those due to reduced transmission). The method was applied to the world's largest TB control programme covering over 500 million people in 12 provinces of China.
Results Counties which had been enrolled in the programme since 1991 were, by 1997, preventing at least 46% (3756%) of the TB deaths that would otherwise have occurred. If replicated across the entire TB control programme area, this would amount to 30 000 (range 26 00059 000) deaths directly prevented each year.
Conclusions Short-course chemotherapy has substantially reduced TB mortality in half of China. The analytical method described here could be applied to TB control operations in many other countries, and should help to quantify the true burden of tuberculosis alleviated by SSCC.
Keywords Disease burden, epidemiology, mathematical modelling, standard short-course chemotherapy, TB
Accepted 8 November 1999
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Introduction |
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In China in 1990, TB accounted for about half of all deaths due to communicable diseases.2 In 1991, the country adopted the WHO TB control strategy (DOTS, directly-observed treatment, short-course) as part of a broader Infectious and Endemic Disease Control (IEDC) Project. Over the past 7 years, this has expanded to become the largest DOTS Programme in the world, covering 1200 counties with over 500 million people. Free diagnosis is provided for all patients with symptoms of TB, and free treatment for those with sputum smear-positive disease. The data collected include reported cases (smear-positive or negative) seeking treatment and re-treatment, as well as the outcomes of short-course chemotherapy (completed treatment, cured, failed treatment, defaulted, died, transferred between health facilities).3 Individual patient records are even richer in information about the history of illness and treatment, including time and place of treatments, as well as personal data on age, sex, occupation and address.
To assess the impact of TB control, Styblo (ref. 3; Styblo K, World Health Organization, unpublished document) suggested calculating the ratio of re-treatment/new smear-positive cases (, or alternatively the re-treatment proportion,
. This is a simple and easily measurable indicator which falls in value in a good control programme because, properly-treated, drug-susceptible cases infrequently require more than a single course of drugs. But it has the major weakness that it cannot be directly related to the change in illness and death. For example, a fall in prevalence will be reflected by a fall in
, but we expect both T and N to change as a result of intervention, so we cannot calculate the change in prevalence knowing only the ratio. The general problem is that we do not yet have a formal description of the properties of this potentially useful index, so its precise meaning remains unclear.
Beginning with the notion that the re-treatment proportion provides a useful measure of the impact of TB control, our aim is to develop a more comprehensible method of measuring how effectively control programmes have reduced illness and deaths due to TB. The latter accounts for most of the burden in terms of years of healthy life lost. This paper concentrates on cases cured and deaths averted, using data from the first 7 years (19911997) of the Chinese DOTS Programme.
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Methods |
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Figure 1 depicts a simple model of the process of treatment and re-treatment for cases producing sputum smears that contain microscopically visible acid fast bacilli. New incident cases enter at the top of the diagram, and we assume that the rate at which they appear is constant through time. Most of these cases are presumed to seek treatment inside or outside the Programme, but some may die before being treated. A proportion of those who are treated will be cured (negative smear, or treatment completion), and the proportion depends on whether they are treated inside or outside the Programme. The rest fail, i.e. they have a persistently positive smear, they default (interrupt treatment), are transferred to another treatment facility, or die. Failures who do not die are likely to seek re-treatment, either inside or outside the Programme, and a proportion of these will also be cured. Again, the cure rate depends on the source of treatment, but re-treatment is generally less successful than primary treatment, partly because poor treatment selects for drug-resistant bacilli.3,4
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Sources of data
Technical details of the Chinese TB control Programme, and the epidemiological background, have been described elsewhere.2,3 The Programme provides, for each enrolled county in each quarter, the numbers of smear-positive cases reporting for primary treatment or re-treatment, and the numbers of these which are cured (negative smear after treatment completion), and which completed treatment, failed (positive smear after treatment completion), defaulted or died. Some cases deemed to have been cured as a result of the first course of treatment will later relapse. In the China control Programme, relapses have been recorded separately from other re-treatment' cases; relapses have been excluded from this analysis because they do not reflect Programme performance. These and all other case definitions within the Programme conform to WHO standards.3,4 Treatment success and case fatality rates outside the Programme have been estimated previously.2,3
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Results |
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The overall cure rate of smear-positive cases on first treatment increased from 50% (3565%) before the Programme to 85% (8298%) after the Programme had become established. The fatality rate of smear-positive cases decreased from 30% (2149%) to 6.1% (0.69.4%) over the same period. If performance were maintained at this level throughout the IEDC Programme area (in 1997, covering 564 million people living in half the country), the number of TB deaths would be reduced from 38 000 (29 00069 000) per year to 8600 (80013 000) per year. In other words, 30 000 (26 00059 000) or 81% (7798%) of deaths would be averted each year.
