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Critical value of prevalence for vaccination programmes. The case of hepatitis A vaccination in Spain
Vaccine, Vol. 15, No. 12/13, pp. 1445-1450. 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0264+410X/97 $17+0.00
PII: SO264-410X(97)00058-3 ELSEVIER
Critical value of prevalence for vaccination programmes. The case of hepatitis A vaccination in Spain Pedro
Plans Rub%*
Programmes using screening and vaccination are ejficient in populations with higher levels of antibodies, while in those with lower levels is more eficient to vaccine the whole target population. The prevalence that makes the cost-effectiveness of vaccination programmes equal to that obtained for programmes using screening and vaccination is dejined as the critical value of prevalence p”. In this study, a mathematical procedure to obtain the critical value of prevalence is developed. The formula obtained is used to decide the best vaccination strategy against hepatitis A in Spain. If V is the vaccination cost, S the screening cost, PV the predictive value of a positive test result, D the mean disease cost, A the attack rate in susceptible individuals, E the vaccine efJicacy and C the vaccination compliance, the critical value of prevalence is equal to: s
‘* = V-((I
-PV)DAEC)
S
= V-AD
The critical value of prevalence obtained for vaccination against hepatitis A in Spain with three doses of vaccine Havrix 720 is 22%. This result show that the optimal decision is to implement vaccination programmes without screening for immunity in individuals aged < 15 years and with screening in those aged > 15 years. 0 1997 Elsevier Science Ltd. Keywords: vaccination
programmes;
critical prevalence; hepatitis A; evaluative studies
analysis is used to assess efficiency vaccination programmes. Programmes using of screening for immunity and vaccination of susceptible individuals can reduce waste of vaccines when the prevalence of protected individuals in the population is high. The value of prevalence that makes the costeffectiveness of vaccination programmes equal to that obtained for programmes using screening and vaccination can be defined as the critical value of prevalence. Cost-effectiveness studies obtain this value of prevalence comparing cost-effectiveness ratios of vaccination strategies for different antibody prevalences’.
Cost-effectiveness
In this study, a mathematical procedure to obtain the critical value of prevalence is developed. The formula obtained is used to the decide the best vaccination strategy against hepatitis A infection in Spain.
*Evaluation
unit, General Direction of Public Health, Department of Health, Travessera de les Cork 131-159, 08028 Barcelona, Spain. (Received 1 July 1996; revised version received 13 January 1997; accepted 12 February 1997)
SCREENING
TEST FOR ANTIBODIES
When a group of individuals is against an infectious disease, population into four categories: positive (b), true negative (c) (Table I). The prevalence of
screened for immunity the test divides the true positive (a), false and false negative (d) antibodies (p) is the
Table 1 Classification of screening results True
category
Positive
Negative
Total
Positive
a
Negative Total
C
b d b+d
a+b c+d n
a+c
individuals with a positive test result individuals with a negative test result true protected individuals true unprotected individuals p = prevalence of antibodies = (a + b)/n Pr = prevalence of true protected individuals
a+b c+ d a +b b +d
= = = =
= (a +c)/n
Vaccine 1997 Volume 15 Number 12/13
1445
Critical vafue of prevalence proportion result:
of screened
for vaccination
individuals
programmes:
with a positive
a4 p=-.
test
(1)
I1
P. Plans RubiC, True negative:
( I ~ Pr)Sp
(10)
False negative:
Pr( I -Sr).
(11)
The prevalence of true protected individuals in the population derived from these equations and the prevalcncc of antibodies (1’) is equal to:
The prevalence of true protected individuals (Pr) in the target population is the proportion of individuals with a true positive and false negative test result:
p - sp - I Pr= Se-S/l-
The sensitivity (Se) of the test is detincd as the ability of the test to identify correctly those who are protected. It is equal to the proportion of protected individuals the test classifies as positive:
The specificity (S[>) of the test, on the other hand, is defined as the ability of the test to identify correctly those who are unprotected. It is equal to the proportion of unprotected individuals the test classifies as negative:
The predictive value of a positive test (Pv) is the proportion of individuals with a positive test result who are protected: PV=A and the predictive value of a negative test (PV-) is the proportion of individuals with a negative result who are unprotected:
CRITICAL VALUE OF PREVALENCE VACCINATION STRATEGIES
Predictive values depends on both the operating characteristics and the prevalence of true protected individuals in the population (Pr). The predictive value of a positive test result (Pv) is:
C,.= VN
Pr&+(
1 - PR)( I - Sp)
1446
CIE, =
pSN+(S+V)(
(13
E I -p)N
C/E,., = E
- AD,, (16)
Disease costs reduced with vaccination (AD,) and screening and vaccination (AD,,) depends on the prevalence of true unprotected individuals in the population (I -Pr), the attack rate in susceptible individuals (A), the mean disease cost (D), the vaccine efficacy (E) and the programme compliance (C):
Pr.Se
(8)
AD, = (I - Pr)NDAEC
(17)
(I ~ Pr)( 1 -Sp)
(9)
AD,,,= (1 - Pr)SpNDAEC
(18)
True positive: False positive:
(14)
VN-AD,
(7)
The true positive rate is the proportion of protected individuals the test classifies correctly as positive, the false positive rate is the proportion of unprotected individuals the test classifies incorrectly as positive, the true negative rate is the proportion of unprotected individuals the test classifies correctly as unprotected, and the false negative rate is the proportion of unprotected individuals the test classifies incorrectly as negative’. These rates can be obtained from the following formulas:
(13) I - p)N.
