# bhm.mcmc: Markov Chain Monte Carlo Estimation (Step 1) of the Bayesian... In mederrRank: Bayesian Methods for Identifying the Most Harmful Medication Errors

## Description

This function implements the Markov Chain Monte Carlo estimation methodology for the Bayesian hierarchical model described in Myers et al. (2011).

## Usage

 1 2 3 bhm.mcmc(dat, nsim = 2000, burnin = 500, scale.factor = 1, adaptive.int = 100, adaptive.max = 1000, prior = NULL, init = NULL, tuneD = NULL, tuneT = NULL) 

## Arguments

 dat an object of class "mederrData". nsim number of iterations. burnin number of burn-in iterations. scale.factor scale factor of the random effects proposal distribution. adaptive.int iteration interval at which the standard error of the random effects proposal distribution is updated. adaptive.max last iteration at which the standard error of the random effects proposal distribution is updated. prior an optional list of the hyperparameters values; see the Details section below. init an optional list of initial values for the model parameters; see the Details section below. tuneD an optional vector of the δ_j proposal distribution variances. tuneT an optional vector of the θ_i proposal distribution variances.

## Details

The Bayesian hierarchical model (with crossed random effects) implemented here for identifying the medication error profiles with the largest log odds of harm is

y_{ij} | N_{ij}, p_{ij} \sim Bin(N_{ij},p_{ij})

logit(p_{ij}) = γ + θ_i + δ_j

θ_i | σ, η, k \sim St(0,σ,k,η), \qquad i=1,…,n

δ_j | τ^2 \sim N(0,τ^2), \qquad j=1,…,J

γ \sim N(g,G)

σ^2 \sim IG(a_1,b_1)

τ^2 \sim IG(a_2,b_2)

k \sim Unif(0,∞)

η \sim Unif(0,∞),

where N_{ij} denotes the number of times that the error profile i is cited on a report from hospital j and y_{ij} is the corresponding number of times that profile i in hospital j was reported with harm. This function implements the first model estimation step in which the values k = ∞ and k = 1, i.e. a symmetric normal distribution, is forced for the error profiles' random effects. A sample from the joint posterior distribution of all other parameters via Markov Chain Monte Carlo with adaptive Metropolis steps for each set of random effects is obtained. For more details see Myers et al. (2011).

## Value

bhm.mcmc returns an object of the class "mederrFit".

## Author(s)

Sergio Venturini [email protected],

Jessica A. Myers [email protected]

## References

Myers, J. A., Venturini, S., Dominici, F. and Morlock, L. (2011), "Random Effects Models for Identifying the Most Harmful Medication Errors in a Large, Voluntary Reporting Database". Technical Report.

bhm.resample, mederrData, mederrFit.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ## Not run: data("simdata", package = "mederrRank") summary(simdata) fit <- bhm.mcmc(simdata, nsim = 1000, burnin = 500, scale.factor = 1.1) resamp <- bhm.resample(fit, simdata, p.resample = .1, k = c(3, 6, 10, 30, 60, Inf), eta = c(.5, .8, 1, 1.25, 2)) fit2 <- bhm.constr.resamp(fit, resamp, k = 3, eta = .8) plot(fit, fit2, simdata) theta0 <- c(10, 6, 100, 100, .1) ans <- mixnegbinom.em(simdata, theta0, 50000, 0.01, se = TRUE, stratified = TRUE) summary(fit2, ans, simdata) ## End(Not run)