The assumption that all patients eventually seek treatment from the Programme is almost certainly incorrect, and means that pSp gives an overestimate of the case detection rate. A recent review1 of TB epidemiology in China estimated the country-wide smear-positive incidence rate to be 51/100 000/year (range 4970/100 000/year) in 1997. Using this higher estimate gives the adjusted Figures in the final column of Table 2. The case detection rate (pSp) falls to 49% (3651%), and the overall cure rate from primary treatment to 65% (6377%). The fatality rate of smear-positive cases falls from 30% before the Programme to 15% (1126%) in 1997; that is, an estimated 47% (3756%) of deaths were prevented, revised downwards from 81%, though the number prevented remained the same.
Sensitivity analysis5,6 reveals that the estimated number of deaths averted is most influenced by uncertainty over b, the equilibrium value of the re-treatment proportion (partial rank correlation coefficient 0.77), and by c, the rate at which that equilibrium is reached (PRCC 0.49). The estimated number of deaths averted was much less sensitive to other components of the model, including the ratio µ/r which ranged widely in value from 0.10.7 (Table 1).
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Discussion |
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There are four important qualifications to be attached to this finding. First, our analysis assumes that the re-treatment proportion has, following the introduction of the Programme in 1991, settled to a new, lower steady value (b). To achieve this, the Programme must impose an immediate change in the quality of TB control, and that change must have been in place long enough for a new equilibrium to be established. The data in Figure 3 indicate that counties which joined the Programme in 1991 are now close to equilibrium. However, model fitting has overestimated b for most provinces (8 out of 12 in Figure 5
) and across the whole Programme. In other words, our analysis is cautious and, for this reason, tends to underestimate the fraction of deaths averted.
Second, the new equilibrium value of R is most strongly influenced by data from the counties that have been enrolled in the Programme since 1991. The estimated number of deaths that could be saved by the whole Programme assumes that the same result on average will be obtained from all 1200 counties in the 12 IEDC provinces. There is no reason to believe that counties which enrolled earlier are different from the rest, but this remains to be seen. The number of cases found each year is still rising across the 12 provinces.
Third, our treatment-re-treatment model assumes that all smear-positive TB cases that are not cured will eventually seek treatment from the Programmethe model assigns to each patient a fixed probability of doing so after each treatment failure. However, there are certain to be some patients that will never be seen by the Programme. For this reason, the smear-positive case detection rate is probably lower than 77%. On the other hand, it is likely to be higher than the 49% obtained by applying the recent nationwide estimate of 51 new smear-positive cases/100 000/year. The reason is that incidence may have declined within the control Programme area since 1991, so that it is now less than the national average. Whatever the true case detection rate, it has no direct influence on the estimated number of deaths prevented: the 30 000 are either a small fraction of a large number, or a large fraction of a small number.
Fourth, the bigger question about falling incidence, if it is falling, is the extent to which it is due to reduced transmission. Our analysis calculates only the direct epidemiological benefits of treatment, and not the indirect benefits gained by preventing deaths of secondary cases. Dynamic transmission models7,8 could, in principle, be used to evaluate these extra, indirect benefits for China.
The re-treatment proportion could in principle be reduced to zero but it appears, across the 12 provinces (now 13, since the creation of Chongqing Municipality), to be settling to a lower value of about 13%. Since cure rates within the Programme are close to 100%, this implies that a proportion of smear-positive cases is first treated outside the Programme. In one county, Changshou (Chongqing Municipality), for which b = 19%, we examined the record cards of 288 patients seeking retreatment between 1994 and 1998. The majority (162/288, 58%) received primary treatment outside the county, 91 (33%) were first treated inside the county but outside the Programme, and 25 (9%) were first treated by the Programme. The re-treatment proportion therefore markedly understates the performance of the Programme within this county. Retreatment cases were mostly itinerant patients who were officially residents of Changshou, but who were living or working elsewhere at the time they became ill. They may have returned to Changshou because they were entitled to free treatment in their home county. It is doubtful that they could have been detected as new smear-positive cases, no matter how good the Programme in Changshou. Whether TB patients are usually charged for treatment away from their home counties, and whether patients who pay are more likely to default, are questions now under further investigation.
