American Journal of Epidemiology Advance Access originally published online on June 20, 2006
American Journal of Epidemiology 2006 164(3):293-294; doi:10.1093/aje/kwj222
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Letter to the Editor |
THE AUTHORS REPLY
1 School of Mathematics and Statistics, University of Plymouth, Plymouth PL4 8AA, United Kingdom
2 Department of Social Medicine, University of Bristol, Bristol BS8 2PR, United Kingdom
(e-mail: issy.bray{at}bristol.ac.uk)
We thank Clements et al. (1
) for their interest in our paper (2). Bayesian age-period-cohort models are just one of several alternative approaches to modeling and projecting cancer rates. Strengths of the Bayesian age-period-cohort approach include its flexibility to deal with both increasing and decreasing rates (3); very low rates such as are observed for incidence of multiple myeloma (4); and diseases other than cancer, for example, stroke (5), asthma (6), and schizophrenia (7); as well as the ease with which covariate information can be incorporated to improve projections (8). Furthermore, Bayesian age-period-cohort models are increasingly used with regard to analyzing social issues. For example, Bravo (9) explores dentist use in Spain between 1987 and 1997.
The aim of this particular paper (2) was not to compare projections using Bayesian age-period-cohort models with alternative methods, but to concentrate on one very specific aspect of the Bayesian age-period-cohort model, namely, the exclusion of younger age groups from the analysis and how this affects the projections.
The need to investigate alternative priors is acknowledged in the literature (refer to the paper by Bray (4)). Knorr-Held and Rainer (8) compare first- and second-order random walk priors and conclude that the latter give considerably better forecasts than do the former, while current postgraduate work at the University of Plymouth is investigating these alternatives when the data exhibit specific trends such as linear, quadratic, and step changes in observed rates.
We note that, in their comparative analyses, Clements et al. (10) do not use all of the available data but instead analyze data for only those aged 25–84 years. Including all data may improve the accuracy and precision of projections from the Bayesian age-period-cohort model (2). In addition, Møller et al. (11) make comparisons with classical rather than Bayesian age-period-cohort models.
We agree that a consistent way of assessing alternative methods of making projections of rates is required. Although Bray (4) and Baker and Bray (2) did not use the predictive deviance or a related measure incorporating precision, we have consistently used the sum of squared standardized residuals (found to be, on average, within 5 percent of the deviance (4)) to assess the accuracy and width of credible interval to assess the precision of projections.
As we conclude in the Discussion (2), there is still much work to be done in determining the best modeling approach in different situations, and we welcome the comments made in this letter (1) as a step in that direction.
ACKNOWLEDGMENTS
Conflict of interest: none declared.
References
- Clements MS, Hakulinen T, Moolgavkar SH. Re: "Bayesian projections: what are the effects of excluding data from younger age groups?" (Letter). Am J Epidemiol 2006;164:292–3.
[Free Full Text] - Baker A, Bray I. Bayesian projections: what are the effects of excluding data from younger age groups? Am J Epidemiol 2005;162:798–805.
[Abstract/Free Full Text] - Hodgen E. Cancer forecasting in New Zealand. (Thesis). Wellington, New Zealand: Victoria University of Wellington, 2003.
- Bray I. Application of Markov chain Monte Carlo methods to projecting cancer incidence and mortality. Appl Stat 2002;51:151–64.
- Yu TS, Tse LA, Wong TW, et al. Recent trends of stroke mortality in Hong Kong: age, period, cohort analyses and implications. Neuroepidemiology 2001;19:265–74.
- Dobbin CJ, Miller J, van der Hoek R, et al. The effects of age, death period and birth cohort on asthma mortality rates in Australia. Int J Tuberc Lung Dis 2004;8:1429–36.[Web of Science][Medline]
- Bray I, Waraich P, Jones W, et al. Increase in schizophrenia incidence rates: findings in a Canadian cohort born 1975–1985. Soc Psychiatry Psychiatr Epidemiol. Advance Access: June 2, 2006. (DOI: 10.1007/s00127-006-0073-z).
- Knorr-Held L, Rainer E. Projections of lung cancer mortality in West Germany: a case study in Bayesian prediction. Biostatistics 2001;2:109–29.[Medline]
- Bravo M. Age-period-cohort analysis of dentist use in Spain from 1987 to 1997. An analysis based on the Spanish National Health Interview Surveys. Eur J Oral Sci 2001;109:149–54.[CrossRef][Web of Science][Medline]
- Clements MS, Armstrong BK, Moolgavkar SH. Lung cancer rate predictions using generalized additive models. Biostatistics 2005;6:576–89.
[Abstract/Free Full Text] - Møller B, Fekjaer H, Hakulinen T, et al. Prediction of cancer incidence in the Nordic countries: empirical comparison of different approaches. Stat Med 2003;22:2751–66.[CrossRef][Web of Science][Medline]
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