The net cost of these programmes is obtained from the total programme cost less averted disease cost due to disease prevention. If AD, and AD,, denote averted disease costs from vaccination and from screening and vaccination, respectively, and E denotes effectiveness, cost-effectiveness of vaccination (C/E,) and screening and vaccination (C/E,,) is equal to:
PrSe PV=
FOR
The critical value of prevalence p* that makes costeffectiveness of vaccination programmes equal to that obtained for programmcs using screening and vaccination is used to decide the best vaccination strategy. The optimal decision is to vaccinate the whole target population when the prevalence of positive test results is lower than the critical value of prevalence, and to screen the whole target population and vaccinate susceptible individuals when the prevalence of positive test results is higher than the critical value. The critical value of prevalence can be derived from a mathematical procedure which takes into account clinical, epidemiological and economical information. The cost-effectiveness of each alternative vaccination strategies is defined as the net programme cost divided by the effectiveness. The cost of vaccinating the whole population (C,) and the cost of screening and vaccinating of susceptible individuals (C,,,) depends on the vaccination cost (C), the screening cost (S), the number of individuals in the target population (N). and the prevalence of individuals with a positive test result @)I
C,, = pSN+(S+V)( PV-=A.
(12)
I
Vaccine 1997 Volume 15 Number 12/l 3
Critical value of prevalence Since the prevalence of true unprotected individuals is equal to the prevalence of true negative and false positive test results [eqn (lo)] 1 -Pr in [eqn (IS)] is: I -Pr=(l
-Pr)Sp-(I
Substituting the value of equation, AD, is equal to: AD,.= (( I -Pr)Sp+(
-Pr)(I 1 -Pr
I -Pr)(
AD,.= (I - Pr)SpNDAEC+(
I -Pr)(
-Sp).
in eqn
(13 (18)
by this
I -Sp))NDAEC
(2W
I -Sp)NDAEC
(21)
AD, = AD,,+( I - Pr)( I -Sp)NDAEC
AD,, =AD,-(
I -Pr)(
(22)
I --Sp)NDAEC.
(23)
This equation shows that averted disease costs with screening and vaccination arc lower than those reduced with vaccination because costs are not reduced in individuals with a false positive test result. Substituting the false positive rate, (1 -Pr)(l -Sp), be the prevalence of antibodies (p) multiplied by one less the predictive value of a positive test (1 - Pv), AD,, is equal to: AD,,. = AD, - p( I - PV)NDAEC
and if AD denotes
(1 - PV)NDAEC,
(24)
AD,,
is:
AD,, = AD, ~ p AD.
(25)
The critical value of prevalence is derived from eqn (15) and eqn (16). Assuming an equal effectiveness for both vaccination strategies, substituting AD,, in eqn (16) by eqn (25) and dividing by N both formulas, the critical value of prevalence p* is derived from the following equation: pS+[(S+V)(I
The critical mathematical
-p)]-(AD,--AD)=
value of procedure
prevalence is:
S P*=v_AD.
V-AD,,.
derived
(26)
from
this
for vaccination
programmes:
P. Plans Rubid
protected against hepatitis A while in 1995 this percentage was 5%‘. A seroepidemiological survey carried out in a representative sample of the adult population of Catalonia in 1995 detected a prevalence of anti-HAV of 31% in the age group of 15-24years, 72% in the age group of 25-44years, 97% in the age group of 45-64 years and 99% in those aged > 64 years’. In the age group of 15-24 years the prevalence of anti-HAV decreased from 43% in 1989 to x 31% in 1995. Exposure to HAV is now less common during childhood resulting in a greater number of unprotected adolescent and young adults and a higher risk for serious complications and fulminant hepatitis A”-‘. Two vaccination strategies are available to protect this increasing number of susceptible individuals in the adult population of Catalonia: to vaccine the whole target population; and to screen for anti-HAV and vaccine susceptible individuals. If the objective of the is to protect the whole population of programme the best immunization strategy is to Catalonia. vaccinate all individuals in the age groups with a prevalence of positive test results lower than the critical value of prevalence, and to screen the whole target group and vaccinate susceptible individuals in those age groups with a prevalence of positive test results higher than the critical value. Epidemiological, clinical and economical information is used to calculate the critical value of prevalence in Catalonia (Table 2). Hepatitis A vaccine (Havrix, 720 ELISA units) is administered in two doses at 0 and 1 month and a booster dose 12 months later. The
Table 2 Clinical and epidemiological information used to estimate cost-effectiveness of vaccination programmes against hepatitis A
Economic data (US$): 22 5 15
Vaccination Havrix 720 Vaccine administration Screening
Treatment casts (lJS$):
(27)
CASE OF HEPATITIS A VACCINATION IN SPAIN
THE