Having established here another measure of the effectiveness of the Chinese Programmeadding deaths prevented to the patient cure rate3we need to know the cost of achieving this success. The Programme was stimulated, in part, by a $55 million loan from the World Bank, matched by counterpart funds provided within China. However, the overall cost/death prevented, and the relative contributions of external and internal funding, have not yet been assessed. It is vital that the economics of this Programme are better understood as external funding comes to an end in the year 2000. The costs and cost-effectiveness of short-course chemotherapy against tuberculosis in China need to be compared with estimates from other TB control programmes,9 and from other health interventions,10 so that TB control can be assigned the correct priority and properly-financed within China.
Finally, China is not alone in reporting the numbers of TB cases seeking treatment and re-treatment, and our method for estimating deaths prevented can in principle be applied to control programmes in other countries. Although the impact of control operations on tuberculosis burden is potentially large it has rarely been quantified; wider application of the technique described here would help to measure the effectiveness of TB control in a variety of different settings.
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Appendix |
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![]() | (1) |
where indicates differentiation with respect to time (following Newton rather than Leibniz). Some cases fail treatment (1, the proportion cured), outside (subscript o) or inside the Programme (subscript p), and are thereby recruited to two classes of failures, Fo and Fp. They remain here until they successfully seek retreatment (per capita rates r
), or die. The (weighted) average proportion of failures that is successfully treated inside and outside the Programme is
F = pFp
Fp + pFo
Fo. Therefore,
![]() | (2) |
![]() | (3) |
Cure is a dead-end state in this model (Figure 1), and is implicit to equations (1)(3)
.
When solving these equations we can set S(0) = 1 by letting , since we will only be concerned with ratios in model fitting. The Programme measures T, the rate at which treatment failures present themselves:
![]() | (4) |
and N, the rate at which new smear positive cases present themselves:
![]() | (5) |
Note that T and N are rates (incidences) while S and F are numbers (prevalences). Initial and asymptotic values are obtained by setting equations 2 and 3 to zero and noting that, at time zero, immediately before the Programme starts, pSp = pFp= 0. This gives
![]() | (6) |
![]() | (7) |
![]() | (8) |
![]() | (9) |
Because the equations for Fo and Fp are independent of each other and we are assuming that S(t) is constant, we can solve for Fo + Fp analytically. Summing equations 2 and 3,
![]() | (10) |
Then, defining , we use equations 4 and 10
to get
![]() | (11) |
![]() | (12) |
and thus,
![]() | (13) |
Due to the introduction of a new control programme, the ratio converges exponentially (equation 13
) from an initial value of a,
![]() | (14) |
to an asymptote b,
![]() | (15) |
at a rate c,
![]() | (16) |
By fitting the data to an exponential curve with a non-zero asymptote we can estimate the three parameters a, b and c.
Epidemiological interpretation of the estimated parameters
In equations 14 and 15 we have seven parameters: two probabilities pSp and pFp (which determine pSo and pFo), four proportions
Sp,
Fp,
So and
Fo, and
, the ratio of the mortality rate to the retreatment rate. With two equations we need a further five constraints. By fixing the four proportions and the ratio
we can solve for p Sp and pFp:
![]() | (17) |
![]() | (18) |
![]() | (19) |
The procedure for parameter estimation is then: (1) Fit an exponential curve to the data using equation 4 to calculate
in terms of the three coefficients a, b and c. (2) Use this to calculate
. (3) Fit the curve
to the data by maximum likelihood11 in order to determine the values and covariance matrix of a, b and c.
A Monte Carlo procedure, carried out with @Risk software (Palisade Corporation), was used to determine the sampling distributions of pSp, pFp and r allowing: (1) a and b (and for the estimation of r, c also) to follow bivariate normal distributions based on the estimated values and covariances, (2) Sp and
Fp to follow independent normal distributions based on Programme estimates, (3)
So and
Fo to follow triangular distributions derived from knowledge of their likely values.
The overall proportion of cases that is cured once the Programme has reached a steady state is:
![]() | (20) |
and the proportion cured before the Programme has started is:
![]() | (21) |
In terms of the fitted parameters:
![]() | (22) |
![]() | (23) |
Again Monte Carlo methods can be used to determine each of these and their sampling distributions, noting that 1 P is the proportion of the initial smear positive cases that dies (the case fatality rate) under each scenario. Each point estimate obtained by Monte Carlo methods is the mode of a distribution obtained from 10 000 simulations, with 5th and 95th centiles used as lower and upper bounds.
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Acknowledgments |
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References |
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