Vaccine - (Page 3) 6158 M. Oviedo et al. / Vaccine 26 (2008) 6157–6164 universal vaccination programme was 97% (95% CI: 78.5–99.6) in an evaluation made at 3 years [11]. Although the reduction in the vaccinated group was substantial, statistical models are necessary in order to differentiate the reduction attributable to vaccination and that due to other factors, such as time and the age of infected people. The negative binomial regression model [13] is proposed to evaluate the vaccination programme and make future predictions. This model corrects the overdispersion (observed variance exceeds the observed mean) that may be present, avoiding erroneous interpretations derived from biased estimates based on few variables: age, year of report and vaccine coverage. Therefore, the proposed model is presented as an alternative, both to the catalytic model [14] which uses Poisson regression and seroprevalence data, and to dynamic models when the data are not available or are not sufficiently up-to-date. The dynamical models [15] fit the mechanism of disease transmission using differential equations, such as SEIR (susceptible-exposed-infectious-recovered) models [16]. The objective of this study was to quantify the reduction in incidence of hepatitis A due to the vaccination programme in order to differentiate the natural reduction of the incidence of hepatitis A from that produced due to the vaccination programme and to predict the evolution of the disease in forthcoming years in different age groups. 2. Materials and methods The study was carried out in Catalonia a region of 7 million inhabitants situated in the northeast of Spain, where hepatitis A has been a notifiable disease since 1991. Reported cases of hepatitis A from 1992 to 2006 were included in the study. 2.1. Data sources The study included the reported incidence of hepatitis A in Catalonia by age, vaccination and year. Age was aggregated in four categories, 0–11 years, 12–18 years, 19–39 years and ≥40 years. Vaccinated cohorts were defined as children reaching 12 years of age during the years 1998–2005 (born in 1987–1993) and the non-vaccinated cohorts as children reaching 12 years of age during the 3 previous years (born in 1984–1986). The coverage vaccination (vac) was 91% in children aged 12 years [17] and it was considered that in the 12–18 years age group the coverage vaccination was 13% in 1999, 26% in 2000, 39% in 2001, 52% in 2002, 65% in 2003, 78% in 2004 and 91% in 2005. The Catalan population by age group and year was obtained from IdesCat [18]. 2.2. Study variables 2.2.1. Dependent variables Reported cases of hepatitis A in Catalonia (cases). 2.2.2. Independent variables or covariates The covariates included in the model were: year of notification (year), two sinusoidal variables: sin(2 t/amplitude) and cos(2 t/amplitude) to adjust for the cycling component, vaccine coverage (vac) and age group broken down into a set of indicative variables. The indicative variables were constructed with a value of 1 if the age belonged to this group and 0 otherwise. Those variables were: (age01) with a value of 1 for children under <12 years, age02 with a value of 1 for children 12–18 years (age03) with a value of 1 for subjects aged 19–39 years and age04 with a value of 1 for people aged ≥40 years. People aged ≥40 years were selected as a reference group, as no differences in age incidence were observed above this age [17]. In addition, seroepidemiological studies show that after 40 years of age most (range 80–100%) people have antibodies, indicating past infection [19]. All the possible interactions were also entered in the model. 2.3. Statistical analysis After testing different models we decided to use negative binomial regression to differentiate the effect of the natural decline in hepatitis A incidence from that produced by the vaccination program. The statistical analysis was carried out using the open source statistical package R, version 2.4.1 (http://cran.r-project.org). The glm.nb function of the MASS package was used to adjust hepatitis A incidence as a generalized linear model (GLM) [20,21] with the logarithmic link and the error was adjusted by negative binomial distribution [13]. Negative binomial regression is appropriate for modelling overdispersed count data and is more flexible in the form of distribution than the Poisson model because it adjusts a dispersion parameter which maintains the asymmetry of count data (see Appendix A.1 and A.2 for statistical details). Model selection and validation took into account the statistical significance of the covariates, Akaike’s information criterion (AIC) and the analysis of the residuals. The residual analysis was based on checking that they were not correlated, with stable variance and following a Normal distribution. The best model to select was considered to be that with the correct residual and the minimum AIC (see Appendix A.3). The statistical significance was established assuming an error = 0.05. Data from 2006 (not published) were used to validate the predictions of the model. The vaccination coverage (vac) in 2006 was 91% in the 12–18 years age group and 4.3% in the 19–39 years age group. 3. Adjusted models The following models were estimated: Model BN0. Incidence (cases) adjusted for year of report (year), age group and population (population) as parameter of offset. log(cases) = ˇ0 + ˇ1 year + ˇ2 age01 + ˇ3 age02 + ˇ4 age03 + log(population) + ε (1) Model BN1. Includes, in addition to the variables in model BN0, two sinusoidal variables: sin(2 t/amplitude) and cos(2 t/amplitude) to adjust for the cycling component: log(cases) = ˇ0 + ˇ1 year + ˇ2 age01 + ˇ3 age02 + ˇ4 age03 + ˇ5 sin 2t amplitude + ˇ6 cos 2t amplitude (2) + log(population) + ε Model BN2. Includes, in addition to the variables in model BN1, the proportion of vaccination coverage (vac): log(cases) = ˇ0 + ˇ1 year + ˇ2 age01 + ˇ3 age02 + ˇ4 age03 + ˇ7 vac + ˇ5 sin 2t amplitude + ˇ6 cos 2t amplitude (3) + log(population) + ε http://cran.r-project.org/
Table of Contents Feed for the Digital Edition of Vaccine Vaccine Vaccine - (Page Cover1) Vaccine - (Page 2) Vaccine - (Page 3) Vaccine - (Page 4) Vaccine - (Page 5) Vaccine - (Page 6) Vaccine - (Page 7) Vaccine - (Page 8) Vaccine - (Page 9)
For optimal viewing of this digital publication, please enable JavaScript and then refresh the page. If you would like to try to load the digital publication without using Flash Player detection, please click here.