Hepatitis A is an inflammatory disease of the liver caused by hepatitis A virus (HAV). In very low endemic regions, such as the Scandinavian countries, the prevalence of anti-HAV is ~20% and the attack rate in susceptibles is <0.003%, while in moderate endemic regions, such as the Southern, Central and Eastern European countries, the prevalence of antiHAV is > 40% and the attack rate is ca O.O1%3-s. In in north-west of S ain with Catalonia, a region P 6 million inhabitants, the attack rate is 0.05%‘. In the last 20years, the epidemiology of hepatitis A infection has been changing in Spain with a continuous decline in the incidence of infection. The prevalence of individuals susceptible to hepatitis A infection at younger ages has been consistently increasing since 1980. In 1985, 13% of individuals aged 6-13 years were
196 229 2344 4045 245
Mild hepatitis Moderate hepatitis Severe hepatitis Fulminant hepatitis Relapsing hepatitis
Clinical data (%): 90 50 30 19.9 0.1
Symptomatic hepatitis Mild hepatitis Moderate hepatitis Severe hepatitis Fulminant hepatitis Relapsing after: Mild hepatitis Moderate hepatitis Severe hepatitis
9 7 2
Compliance (%): 100 75
First dose Second dose and booster dose Screening data (%): Sensitivity Specificity
99 99
Attack rate (%): Vaccination
0.005
efficacy (%):
Vaccine
1997 Volume
90
15 Number 12/13
1447
following assumptions are taken into account: 90% for vaccination efficacy at the primary health care centresV 100%
s
s
“:=v--nD
=V-[(I
-PV)DAEC]
The value of AD is equal to ( I -PV)DAEC, with PI/ being the predictive value of a positive test, D the mean disease cost, A the attack rate, E the vaccine efficacy and C the vaccination compliance. The mean disease costs (D) for hepatitis A infection according to the distribution of hepatitis A in Catalonia” and disease costs”.” is equal to $588.9. The vaccination cost (v) is equal to: = 27 x I+27 x 0.75+27
V = V,C,+VzC:+VCj
x 0.75
= US$67.5. The predictive value of a positive test is obtained from the prevalence of true protected individuals in the population, the prevalence of antibodies and the operating characteristics of the screening test [eqn (7) and (12)]. The prevalence of true protected individuals in the population obtained for a prevalence of antibodies of 30% and a 99% sensitivity and specificity obtained from eqn (12) is: Pr=
p+sp-
I
0.3+0.99 - I
= 0.29
Se+Sp - I = 0.99+0.99 - I and the predictive value obtained from eqn (7) is:
of
a
positive
(PV)
0.29 0.99
PrSe PV=
test
PrSe+( I - Pr)( 1 -Sp)
= 0.3 0.99+0.7 1 0.01
= 0.98. The value therefore:
obtained
for the
correction
factor
AD
is
Table 3 More efficient vaccination A infection in Spain
programmes
against hepatitis
Prevalence of anti-HAV Age
%
Cl
More efficient vaccination
Men 6-7 10-11 13-14 15-24 25-34 35-44 45-54 55-64 > 64
3.2 4.1 8.6 35.0 55.0 85.6 97.9 99.0 98.4
1.7-4.7 2.8-5.4 6.7-l 0.5 22.9-47.1 46.1-63.9 78.9-92.3 95.9-99.9 97.1-100 96.2-100
Vaccination Vaccination Vaccination Screening Screening Screening Screening Screening Screening
and and and and and and
vaccination vaccination vaccination vaccination vaccination vaccination
Women 6-7 10-11 13-14 15-24 25-34 35-44 45-54 55-64 > 64
3.2 4.1 8.6 27.6 59.4 88.1 93.7 99.2 99.2
1.7-4.7 2.8-5.4 6.7-10.5 16.1-39.1 49.6-69.2 82.3-93.9 89.5-97.9 97.6-100 97.9-100
Vaccination Vaccination Vaccination Screening and Screening and Screening and Screening and screening and Screening and
vaccination vaccination vaccination vaccination vaccination vaccination
strategy
Prevalence of antibodies for HAV in 1994; Cl, 95% confidence interval of the prevalence of anti-HAV
risk for hepatitis A infection, the optimal decision is to vaccine all individuals aged < 15 years and to screen and vaccine susceptible individuals aged > 15 years (T&e 3). Sensitivity analysis has been carried out in order to assess the effects of the vaccination strategy on the critical value of prevalence (Table 4). The value of prevalence is sensitive to variations in screening and vaccination costs, while it is less sensitive to variations in the variables taken into account to calculate the correction factor AD: predictive value of a positive test result, sensitivity and specificity of the screening test, mean disease cost, attack rate, vaccine efficacy and programme compliance. When screening and vaccination costs increases or decreases by IO%, the value of prevalence increases or decreases by 10%. When compliance for the second and booster dose varied from 75% to 60 and 90% ( ?20%), the value of prevalence changed by +13 and - 1l%, respectively. Using only two doses of vaccine the critical value of prevalence increases to 31.7% due to the lower cost of the vaccination programme. The value for the correction factor AD is very low, and decisions about the best vaccination strategy depends only on vaccination and screening costs.
AD = 0.02 x 588.9 x 0.00005 x 0.9 x 0.75 = 0.0004. The critical (27) is:
value
of mevalence
s ‘* =V--AD
D* derived
1
I5
from
eqn
= 0.222.
