Package 'mederrRank'

Bayesian Methods for Identifying the Most Harmful Medication Errors

Description

Two distinct but related statistical approaches to the problem of identifying the combinations of medication error characteristics that are more likely to result in harm are implemented in this package: 1) a Bayesian hierarchical model with optimal Bayesian ranking on the log odds of harm, and 2) an empirical Bayes model that estimates the ratio of the observed count of harm to the count that would be expected if error characteristics and harm were independent. In addition, for the Bayesian hierarchical model, the package provides functions to assess the sensitivity of results to different specifications of the random effects distributions.

Details

The package is loaded with the usual library(mederrRank) command. The most important functions are bhm.mcmc, bhm.resample and mixnegbinom.em.

Author(s)

Sergio Venturini, Jessica Myers

Maintainer: Sergio Venturini <[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.

See Also

bayes.rank, bhm.mcmc, bhm.resample, mixnegbinom.em.

---

Optimal Bayesian Ranking

Description

This function estimates the ranks of the log odds of harm of the various medication error profiles as described in Myers et al. (2011).

Usage

bayes.rank(model)

Arguments

model

a mederrFit object.

Details

Using the posterior samples of the $\theta_i$, the function estimates the ranks of the log odds of harm of the various error profiles. Optimal Bayesian ranking gives estimates of rank for profile $i$ as

$\hat{R}_i = \sum_{k=1}^{n}{\hat{P}(\theta_k \leq \theta_i | \boldsymbol{y}, \boldsymbol{N})},$

where $\hat{P}(\theta_k \leq \theta_i | \boldsymbol{y}, \boldsymbol{N})$ is the posterior probability that $\theta_k \leq \theta_i$.

Value

bayes.rank returns the numerical vector of Optimal Bayesian ranks for the chosen mederrFit model (see the references for the details).

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.

See Also

bhm.constr.resamp, bhm.mcmc.

Examples

## Not run: 
data("simdata", package = "mederrRank")
summary(simdata)

fit <- bhm.mcmc(simdata, nsim = 1000, burnin = 500, scale.factor = 1.1)
ranks <- bayes.rank(fit)

summary(ranks)

## End(Not run)

---

Markov Chain Monte Carlo Estimation (Step 2) of the Bayesian Hierarchical Model for Identifying the Most Harmful Medication Errors

Description

This function represents the "constructor" function for the resampling procedure used in this package. bhm.resample calculates the importance ratios, and performs the sampling, and then this function constructs the resampled model based on that information.

Usage

bhm.constr.resamp(model, resample, k, eta)

Arguments

model	an object of class "mederrFit".
resample	an object of class "mederrResample".
k	$k$ (number of degrees of freedom) value to use in the resampling procedure.
eta	$\eta$ (skewing paramter) value to use in the resampling procedure.

Details

Deviations from the normal, i.e. $(k = \infty, \eta = 1)$, random effects distribution using a different pair of $k$ and $\eta$ values are considered. The methodology implemented here is the importance link function resampling approach introduce by MacEachern and Peruggia (2000): based on the $(k = \infty, \eta = 1)$ chain, new posterior samples under a new set of $(k, \eta)$ values is obtained.

Value

bhm.constr.resamp returns an object of the class "mederrFit".

Author(s)

Sergio Venturini [email protected],

Jessica A. Myers [email protected]

References

MacEachern, S. and Peruggia, M. (2000), "Importance Link Function Estimation for Markov Chain Monte Carlo Methods", Journal of Computational and Graphical Statistics, 9, 99-121.

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.

See Also

bhm.mcmc, bhm.resample, mederrData, mederrFit.

Examples

## 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)

---

Markov Chain Monte Carlo Estimation (Step 1) of the Bayesian Hierarchical Model 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

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 $\delta_j$ proposal distribution variances.
tuneT	an optional vector of the $\theta_i$ 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

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

$logit(p_{ij}) = \gamma + \theta_i + \delta_j$

$\theta_i | \sigma, \eta, k \sim St(0,\sigma,k,\eta), \qquad i=1,\ldots,n$

$\delta_j | \tau^2 \sim N(0,\tau^2), \qquad j=1,\ldots,J$

$\gamma \sim N(g,G)$

$\sigma^2 \sim IG(a_1,b_1)$

$\tau^2 \sim IG(a_2,b_2)$

$k \sim Unif(0,\infty)$

$\eta \sim Unif(0,\infty),$

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 $k = \infty$ 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.

