Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Held, Leonhard and Paul, Michaela 2013. Infectious Disease Surveillance.

    Oviedo, M. Muñoz, M.P. and Domínguez, Á. 2013. Estimación de la incidencia de la hepatitis B en Cataluña mediante modelos aditivos generalizados y su relación con las tasas de inmigración y vacunación. Vacunas, Vol. 14, Issue. 3, p. 103.

    HERZOG, S. A. PAUL, M. and HELD, L. 2011. Heterogeneity in vaccination coverage explains the size and occurrence of measles epidemics in German surveillance data. Epidemiology and Infection, Vol. 139, Issue. 04, p. 505.

    HENS, N. AERTS, M. FAES, C. SHKEDY, Z. LEJEUNE, O. VAN DAMME, P. and BEUTELS, P. 2010. Seventy-five years of estimating the force of infection from current status data. Epidemiology and Infection, Vol. 138, Issue. 06, p. 802.

    Yoshikawa, A. Suzuki, K. Abe, A. Tanaka, T. Yamaguchi, K. Tanaka, T. Ishikawa, Y. Minegishi, K. Gotanda, Y. Yugi, H. Uchida, S. Satake, M. Mizoguchi, H. and Tadokoro, K. 2009. Effect of selective vaccination on a decrease in the rate of hepatitis B virus-positive Japanese first-time blood donors. Transfusion Medicine, Vol. 19, Issue. 4, p. 172.


Estimating the impact of vaccination using age–time-dependent incidence rates of hepatitis B

  • N. HENS (a1), M. AERTS (a1), Z. SHKEDY (a1), P. KUNG'U KIMANI (a2), M. KOJOUHOROVA (a3), P. VAN DAMME (a4) and Ph. BEUTELS (a4)
  • DOI:
  • Published online: 01 May 2007

The objective of this study was to model the age–time-dependent incidence of hepatitis B while estimating the impact of vaccination. While stochastic models/time-series have been used before to model hepatitis B cases in the absence of knowledge on the number of susceptibles, this paper proposed using a method that fits into the generalized additive model framework. Generalized additive models with penalized regression splines are used to exploit the underlying continuity of both age and time in a flexible non-parametric way. Based on a unique case notification dataset, we have shown that the implemented immunization programme in Bulgaria resulted in a significant decrease in incidence for infants in their first year of life with 82% (79–84%). Moreover, we have shown that conditional on an assumed baseline susceptibility percentage, a smooth force-of-infection profile can be obtained from which two local maxima were observed at ages 9 and 24 years.

Corresponding author
*Author for correspondence: Dr N. Hens, Center for Statistics, Hasselt University, Campus Diepenbeek, Agoralaan 1, 3590 Diepenbeek, Belgium. (Email:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

2. CN Shapiro . Epidemiology of hepatitis B. Pediatric Infectious Disease Journal 1993; 12: 443447.

3. WJ Edmunds , GF Medley , DJ Nokes . The influence of age on the development of the hepatitis B carrier state. Proceedings of the Royal Society of London Series B, Biological Sciences 1993; 253: 197201.

5. L Held , A statistical framework for the analysis of multivariate infectious disease surveillance data. Statistical Modelling 2005; 5: 187199.

6. L Held , A two component model for counts of infectious diseases. Biostatistics 2006; 7: 422437.

7. BD Marx , PHC Eilers . Direct generalized additive modelling with penalized likelihood. Computational Statistics and Data Analysis 1998; 28: 193209.

8. SN Wood . Modelling and smoothing parameter estimation with multiple quadratic penalties. Journal of the Royal Statistical Society, Series B 2000; 62: 413428.

9. M Aerts , Some theory for penalized spline additive models. Journal of Statistical Planning and Inference 2002; 103: 455470.

10. S Thurston , Negative binomial additive models. Biometrics 2000; 56: 139144.

11. I Currie , Smoothing and forecasting mortality rates. Statistical Modelling 2004; 4: 279298.

13. P McCullagh , J Nelder . Generalized Linear Models. Chapman & Hall, 1989.

14. L Smith , Spline interpolation for demographic variables: the monotonicity problem. Journal of Population Research 2004; 21: 9598.

17. P Craven , G Wahba . Smoothing noisy data with spline functions. Numerische Mathematik 1979; 31: 377403.

19. SN Wood . Thin plate regression splines. Journal of the Royal Statistical Society 2003; 65: 95114.

21. G Wahba . Spline Models for Observational Data, CBMS-NSF series. Philadelphia: SIAM, 1990.

22. T Hastie , R Tibshirani . Generalized additive models: some applications. Journal of the American Statistical Association 1987; 82: 371386.

24. SN Wood . Stable and efficient multiple smoothing parameter estimation for generalized additive models. Journal of the American Statistical Association 2004; 99: 673686.

25. A Agresti . Categorical Data Analysis. Wiley & Sons, 2002.

29. P Beutels , Hepatitis B in St Petersburg, Russia (1994–1999): incidence, prevalence and force of infection. Journal of Viral Hepatitis 2003; 10: 141149.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Epidemiology & Infection
  • ISSN: 0950-2688
  • EISSN: 1469-4409
  • URL: /core/journals/epidemiology-and-infection
Please enter your name
Please enter a valid email address
Who would you like to send this to? *