=67.5 -0.0004
p* = 22.2% If a programme of vaccination against hepatitis A is at implemented in Catalonia to protect all individuals
1448
Vaccine
1997 Volume 15 Number 12/13
DISCUSSION Cost-effectiveness analysis of immunization programmes can be carried out taking into account clinical and epidemiological information presented in this study, but also the duration of immunity, survival probability according to disease outcomes and life tables of the target population. These information is not always available and cost-effectiveness ratios arc calculated with a decision-analysis programme. When the question is whether to vaccine the whole target
Critical value of prevalence Table 4
Sensitivity
analysis
for the critical
value
of prevalence
@*) Variable
p* (%) Change (%)
Study result
22.2
Vaccination +lo% -10%
costs: 20.2 24.7
-10 f10
24.4 20.0
+lO -10
Screening costs: +lO% -10% Predictive value of a positive test: +lO% -10% Specificity: 100%
95% Sensitivity: 100%
95% Attack rate: 0.001% 0.01% Compliance 90% 60%
for the second and booster dose:
Vaccination
with only two doses:
22.2 22.2
0 0
22.2 22.2
0 0
22.2 22.2
0 0
22.2 22.2
0 0
19.8 25.2
-11 +13
31.7
+43
or to screen and vaccine only susceptible individuals, the critical value of prevalence p* can be obtained using the formula developed in this study. Sensitivity analysis carried out in this study shows that the value of prevalence is sensitive to variations in screening and vaccination costs, while it is less sensitive to variations in compliance and epidemiological information. The critical value of prevalence is sensitive to variations in vaccination compliance because this variable is related directly to the vaccination cost. Its effect on the correction factor of the formula, however, is very low. The duration of protection against hepatitis A infection is not taken into account because an equal duration of immunity and effectiveness is assumed for both vaccination strategies. If a programme of vaccination against hepatitis A is implemented in Catalonia with the objective to protect all individuals at risk for hepatitis A infection, the critical value of prevalence obtained in this study shows that the optimal decision is to vaccine all individuals aged < I5 years and to screen and vaccine susceptible individuals aged > 15 years (Table 3). If the 95% confidence interval of the prevalence of anti-HAV is taken into account, both strategies have a similar efficiency in the age group of 15-24 years. Passive immunization with immune globulin is only efficient for a short-term prophylaxis (3-6 months). For longer durations of protection passive immunization is not an efficient strategy because vaccination is safe, less expensive and provides protection for years. Bryan and Nelson’” developed a cost-analysis model to evaluate active and passive immunization when short-
group
for vaccination
programmes:
P. Plans Rubid
term protection against hepatitis A is required. This model incorporates the cost of hepatitis A vaccine, immune globulin and test for anti-HAV, and the prevalence of anti-HAV in the population. These authors found that passive immunization with immune globulin was less expensive than vaccination for a prophylaxis period < 6 months. Tormans et a/.” evaluated cost-effectiveness of hepatitis A prevention in travellers from Europe to high-endemic countries. These authors used a decisionanalysis model which incorporated clinical, epidemiological and economical information. Three alternative strategies were evaluated: passive immunization; vaccination of the whole target population; and screening and vaccination of susceptible individuals. Estimated costs were $43 for screening and $24 per dose of vaccine plus $15 for its administration. A 100% compliance was assumed for the first dose. 60% for the second one, and 50% for the booster dose. These authors found a critical value of prevalence of 55%. Using the formula developed in this study the value of prevalence obtained was 52.5% (43/81.9). This prevalence is higher than the value obtained in Spain because a cost of $43 was assumed for the screening. Reducing this cost to US$15 the value of prevalence is 18%. The formula developed in this study can be used to answer questions related to the efficiency of vaccination programmes with and without screening for antibodies. Cost-effectiveness analysis is an expensive evaluative method to assess efficiency of vaccination strategies which requires precise clinical, epidemiologIn most cases, ical and economical information. is not available and however, this information resources are not enough to carry out a cost-effectiveness analysis. The formula developed in this study can be used in these situations, reducing time and cost of the decision process. REFERENCES 1
5
6 7 8 9
10
Van Doorslaer, E., Tormans, G. and Van Damme, P. Costeffectiveness analysis of vaccination against hepatitis A in travellers. J. Med. Virol. 1994, 44, 463-469. Feinstein, AR. Clinical Epidemiology. W.B. Saunders, London, 1985. Papaevanqelou, G. Epidemiology of hepatitis A in Mediterranean cointries. Vacdine 1992,7-O, (suppI. l), S63-S66. Shaoiro. C.N.. Coleman. P.J.. McQuillan, G.M.. Alter, M.J. and Marbolis, H.S: Epidemidlogy of hepatitis A: seroepidemiology and risk groups in the USA. Vaccine 1992, 10, (suppl. l), S59-S62. Hadler, S.C. Global impact of hepatitis A virus infection: changing patterns. In: Viral Hepatitis and Liver Disease (Eds Hollinaer F.B.. Lemon S.M. and Maraolis H.S.). Williams and Wilkins, Baltimore, 1991, pp. 14-20. ’ Direcci6 General de Salut Ptiblica. Brots epidemics declarats a Catalunya I’any 1995. BEC 1996, 27, 108-l 23. Salleras, L., Bruguera, M. and Vidal, J. et a/. Cambio del patrbn epidemiol6gico de la hepatitis A en Esparia. Med. C/in. (Bare.) 1992, 99, 87-89. General Direction of Public Health Prevalencia de anficuerpos frente al virus de /a hepatitis A en Cataluria en 7994. Departament de Sanitat, Barcelona, 1996. Wiedermannn, G., Ambrosch, F. and Kollaritsch, H. et al. Safety and immunogenicity of an inactivated hepatitis A candidate vaccine in healthy adult volunteers. Vaccine 1990, 8, 581-584. Hadler, S.G. and Purcell, R.H. The prospects for immunizing against hepatitis A virus. In: New Vaccine Development, Vol. 1. National Academic Press, Washington, 1985. pp. 252-260.
Vaccine 1997 Volume 15 Number 12/13
1449
Critical value of prevalence 11
12 13
14
for vaccination
programmes:
Sjogren, M.H., Tanno, H.F., Sileoni, S., Cohen, B.D., Burke, D.S. and Feighny, R.J. Hepatitis A virus in stool during clinical relapse. Ann. Intern. Med. 1987, 106, 221-226. Cattilogo de Especialidades Farmactkticas. Coelgio Oficial de Farmactkticos de Espatia. C.O.F.E., Madrid, 1995. Polesky. H. and Hanson, M. Comparison of viral hepatitis marker test methods based on AABB-CAP survey data. Am. J. C/in. Pathol. 1981, 76, 521-524. Antonanzas, F., Forcen, T. and Garuz, R. Analisis coste-efecti-
1450
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1997 Volume 15 Number 12/13
P. Plans Rubid
15 16 17
vidad dela vacunacion frente al virus de la hepatitis. Med. C/in. @arc.) 1992, 99, 41-46. INSALUD. Informme econdmico-financiero de /a Seguridad Social 7987-7993. Ministerio de Sanidad, Madrid, 1994. Koff, R.S. Preventing hepatitis A infection in travellers to endemic areas. Am. J. Trap. Med. Hyg. 1995, 53, 586-590. Tormans, G., Van Damme, P. and Van Doorslaer, E. Costeffectiveness analysis of hepatitis A prevention in travellers. Vaccine 1992. 10, (suppl. 1). S88-592.