See Also

bhm.resample, mederrData, mederrFit.

Examples

## 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)

---

Resampling Transformation for the Markov Chain Monte Carlo Estimation Simulation of the Bayesian Hierarchical Model for Identifying the Most Harmful Medication Errors

Description

This function implements the transformation needed to apply the importance link function resampling methodology based on the Markov Chain Monte Carlo simulations obtained with the bhm.mcmc command (see the References).

Usage

bhm.resample(model, dat, p.resample = 0.1, k, eta)

Arguments

model	an object of class "mederrFit".
dat	an object of class "mederrData".
p.resample	proportion of simulations resampled from the model argument.
k	required vector of $k$ values to be used in the resampling process.
eta	required vector of $\eta$ values to be used in the resampling process.

Value

bhm.resample returns an object of the class "mederrResample".

Author(s)

Sergio Venturini [email protected],

Jessica A. Myers [email protected]

References

MacEachern, S. and Peruggia, M. (2000), "Importance Link Function Estimation for Markov Chain Monte Carlo Methods", Journal of Computational and Graphical Statistics, 9, 99-121.

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.

See Also

mederrData, mederrFit, bhm.mcmc.

Examples

## 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)

---

The Negative Binomial Mixture Distribution

Description

Density function for a mixture of two negative binomial distributions.

Usage

dmixnegbinom(x, theta, E, log.p = FALSE)

Arguments

x	vector of (non-negative integer) quantiles.
theta	vector of parameters for the negative binomial distribution mixture.
E	vector of (non-negative integer) expected counts.
log.p	logical; if TRUE, probabilities p are given as log(p).

Details

The mixture of two negative binomial distributions has density

$P(N = x) = theta[5] f(x;theta[1],theta[2],E) + (1 - theta[5]) f(x;theta[3],theta[4],E),$

where

$f(x;\alpha,\beta,E) = \frac{\Gamma(\alpha + x)}{\Gamma(\alpha) x!}\frac{1}{(1 + \beta/E)^x}\frac{1}{(1 + E/\beta)^\alpha}$

for $x = 0,1,\ldots,\alpha$, $\alpha, \beta, E > 0$ and $0 < theta[5] \leq 1$. The mixture of two negative binomial distributions represents the marginal distribution of the counts $N$ coming from Poisson data with parameter $\lambda$ and a mixture of two gamma distributions as its prior. For details see the paper by Dumouchel (1999).

Value

dmixnegbinom gives the density corresponding to the E and theta values provided.

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.

See Also

dnbinom, rmixnegbinom.

Examples

## Not run: 
data("simdata", package = "mederrRank")
ni <- simdata@numi
theta0 <- c(10, 6, 100, 100, .1)
ans <- mixnegbinom.em(simdata, theta0, 50000, 0.01,
	se = FALSE, stratified = TRUE)
theta <- ans$theta.hat
N.E <- cbind(ans$N[1:ni], ans$E[1:ni])[sort(ans$N[1:ni], index.return = TRUE)$ix, ]
N.ix <- match(unique(N.E[, 1]), N.E[, 1])
N <- N.E[N.ix, 1]
E <- N.E[N.ix, 2]
dens <- dmixnegbinom(N, theta, E)
hist(N.E[, 1], breaks = 40, freq = FALSE)
points(N, dens)

## End(Not run)

---

The Negative Binomial Distribution

Description

Density function for the negative binomial distribution with parameters alpha and prob.

Usage

dnegbinom(x, alpha, prob, log.p = FALSE)

Arguments

x	vector of (non-negative integer) quantiles.
alpha	target for number of successful trials. Must be strictly positive, need not be integer.
prob	probability of success in each trial. 0 < prob <= 1.
log.p	logical; if TRUE, probabilities p are given as log(p).

Details

The negative binomial distribution with parameters alpha = $\alpha$ and prob = $p$ has density

$\frac{\Gamma(x + \alpha)}{\Gamma(\alpha) x!} p^\alpha (1-p)^x$

for $x = 0,1,\ldots,\alpha > 0$ and $0 < p \leq 1$. This represents the number of failures which occur in a sequence of Bernoulli trials before a target number of successes is reached.

