# negbinom.em: Expectation-Maximization Algorithm for the Negative Binomial... In mederrRank: Bayesian Methods for Identifying the Most Harmful Medication Errors

## Description

This function provides the empirical Bayes estimates for the parameters `theta` of a negative binomial distribution (see `dnegbinom`) using an Expectation-Maximization algorithm.

## Usage

 ```1 2``` ```negbinom.em(dat, theta0, maxiter = 50000, toler = 0.01, se = TRUE, stratified = FALSE) ```

## Arguments

 `dat` an object of class "mederrData". `theta0` initial values for the parameters to be optimized over. `maxiter` a positive integer specifying the maximum number of iterations to be performed before the program is terminated. `toler` a positive scalar giving the tolerance at which the scaled gradient is considered close enough to zero to terminate the algorithm. `se` logical; if TRUE the standard errors of the estimates are also returned. `stratified` logical; if TRUE the analysis will be performed by stratifying on the hospitals.

## Details

For further details see Myers et al. (2011).

## Value

`negbinom.em` returns a list with components:

 `theta.hat ` The best set of parameters found. `final.err ` The last change in the log-likelihood; it has to be smaller than the `toler` argument. `final.ll ` The likelihood value corresponding to `theta.hat`. `final.score ` The log-likelihood score value corresponding to `theta.hat`. `num.iter ` The number of iterations performed to find the proposed solution. `se ` Only if argument `se` is true. A vector of estimates standard errors for the solution found. `N ` The vector of observed error profiles counts. `E ` The vector of expected error profiles counts. `prior ` A character string giving the prior used; for this function is set to "gamma", i.e. a gamma distribution.

## Author(s)

Sergio Venturini [email protected],

Jessica A. Myers [email protected]

## References

DuMouchel W. (1999), "Bayesian Data Mining in Large Frequency Tables, with an Application to the FDA Spontaneous Reporting System". The American Statistician, 53, 177-190.

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.

`dnegbinom`, `EBGM`, `mixnegbinom.em`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```data("simdata", package = "mederrRank") summary(simdata) ## Not run: 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) ## End(Not run) theta0 <- runif(2, 0, 5) ans <- negbinom.em(simdata, theta0, 50000, 0.01, se = TRUE, stratified = TRUE) ans\$theta ans\$se ## Not run: summary(fit2, ans, simdata) ## End(Not run) ```