PII: SO264-410X(97)00058-3 ELSEVIER
Critical value of prevalence for vaccination programmes. The case of hepatitis A vaccination in Spain Pedro
Plans Rub%*
Programmes using screening and vaccination are ejficient in populations with higher levels of antibodies, while in those with lower levels is more eficient to vaccine the whole target population. The prevalence that makes the cost-effectiveness of vaccination programmes equal to that obtained for programmes using screening and vaccination is dejined as the critical value of prevalence p”. In this study, a mathematical procedure to obtain the critical value of prevalence is developed. The formula obtained is used to decide the best vaccination strategy against hepatitis A in Spain. If V is the vaccination cost, S the screening cost, PV the predictive value of a positive test result, D the mean disease cost, A the attack rate in susceptible individuals, E the vaccine efJicacy and C the vaccination compliance, the critical value of prevalence is equal to: s
‘* = V-((I
-PV)DAEC)
S
= V-AD
The critical value of prevalence obtained for vaccination against hepatitis A in Spain with three doses of vaccine Havrix 720 is 22%. This result show that the optimal decision is to implement vaccination programmes without screening for immunity in individuals aged < 15 years and with screening in those aged > 15 years. 0 1997 Elsevier Science Ltd. Keywords: vaccination
programmes;
critical prevalence; hepatitis A; evaluative studies
analysis is used to assess efficiency vaccination programmes. Programmes using of screening for immunity and vaccination of susceptible individuals can reduce waste of vaccines when the prevalence of protected individuals in the population is high. The value of prevalence that makes the costeffectiveness of vaccination programmes equal to that obtained for programmes using screening and vaccination can be defined as the critical value of prevalence. Cost-effectiveness studies obtain this value of prevalence comparing cost-effectiveness ratios of vaccination strategies for different antibody prevalences’.
Cost-effectiveness
In this study, a mathematical procedure to obtain the critical value of prevalence is developed. The formula obtained is used to the decide the best vaccination strategy against hepatitis A infection in Spain.
*Evaluation
unit, General Direction of Public Health, Department of Health, Travessera de les Cork 131-159, 08028 Barcelona, Spain. (Received 1 July 1996; revised version received 13 January 1997; accepted 12 February 1997)
SCREENING
TEST FOR ANTIBODIES
When a group of individuals is against an infectious disease, population into four categories: positive (b), true negative (c) (Table I). The prevalence of
screened for immunity the test divides the true positive (a), false and false negative (d) antibodies (p) is the
Table 1 Classification of screening results True
category
Positive
Negative
Total
Positive
a
Negative Total
C
b d b+d
a+b c+d n
a+c
individuals with a positive test result individuals with a negative test result true protected individuals true unprotected individuals p = prevalence of antibodies = (a + b)/n Pr = prevalence of true protected individuals
a+b c+ d a +b b +d
= = = =
= (a +c)/n
Vaccine 1997 Volume 15 Number 12/13
1445
Critical vafue of prevalence proportion result:
of screened
for vaccination
individuals
programmes:
with a positive
a4 p=-.
test
(1)
I1
P. Plans RubiC, True negative:
( I ~ Pr)Sp
(10)
False negative:
Pr( I -Sr).
(11)
The prevalence of true protected individuals in the population derived from these equations and the prevalcncc of antibodies (1’) is equal to:
The prevalence of true protected individuals (Pr) in the target population is the proportion of individuals with a true positive and false negative test result:
p - sp - I Pr= Se-S/l-
The sensitivity (Se) of the test is detincd as the ability of the test to identify correctly those who are protected. It is equal to the proportion of protected individuals the test classifies as positive:
The specificity (S[>) of the test, on the other hand, is defined as the ability of the test to identify correctly those who are unprotected. It is equal to the proportion of unprotected individuals the test classifies as negative:
The predictive value of a positive test (Pv) is the proportion of individuals with a positive test result who are protected: PV=A and the predictive value of a negative test (PV-) is the proportion of individuals with a negative result who are unprotected:
CRITICAL VALUE OF PREVALENCE VACCINATION STRATEGIES
Predictive values depends on both the operating characteristics and the prevalence of true protected individuals in the population (Pr). The predictive value of a positive test result (Pv) is:
C,.= VN
Pr&+(
1 - PR)( I - Sp)
1446
CIE, =
pSN+(S+V)(
(13
E I -p)N
C/E,., = E
- AD,, (16)
Disease costs reduced with vaccination (AD,) and screening and vaccination (AD,,) depends on the prevalence of true unprotected individuals in the population (I -Pr), the attack rate in susceptible individuals (A), the mean disease cost (D), the vaccine efficacy (E) and the programme compliance (C):
Pr.Se
(8)
AD, = (I - Pr)NDAEC
(17)
(I ~ Pr)( 1 -Sp)
(9)
AD,,,= (1 - Pr)SpNDAEC
(18)
True positive: False positive:
(14)
VN-AD,
(7)
The true positive rate is the proportion of protected individuals the test classifies correctly as positive, the false positive rate is the proportion of unprotected individuals the test classifies incorrectly as positive, the true negative rate is the proportion of unprotected individuals the test classifies correctly as unprotected, and the false negative rate is the proportion of unprotected individuals the test classifies incorrectly as negative’. These rates can be obtained from the following formulas:
(13) I - p)N.