Value

dnegbinom gives the density corresponding to the alpha and prob values provided.

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.

See Also

dmixnegbinom, dnbinom.

---

The Skewed Student t Distribution

Description

Density function for the skewed t distribution with k degrees of freedom, scale parameter sigma and skewness eta .

Usage

dst(x, sigma, k, eta)

Arguments

x	vector of quantiles.
sigma	scale parameter ($> 0$).
k	degrees of freedom ($> 0$, maybe non-integer). df = Inf is allowed.
eta	skewness parameter ($> 0$).

Details

This distribution is based on introducing skewing into the symmetric scaled t distribution, as described in Fernandez and Steel (1998). The parameters characterizing the center (here set at 0) and the spread (sigma) refer to the mean and standard deviation of the underlying symmetric distribution. In the skewed t distribution, the centrality parameter defines the mode of the distribution, but it is no longer either the mean or the median. Similarly, in the skewed t distribution, sigma still characterizes the spread, but it can no longer be interpreted directly as the standard deviation of the distribution.

Value

dst gives the density corresponding to the simga, k and eta values provided.

Author(s)

Sergio Venturini [email protected],

Jessica A. Myers [email protected]

References

Fernandez, C. and Steel, M. (1998), "On Bayesian Modeling of Fat Tails and Skewness". Journal of the American Statistical Association, 93, 359-371.

Lee, K. and Thompson, S. (2008), "Flexible Parametric Models for Random-Effects Distributions". Statistics in Medicine, 27, 418-434.

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.

See Also

dt.

---

Geometric Mean of the Relative Risk Empirical Bayes Posterior Distribution

Description

This function computes the geometric mean of the empirical Bayes posterior distribution for the observed vs. expected count relative risk.

Usage

EBGM(eb.result)

Arguments

eb.result

output of the mixnegbinom.em or negbinom.em commands.

Details

For further details see DuMouchel (1999).

Value

EBGM returns the vector of geometric means.

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.

See Also

mixnegbinom.em, negbinom.em.

Examples

## 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)

theta0 <- c(10, 6, 100, 100, .1)
ans <- mixnegbinom.em(simdata, theta0, 50000, 0.01,
	se = FALSE, stratified = TRUE)

ni <- simdata@numi
rank(EBGM(ans)[1:ni])
summary(fit2, ans, simdata)
## End(Not run)

---

Log-Likelihood Difference for the $\delta_j$ Parameters

Description

This function computes the log-likelihood difference for the candidate $\delta_j$ random effects. It is a helper function and not meant to be used on its own.

Usage

llDiffD(dat, deltaj, cand, thetai, gamma, tau2)

Arguments

dat	data frame containing the observed sample counts.
deltaj	vector of previous accepted values for the $\delta_j$ random effects.
cand	vector of candidate values for the $\delta_j$ random effects.
thetai	vector of previous accepted values for the $\theta_i$ random effects.
gamma	last sampled value for the $\gamma$ parameter.
tau2	last sampled value for the $\tau^2$ parameter.

Details

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

Value

llDiffD returns the vector of log-likelihood differences.

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.

See Also

bhm.constr.resamp, bhm.mcmc, bhm.resample.

---

Log-Likelihood Difference for the $\theta_i$ Parameters

Description

This function computes the log-likelihood difference for the candidate $\theta_i$ random effects. It is a helper function and not meant to be used on its own.

Usage

llDiffT(dat, thetai, cand, deltaj, gamma, sigma2)

Arguments

dat	data frame containing the observed sample counts.
thetai	vector of previous accepted values for the $\theta_i$ random effects.
cand	vector of candidate values for the $\delta_j$ random effects.
deltaj	vector of previous accepted values for the $\delta_j$ random effects.
gamma	last sampled value for the $\gamma$ parameter.
sigma2	last sampled value for the $\sigma^2$ parameter.

Details

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

Value

llDiffT returns the vector of log-likelihood differences.

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.

See Also

bhm.constr.resamp, bhm.mcmc, bhm.resample.

