# Bayesian Diabetes Projections by CDC

October 22, 2010
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(This article was first published on BioStatMatt » R, and kindly contributed to R-bloggers)

Bayesian methods are supporting decisions and news at the national level!

The Centers for Disease Control and Prevention summarizes a report published in the journal Population Health Metrics. The news also made it to the national media. The report (JP Boyle, TJ Thompson, EW Gregg, LE Barker, and DF Williamson (2010) “Projection of the year 2050 burden of diabetes in the US adult population: dynamic modeling of incidence, mortality, and prediabetes prevalence.”Population Health Metrics. 8:29) projects a two fold increase in the annual incidence of diabetes among American adults. The authors project the prevalence of diabetes to increase from 14% to between 25% and 28% by 2050. However, the authors claim that “these projected increases are largely attributable to the aging of the US population, increasing numbers of members of higher-risk minority groups in the population, and people with diabetes living longer.”

The authors model the incidence of diabetes $y_t$ at year $t$ according to the Bayesian nonlinear model:

$begin{array}{r c l} y_t & sim & N(mu_t, s_t^2) \ mu_t & = & rho / ( 1 + exp(lambda_0 + lambda_1t)) + epsilon_t \ rho & sim & beta(14, 848), end{array}$

where $mu_t$ is a logistic function of time with asymptote $rho$. The parameters $lambda_0$ and $lambda_1$ were given diffuse normal priors, and $epsilon_t$ was modeled using a variety of autoregressive strategies. The authors use WinBUGS for posterior summary, also citing Bayesian Data Analysis by Gelman et al. (2004).

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