Bayesian Age-Period-Cohort Modeling for the analyze of incidence or mortality data on the Lexis diagram.
For each pixel in the Lexis diagram (that is for a specific age group and specific period) data must be available on the number of persons under risk (population number) and the number of disease cases (typically cancer incidence or mortality).
A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order (RW1 or RW2) available.
Deviance information criterion and effective number of parameters is computed for model comparison.
Note that there is a non-identifiability in the likelihood of the APC-model, see e.g. Clayton and Schifflers (1987, DOI:10.1002/sim.4780060406), which indices some problems in interpreting the latent effects. Only for RW1 model, the parameters are (weakly) identifiable.
Period and age groups do not need to be on the same grid, for example periods can be in one year intervals and age groups in five year intervals.
Additionally to the model described in Knorr-Held and Rainer (2001, DOI:10.1093/biostatistics/2.1.109), bamp can handle
models with and without global heterogeneity parameter (overdispersion),
models with additional age, period and/or cohort heterogeneity,
additional covariates.
bamp(
cases,
population,
age,
period,
cohort,
overdisp = FALSE,
period_covariate = NULL,
cohort_covariate = NULL,
periods_per_agegroup,
mcmc.options = list(number_of_iterations = 1e+05, burn_in = 50000, step = 50, tuning =
500),
hyperpar = list(age = c(1, 0.5), period = c(1, 5e-04), cohort = c(1, 5e-04), overdisp =
c(1, 0.05)),
dic = TRUE,
parallel = TRUE,
verbose = FALSE
)number of cases
population number
prior for age groups ("rw1", "rw2", "rw1+het", "rw2+het", " ")
prior for periods ("rw1", "rw2", "rw1+het", "rw2+het", " ")
prior for cohorts ("rw1", "rw2", "rw1+het", "rw2+het", " ")
logical, add overdispersion to model
covariate for period
covariate for cohort
periods per age group
list of options for MCMC.
burn_in: number of iterations used as burnin at the beginning of the algorithm, these iterations will be removed.
step: Step size, for example default is 50, so only every 50th iterations will be stored.
tuning: number of iterations for automatic tuning. Depending on the model, the MCMC algorithm will tune certain parameters for more efficient MCMC chains. After tuning, the algorithm is restarted.
list of hyper parameters. The hyper prior for the precision (inverse variance) in the random walk priors is a Gamma distribution with parameters \(a\) and \(b\); expected value is \(a/b\), variance is \(a/b^2\). Weak hyper parameters are suggested, defaults are \(a=1, b=0.5\) for age, \(a=1, b=0.0005\) for period and cohort effects and \(a=1, b=0.05\) for overdispersion (if added). It is recommended to choose the hyper priors depending on the model, in particular on the order of the random walk.
logical. If true. DIC will be computed
logical, should computation be done in parallel. This uses the parallel package, which does not allow parallel computing under Windows.
verbose mode
This functions returns an apc object.
Only samples from the posterior are computed, point estimates and credible intervals will be computed in effects.apc, print.apc and plot.apc.
predict_apc can be used for for prediction of the future rates and number of cases and for a retrospective prediction for model checking.
if (FALSE) {
data(apc)
model <- bamp(cases, population, age="rw1", period="rw1", cohort="rw1", periods_per_agegroup = 5)
}