---

Negative Log-Posterior Function of the Bayesian Hierarchical Model for Identifying the Most Harmful Medication Errors

Description

This function computes the negative log-posterior distribution of the Bayesian hierarchical model described in Myers et al (2011). It is a helper function and not meant to be used on its own.

Usage

logp(theta, deltaj, sigma2, i, k, eta, dat)

Arguments

theta	value of the error profile random effect at which the log.posterior distribution is calculated.
deltaj	vector of hospital random effect values.
sigma2	scale parameter ($> 0$).
i	error profile index for which the calculate of the log.posterior distribution is needed.
k	degrees of freedom ($> 0$, maybe non-integer). df = Inf is allowed.
eta	skewness parameter ($> 0$).
dat	an object of class "mederrData".

Details

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

Value

logp returns a vector of log-posterior values.

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.

See Also

bhm.constr.resamp, bhm.mcmc, bhm.resample.

---

Unnormalized Marginal Posterior Distributions for $k$ and $\eta$

Description

This functions computes the unnormalized marginal posterior distributions for the $k$ and $\eta$ parameters as described in Myers et al (2011).

Usage

logunpost(resample)

Arguments

resample

an object of class "mederrResample".

Details

logunpost is used in the plot method for a mederrResample object.

Value

logunpost returns an array with the posterior distribution values.

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.

See Also

bhm.constr.resamp, bhm.mcmc, bhm.resample, mederrResample.

---

Class "mederrData". Data Specification for Identifying the Most Harmful MEdication Errors using a Bayesian Hierarchical Model.

Description

This class encapsulates the data specification for a Bayesian Hierarchical Model used to identify the most harmful medication errors as described in Myers et al. (2011).

Objects from the Class

Objects can be created by calls of the form new("mederrData", data), where the data argument has to be a matrix or a data frame object that contains the following (numeric) information for each error profile/hospital combination:

1. the number of times ($y$) that profile $i$ in hospital $j$ was reported with harm;

2. the total number of times ($N$) that the error profile $i$ is cited on a report from hospital $j$,

3. the error profile $i$ identification code,

4. the hospital $j$ identification code.

Slots

data:

Object of class "data.frame"; data in the standard data.frame form.

size:

Object of class "numeric"; total number of observations in the data set.

numi:

Object of class "numeric"; number of error profiles available in the data set.

numj:

Object of class "numeric"; number of hospitals available in the data set.

Methods

plot

signature(x = "mederrData", y = "missing"): Provides a pictorial representation for a sample of error profiles reported by some hospitals.

summary

signature(object = "mederrData"): Summarizes information about an mederrData object.

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.

See Also

bayes.rank, bhm.mcmc, bhm.resample, mixnegbinom.em.

Examples

ng <- 50
i <- rep(1:ng, ng)
j <- rep(1:ng, each = ng)
N <- rpois(ng^2, 3 + .05*i - .01*j) + 1

theta_i <- rgamma(ng, 5, 5) - 4/5
delta_j <- rnorm(ng, 0, .2)
logit <- -3 + theta_i[i] + delta_j[j]
y <- rbinom(ng^2, N, exp(logit)/(1 + exp(logit)))

simdata <- new("mederrData", data = cbind(y, N, i, j))

---

Class "mederrFit". Simulated Monte Carlo Chains (Step 1) for the Bayesian Hierarchical Model Used to Identify the Most Harmful Medication Errors.

Description

This class encapsulates the simulated Monte Carlo chains for the Bayesian Hierarchical Model as described in Myers et al. (2011) forcing a symmetric normal distribution on the $\theta_i$, $i=1,\ldots,n$.

Objects from the Class

Objects can be created by calls of the form new("mederrFit", thetai, deltaj, gamma, sigma2, tau2, p.acc.i, p.acc.j, tune.theta, tune.delta, k, eta), but most often as the result of a call to bhm.mcmc or to bhm.constr.resamp.