The net cost of these programmes is obtained from the total programme cost less averted disease cost due to disease prevention. If AD, and AD,, denote averted disease costs from vaccination and from screening and vaccination, respectively, and E denotes effectiveness, cost-effectiveness of vaccination (C/E,) and screening and vaccination (C/E,,) is equal to:
PrSe PV=
FOR
The critical value of prevalence p* that makes costeffectiveness of vaccination programmes equal to that obtained for programmcs using screening and vaccination is used to decide the best vaccination strategy. The optimal decision is to vaccinate the whole target population when the prevalence of positive test results is lower than the critical value of prevalence, and to screen the whole target population and vaccinate susceptible individuals when the prevalence of positive test results is higher than the critical value. The critical value of prevalence can be derived from a mathematical procedure which takes into account clinical, epidemiological and economical information. The cost-effectiveness of each alternative vaccination strategies is defined as the net programme cost divided by the effectiveness. The cost of vaccinating the whole population (C,) and the cost of screening and vaccinating of susceptible individuals (C,,,) depends on the vaccination cost (C), the screening cost (S), the number of individuals in the target population (N). and the prevalence of individuals with a positive test result @)I
C,, = pSN+(S+V)( PV-=A.
(12)
I
Vaccine 1997 Volume 15 Number 12/l 3
Critical value of prevalence Since the prevalence of true unprotected individuals is equal to the prevalence of true negative and false positive test results [eqn (lo)] 1 -Pr in [eqn (IS)] is: I -Pr=(l
-Pr)Sp-(I
Substituting the value of equation, AD, is equal to: AD,.= (( I -Pr)Sp+(
-Pr)(I 1 -Pr
I -Pr)(
AD,.= (I - Pr)SpNDAEC+(
I -Pr)(
-Sp).
in eqn
(13 (18)
by this
I -Sp))NDAEC
(2W
I -Sp)NDAEC
(21)
AD, = AD,,+( I - Pr)( I -Sp)NDAEC
AD,, =AD,-(
I -Pr)(
(22)
I --Sp)NDAEC.
(23)
This equation shows that averted disease costs with screening and vaccination arc lower than those reduced with vaccination because costs are not reduced in individuals with a false positive test result. Substituting the false positive rate, (1 -Pr)(l -Sp), be the prevalence of antibodies (p) multiplied by one less the predictive value of a positive test (1 - Pv), AD,, is equal to: AD,,. = AD, - p( I - PV)NDAEC
and if AD denotes
(1 - PV)NDAEC,
(24)
AD,,
is:
AD,, = AD, ~ p AD.
(25)
The critical value of prevalence is derived from eqn (15) and eqn (16). Assuming an equal effectiveness for both vaccination strategies, substituting AD,, in eqn (16) by eqn (25) and dividing by N both formulas, the critical value of prevalence p* is derived from the following equation: pS+[(S+V)(I
The critical mathematical
-p)]-(AD,--AD)=
value of procedure
prevalence is:
S P*=v_AD.
V-AD,,.
derived
(26)
from
this
for vaccination
programmes:
P. Plans Rubid
protected against hepatitis A while in 1995 this percentage was 5%‘. A seroepidemiological survey carried out in a representative sample of the adult population of Catalonia in 1995 detected a prevalence of anti-HAV of 31% in the age group of 15-24years, 72% in the age group of 25-44years, 97% in the age group of 45-64 years and 99% in those aged > 64 years’. In the age group of 15-24 years the prevalence of anti-HAV decreased from 43% in 1989 to x 31% in 1995. Exposure to HAV is now less common during childhood resulting in a greater number of unprotected adolescent and young adults and a higher risk for serious complications and fulminant hepatitis A”-‘. Two vaccination strategies are available to protect this increasing number of susceptible individuals in the adult population of Catalonia: to vaccine the whole target population; and to screen for anti-HAV and vaccine susceptible individuals. If the objective of the is to protect the whole population of programme the best immunization strategy is to Catalonia. vaccinate all individuals in the age groups with a prevalence of positive test results lower than the critical value of prevalence, and to screen the whole target group and vaccinate susceptible individuals in those age groups with a prevalence of positive test results higher than the critical value. Epidemiological, clinical and economical information is used to calculate the critical value of prevalence in Catalonia (Table 2). Hepatitis A vaccine (Havrix, 720 ELISA units) is administered in two doses at 0 and 1 month and a booster dose 12 months later. The
Table 2 Clinical and epidemiological information used to estimate cost-effectiveness of vaccination programmes against hepatitis A
Economic data (US$): 22 5 15
Vaccination Havrix 720 Vaccine administration Screening
Treatment casts (lJS$):
(27)
CASE OF HEPATITIS A VACCINATION IN SPAIN
THE