Slots

thetai:

Object of class "matrix"; simulated chains for the $\theta_i$, $i = 1,\ldots,n$, error profiles random effects; see bhm.mcmc.

deltaj:

Object of class "matrix"; simulated chains for the $\delta_j$, $i = j,\ldots,J$, hospitals random effects; see bhm.mcmc.

gamma:

Object of class "numeric"; simulated chain for the $\gamma$ parameter; see bhm.mcmc.

sigma2:

Object of class "numeric"; simulated chain for the $\sigma^2$ parameter; see bhm.mcmc.

tau2:

Object of class "numeric"; simulated chain for the $\tau^2$ parameter; see bhm.mcmc.

p.acc.i:

Object of class "numeric"; acceptance rates for the error profiles random effects.

p.acc.j:

Object of class "numeric"; acceptance rates for the hospitals random effects.

tune.theta:

Object of class "numeric"; last updated values of the $\theta_i$ working variances for the Metropolis step.

tune.delta:

Object of class "numeric"; last updated values of the $\delta_j$ working variances for the Metropolis step.

k:

Object of class "numeric"; $k$ value used in the simulation.

eta:

Object of class "numeric"; $\eta$ value used in the simulation.

Methods

plot

signature(x = "mederrFit", y = "mederrFit"): Provides a graphical representation of the estimates.

summary

signature(object = "mederrFit"): Summarizes the information regarding the estimates.

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.

See Also

bayes.rank, bhm.constr.resamp, bhm.mcmc.

---

Class "mederrResample". Simulated Monte Carlo Chains (Step 2) for the Bayesian Hierarchical Model Used to Identify the Most Harmful Medication Errors.

Description

This class encapsulates the information needed to resample the Monte Carlo chains for the Bayesian Hierarchical Model as described in Myers et al. (2011) using user defined values for $k$ and $eta$.

Objects from the Class

Objects can be created by calls of the form new("mederrResample", log.ir, samp, A, t.new, t.old, grd), but most often as the result of a call to bhm.resample.

Slots

log.ir:

Object of class "array"; logarithm of the importance ratio for each pair of $(k,\eta)$ values.

samp:

Object of class "array"; resampled MCMC simulation indexes.

A:

Object of class "array"; transformation ratio for each pair of $(k,\eta)$ values.

t.new:

Object of class "array"; $\theta_i$ posterior modes using $(k = \infty, \eta = 1)$.

t.old:

Object of class "numeric"; $\theta_i$ posterior modes using user defined $(k, \eta)$ values.

grd:

Object of class "list"; grid of required $(k, \eta)$ values.

Methods

plot

signature(x = "mederrResample", y = "missing"): : Provides a graphical representation of a mederrResample object.

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.

See Also

bayes.rank. bhm.constr.resamp, bhm.mcmc.

---

Subset of the MEDMARX Data

Description

Subset of the MEDMARX data included for illustrative purposes only in the mederrRank package.

Usage

data(MEDMARX)

Format

An object of class mederrData.

Details

The data contained in this object are reproduced by gentle permission of Quantros, Inc., 690 N. McCarthy Blvd., Suite 200, Milpitas, CA 95035.

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.

See Also

bhm.mcmc, mederrData, mederrFit.

Examples

data("MEDMARX", package = "mederrRank")
summary(MEDMARX)
plot(MEDMARX, nbins.err = 20, nbins.hosp = 10)

---

Expectation-Maximization Algorithm for the Mixture of Negative Binomial Distributions

Description

This function provides the empirical Bayes estimates for the parameters theta of a mixture of two negative binomial distributions (see dmixnegbinom) using an Expectation-Maximization algorithm.

Usage

mixnegbinom.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 change in the log-likelihood 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

mixnegbinom.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 "mixgamma", i.e. a mixture of two gamma distributions as in DuMouchel (1999).

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.

See Also

dmixnegbinom, EBGM, negbinom.em.

Examples

## 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)
ans$theta
ans$se

summary(fit2, ans, simdata)
## End(Not run)

---

Log-Likelihood Function for the Mixture of Negative Binomial Distributions

Description

This function computes the log-likelihood function for the mixture of two negative binomial distributions as described in dmixnegbinom.

Usage

mixnegbinom.loglik(theta, N, E)

Arguments

theta	vector of parameter values.
N	vector of observed error profiles counts.
E	vector of expected error profiles counts.

Details

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

Value

mixnegbinom.loglik returns the log-likelihood value for the negative binomial mixture.

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.

See Also

dmixnegbinom, mixnegbinom.em, mixnegbinom.score.

---

Log-Likelihood Score Function for the Mixture of Negative Binomial Distributions

Description

This function computes the log-likelihood score for the mixture of two negative binomial distributions as described in dmixnegbinom.