Hepatitis A is an inflammatory disease of the liver caused by hepatitis A virus (HAV). In very low endemic regions, such as the Scandinavian countries, the prevalence of anti-HAV is ~20% and the attack rate in susceptibles is <0.003%, while in moderate endemic regions, such as the Southern, Central and Eastern European countries, the prevalence of antiHAV is > 40% and the attack rate is ca O.O1%3-s. In in north-west of S ain with Catalonia, a region P 6 million inhabitants, the attack rate is 0.05%‘. In the last 20years, the epidemiology of hepatitis A infection has been changing in Spain with a continuous decline in the incidence of infection. The prevalence of individuals susceptible to hepatitis A infection at younger ages has been consistently increasing since 1980. In 1985, 13% of individuals aged 6-13 years were
196 229 2344 4045 245
Mild hepatitis Moderate hepatitis Severe hepatitis Fulminant hepatitis Relapsing hepatitis
Clinical data (%): 90 50 30 19.9 0.1
Symptomatic hepatitis Mild hepatitis Moderate hepatitis Severe hepatitis Fulminant hepatitis Relapsing after: Mild hepatitis Moderate hepatitis Severe hepatitis
9 7 2
Compliance (%): 100 75
First dose Second dose and booster dose Screening data (%): Sensitivity Specificity
99 99
Attack rate (%): Vaccination
0.005
efficacy (%):
Vaccine
1997 Volume
90
15 Number 12/13
1447
following assumptions are taken into account: 90% for vaccination efficacy at the primary health care centresV 100%
s
s
“:=v--nD
=V-[(I
-PV)DAEC]
The value of AD is equal to ( I -PV)DAEC, with PI/ being the predictive value of a positive test, D the mean disease cost, A the attack rate, E the vaccine efficacy and C the vaccination compliance. The mean disease costs (D) for hepatitis A infection according to the distribution of hepatitis A in Catalonia” and disease costs”.” is equal to $588.9. The vaccination cost (v) is equal to: = 27 x I+27 x 0.75+27
V = V,C,+VzC:+VCj
x 0.75
= US$67.5. The predictive value of a positive test is obtained from the prevalence of true protected individuals in the population, the prevalence of antibodies and the operating characteristics of the screening test [eqn (7) and (12)]. The prevalence of true protected individuals in the population obtained for a prevalence of antibodies of 30% and a 99% sensitivity and specificity obtained from eqn (12) is: Pr=
p+sp-
I
0.3+0.99 - I
= 0.29
Se+Sp - I = 0.99+0.99 - I and the predictive value obtained from eqn (7) is:
of
a
positive
(PV)
0.29 0.99
PrSe PV=
test
PrSe+( I - Pr)( 1 -Sp)
= 0.3 0.99+0.7 1 0.01
= 0.98. The value therefore:
obtained
for the
correction
factor
AD
is
Table 3 More efficient vaccination A infection in Spain
programmes
against hepatitis
Prevalence of anti-HAV Age
%
Cl
More efficient vaccination
Men 6-7 10-11 13-14 15-24 25-34 35-44 45-54 55-64 > 64
3.2 4.1 8.6 35.0 55.0 85.6 97.9 99.0 98.4
1.7-4.7 2.8-5.4 6.7-l 0.5 22.9-47.1 46.1-63.9 78.9-92.3 95.9-99.9 97.1-100 96.2-100
Vaccination Vaccination Vaccination Screening Screening Screening Screening Screening Screening
and and and and and and
vaccination vaccination vaccination vaccination vaccination vaccination
Women 6-7 10-11 13-14 15-24 25-34 35-44 45-54 55-64 > 64
3.2 4.1 8.6 27.6 59.4 88.1 93.7 99.2 99.2
1.7-4.7 2.8-5.4 6.7-10.5 16.1-39.1 49.6-69.2 82.3-93.9 89.5-97.9 97.6-100 97.9-100
Vaccination Vaccination Vaccination Screening and Screening and Screening and Screening and screening and Screening and
vaccination vaccination vaccination vaccination vaccination vaccination
strategy
Prevalence of antibodies for HAV in 1994; Cl, 95% confidence interval of the prevalence of anti-HAV
risk for hepatitis A infection, the optimal decision is to vaccine all individuals aged < 15 years and to screen and vaccine susceptible individuals aged > 15 years (T&e 3). Sensitivity analysis has been carried out in order to assess the effects of the vaccination strategy on the critical value of prevalence (Table 4). The value of prevalence is sensitive to variations in screening and vaccination costs, while it is less sensitive to variations in the variables taken into account to calculate the correction factor AD: predictive value of a positive test result, sensitivity and specificity of the screening test, mean disease cost, attack rate, vaccine efficacy and programme compliance. When screening and vaccination costs increases or decreases by IO%, the value of prevalence increases or decreases by 10%. When compliance for the second and booster dose varied from 75% to 60 and 90% ( ?20%), the value of prevalence changed by +13 and - 1l%, respectively. Using only two doses of vaccine the critical value of prevalence increases to 31.7% due to the lower cost of the vaccination programme. The value for the correction factor AD is very low, and decisions about the best vaccination strategy depends only on vaccination and screening costs.
AD = 0.02 x 588.9 x 0.00005 x 0.9 x 0.75 = 0.0004. The critical (27) is:
value
of mevalence
s ‘* =V--AD
D* derived
1
I5
from
eqn
= 0.222.
=67.5 -0.0004
p* = 22.2% If a programme of vaccination against hepatitis A is at implemented in Catalonia to protect all individuals
1448
Vaccine
1997 Volume 15 Number 12/13
DISCUSSION Cost-effectiveness analysis of immunization programmes can be carried out taking into account clinical and epidemiological information presented in this study, but also the duration of immunity, survival probability according to disease outcomes and life tables of the target population. These information is not always available and cost-effectiveness ratios arc calculated with a decision-analysis programme. When the question is whether to vaccine the whole target
Critical value of prevalence Table 4
Sensitivity
analysis
for the critical
value
of prevalence
@*) Variable
p* (%) Change (%)
Study result
22.2
Vaccination +lo% -10%
costs: 20.2 24.7
-10 f10
24.4 20.0
+lO -10
Screening costs: +lO% -10% Predictive value of a positive test: +lO% -10% Specificity: 100%
95% Sensitivity: 100%
95% Attack rate: 0.001% 0.01% Compliance 90% 60%
for the second and booster dose:
Vaccination
with only two doses:
22.2 22.2
0 0
22.2 22.2
0 0
22.2 22.2
0 0
22.2 22.2
0 0
19.8 25.2
-11 +13
31.7
+43
or to screen and vaccine only susceptible individuals, the critical value of prevalence p* can be obtained using the formula developed in this study. Sensitivity analysis carried out in this study shows that the value of prevalence is sensitive to variations in screening and vaccination costs, while it is less sensitive to variations in compliance and epidemiological information. The critical value of prevalence is sensitive to variations in vaccination compliance because this variable is related directly to the vaccination cost. Its effect on the correction factor of the formula, however, is very low. The duration of protection against hepatitis A infection is not taken into account because an equal duration of immunity and effectiveness is assumed for both vaccination strategies. If a programme of vaccination against hepatitis A is implemented in Catalonia with the objective to protect all individuals at risk for hepatitis A infection, the critical value of prevalence obtained in this study shows that the optimal decision is to vaccine all individuals aged < I5 years and to screen and vaccine susceptible individuals aged > 15 years (Table 3). If the 95% confidence interval of the prevalence of anti-HAV is taken into account, both strategies have a similar efficiency in the age group of 15-24 years. Passive immunization with immune globulin is only efficient for a short-term prophylaxis (3-6 months). For longer durations of protection passive immunization is not an efficient strategy because vaccination is safe, less expensive and provides protection for years. Bryan and Nelson’” developed a cost-analysis model to evaluate active and passive immunization when short-
group
for vaccination
programmes:
P. Plans Rubid
term protection against hepatitis A is required. This model incorporates the cost of hepatitis A vaccine, immune globulin and test for anti-HAV, and the prevalence of anti-HAV in the population. These authors found that passive immunization with immune globulin was less expensive than vaccination for a prophylaxis period < 6 months. Tormans et a/.” evaluated cost-effectiveness of hepatitis A prevention in travellers from Europe to high-endemic countries. These authors used a decisionanalysis model which incorporated clinical, epidemiological and economical information. Three alternative strategies were evaluated: passive immunization; vaccination of the whole target population; and screening and vaccination of susceptible individuals. Estimated costs were $43 for screening and $24 per dose of vaccine plus $15 for its administration. A 100% compliance was assumed for the first dose. 60% for the second one, and 50% for the booster dose. These authors found a critical value of prevalence of 55%. Using the formula developed in this study the value of prevalence obtained was 52.5% (43/81.9). This prevalence is higher than the value obtained in Spain because a cost of $43 was assumed for the screening. Reducing this cost to US$15 the value of prevalence is 18%. The formula developed in this study can be used to answer questions related to the efficiency of vaccination programmes with and without screening for antibodies. Cost-effectiveness analysis is an expensive evaluative method to assess efficiency of vaccination strategies which requires precise clinical, epidemiologIn most cases, ical and economical information. is not available and however, this information resources are not enough to carry out a cost-effectiveness analysis. The formula developed in this study can be used in these situations, reducing time and cost of the decision process. REFERENCES 1
5
6 7 8 9
10
Van Doorslaer, E., Tormans, G. and Van Damme, P. Costeffectiveness analysis of vaccination against hepatitis A in travellers. J. Med. Virol. 1994, 44, 463-469. Feinstein, AR. Clinical Epidemiology. W.B. Saunders, London, 1985. Papaevanqelou, G. Epidemiology of hepatitis A in Mediterranean cointries. Vacdine 1992,7-O, (suppI. l), S63-S66. Shaoiro. C.N.. Coleman. P.J.. McQuillan, G.M.. Alter, M.J. and Marbolis, H.S: Epidemidlogy of hepatitis A: seroepidemiology and risk groups in the USA. Vaccine 1992, 10, (suppl. l), S59-S62. Hadler, S.C. Global impact of hepatitis A virus infection: changing patterns. In: Viral Hepatitis and Liver Disease (Eds Hollinaer F.B.. Lemon S.M. and Maraolis H.S.). Williams and Wilkins, Baltimore, 1991, pp. 14-20. ’ Direcci6 General de Salut Ptiblica. Brots epidemics declarats a Catalunya I’any 1995. BEC 1996, 27, 108-l 23. Salleras, L., Bruguera, M. and Vidal, J. et a/. Cambio del patrbn epidemiol6gico de la hepatitis A en Esparia. Med. C/in. (Bare.) 1992, 99, 87-89. General Direction of Public Health Prevalencia de anficuerpos frente al virus de /a hepatitis A en Cataluria en 7994. Departament de Sanitat, Barcelona, 1996. Wiedermannn, G., Ambrosch, F. and Kollaritsch, H. et al. Safety and immunogenicity of an inactivated hepatitis A candidate vaccine in healthy adult volunteers. Vaccine 1990, 8, 581-584. Hadler, S.G. and Purcell, R.H. The prospects for immunizing against hepatitis A virus. In: New Vaccine Development, Vol. 1. National Academic Press, Washington, 1985. pp. 252-260.
Vaccine 1997 Volume 15 Number 12/13
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Critical value of prevalence 11
12 13
14
for vaccination
programmes:
Sjogren, M.H., Tanno, H.F., Sileoni, S., Cohen, B.D., Burke, D.S. and Feighny, R.J. Hepatitis A virus in stool during clinical relapse. Ann. Intern. Med. 1987, 106, 221-226. Cattilogo de Especialidades Farmactkticas. Coelgio Oficial de Farmactkticos de Espatia. C.O.F.E., Madrid, 1995. Polesky. H. and Hanson, M. Comparison of viral hepatitis marker test methods based on AABB-CAP survey data. Am. J. C/in. Pathol. 1981, 76, 521-524. Antonanzas, F., Forcen, T. and Garuz, R. Analisis coste-efecti-
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15 16 17
vidad dela vacunacion frente al virus de la hepatitis. Med. C/in. @arc.) 1992, 99, 41-46. INSALUD. Informme econdmico-financiero de /a Seguridad Social 7987-7993. Ministerio de Sanidad, Madrid, 1994. Koff, R.S. Preventing hepatitis A infection in travellers to endemic areas. Am. J. Trap. Med. Hyg. 1995, 53, 586-590. Tormans, G., Van Damme, P. and Van Doorslaer, E. Costeffectiveness analysis of hepatitis A prevention in travellers. Vaccine 1992. 10, (suppl. 1). S88-592.