Usage

mixnegbinom.score(theta, N, E)

Arguments

theta	vector of parameter values.
N	vector of observed error profiles counts.
E	vector of expected error profiles counts.

Details

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

Value

mixnegbinom.score returns the vector of log-likelihood score values for the negative binomial mixture.

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.

See Also

dmixnegbinom, mixnegbinom.em, mixnegbinom.loglik.

---

Expectation-Maximization Algorithm for the Negative Binomial Distribution

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

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.

See Also

dnegbinom, EBGM, mixnegbinom.em.

Examples

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)

---

Log-Likelihood Function for the Mixture of Negative Binomial Distributions

Description

This function computes the log-likelihood function for the mixture of two negative binomial distribution as described in dmixnegbinom.

Usage

negbinom.loglik(theta, N, E)

Arguments

theta	vector of parameter values.
N	vector of observed error profiles counts.
E	vector of expected error profiles counts.

Details

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

Value

negbinom.loglik returns the log-likelihood value for the negative binomial 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.

See Also

dnegbinom, negbinom.em, negbinom.score.

---

Log-Likelihood Score Function for the Negative Binomial Distribution

Description

This function computes the log-likelihood score for the negative binomial distribution as described in dmixnegbinom.

Usage

negbinom.score(theta, N, E)

Arguments

theta	vector of parameter values.
N	vector of observed error profiles counts.
E	vector of expected error profiles counts.

Details

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

Value

negbinom.score returns the vector of log-likelihood score values for the negative binomial 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.

See Also

dnegbinom, negbinom.em, negbinom.loglik.

---

Posterior Predictive Test statistics

Description

This function computes posterior predictive test statistics as described in Myers et al. (2011).

Usage

p.value(reps)

Arguments

reps	list of replications created with the post.rep function.

Details

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

Value

p-value creates a list of p-values.

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.

See Also

bhm.constr.resamp, bhm.mcmc, bhm.resample, post.rep.

Examples

## 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)
reps <- post.rep(fit2, simdata)
pvalues <- p.value(reps)

## End(Not run)

---

Plot of Medication Error Data and Analysis

Description

Methods for function plot in Package ‘graphics’ to be used with "mederrData", mederrFit and "mederrResample" objects.

Methods

signature(x = "mederrData", y = "missing")

Pictorial representation for a "mederrData" object.

signature(x = "mederrFit", y = "mederrFit")

Graphical representation of Markov Chain Monte Carlo simulations for a "mederrFit" object.

signature(x = "mederrResample", y = "missing")

Graphical representation of the resampling transformation for a "mederrResample" object.

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.

See Also

bhm.mcmc, bhm.resample.

---

Posterior Predictive Data Replications

Description

This function creates a list of replicated data for posterior predictive checking as described in Myers et al. (2011).

Usage

post.rep(model, dat)

Arguments

model	an object of class "mederrFit".
dat	an object of class "mederrData".

Details

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

Value

post.rep returns a list of replicated data.

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.

See Also

bhm.constr.resamp, bhm.mcmc, bhm.resample, p.value.

---

The Negative Binomial Mixture Distribution

Description

Random generation for a mixture of two negative binomial distributions.

Usage

rmixnegbinom(n, theta, E)

Arguments

n	number of observations.
theta	vector of parameters for the negative binomial distribution mixture.
E	vector of (non-negative integer) expected counts.

Value

rmixnegbinom generates random deviates corresponding to the E and theta values provided.

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.

See Also

dmixnegbinom, rnbinom.

---

Simulated Data

Description

Simulated data to use for illustrative purposes in the mederrRank package.

Usage

data(simdata)

Format

An object of class mederrData.

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.

See Also

bhm.mcmc, mederrData, mederrFit.

Examples

data("simdata", package = "mederrRank")
summary(simdata)
plot(simdata)

---

Summary of Medication Error Data and Analysis

Description

Methods for function summary in Package ‘base’ to be used with "mederrData" and "mederrFit" objects.

Methods

signature(object = "mederrData")

Extracts summary information about the slots of a "mederrData" object.

signature(object = "mederrFit")

Extracts summary information about the slots of a "mederrFit" object.

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.

See Also

bayes.rank, bhm.mcmc.

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