EpiBayes_ns: Disease Model without Storage
In EpiBayes: Implements Hierarchical Bayesian Models for Epidemiological Applications
Description
Usage
Arguments
Details
Value
Parameter Meanings
References
See Also
Examples
Description
This function is used to model disease (freedom and prevalence estimation) using
a Bayesian hierarchical model with one, two, or three levels of sampling.
The most general, the three level, would be represented by the hierarchy:
(region -> subzone -> cluster -> subject) and the two- and one- level sampling would
simply be the same with either subzone removed or subzone and cluster
removed, respectively. This function is the 'no storage' model and hence stores
only immediately relevant output.
Usage
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EpiBayes_ns(H, k, n, seasons, reps, MCMCreps, poi = "tau", y = NULL,
mumodes = matrix(c(0.5, 0.7, 0.5, 0.7, 0.02, 0.5, 0.02, 0.5), 4, 2, byrow =
TRUE), pi.thresh = 0.02, tau.thresh = 0.05, gam.thresh = 0.1,
tau.T = 0, poi.lb = 0, poi.ub = 1, p1 = 0.95, psi = 4,
omegaparm = c(100, 1), gamparm = c(100, 1), tauparm = c(1, 1),
etaparm = c(100, 6), thetaparm = c(100, 6), burnin = 1000)
Arguments
H
Number of subzones/states. Should be a 1 if there are only one or two levels
of sampling. Integer scalar.
k
Number of clusters / farms / ponds / herds. Should be a 1 if there is only one
level of sampling. Integer vector (H x 1).
n
Number of subjects / animals / mussels / pigs per cluster (can differ among
clusters). Integer vector (sum(k) x 1).
seasons
Numeric season for each cluster in the order: Summer (1), Fall (2),
Winter (3), Spring (4). Integer vector (sum(k) x 1).
reps
Number of (simulated) replicated data sets. Integer scalar.
MCMCreps
Number of iterations in the MCMC chain per replicated data set.
Integer scalar.
poi
The p(arameter) o(f) i(nterest) specifies one of the subzone-level prevalence
(gam) or the cluster-level prevalence (tau), indicating which variable
with which to compute the simulation output p2.tilde, p4.tilde, and
p6.tilde. Character scalar.
y
An optional input of sums of positive diagnostic testing results if one has a
specific set of diagnostic testing outcomes for every subject (will simulate these
if this is left as NULL). Integer matrix (reps x sum(k)).
mumodes
Modes and (a) 95th percentiles for mode ≤q 0.50 or (b) 5th
percentiles for mode > 0.5 for season-specific mean prevalences for
diseased clusters in the order: Summer, Fall, Winter, Spring.
Real matrix (4 x 2).
pi.thresh
Threshold that we must show subject-level prevalence is below to
declare disease freedom. Real scalar.
tau.thresh
Threshold that we must show cluster-level prevalence is below to
declare disease freedom. Real scalar.
gam.thresh
Threshold that we must show subzone-level prevalence is below to
declare disease freedom. Real scalar.
tau.T
Assumed true cluster-level prevalence (used to simulate data to feed
into the Bayesian model). Real scalar.
poi.lb,poi.ub
Lower and upper bounds for posterior poi prevalences
to show ability to capture poi with certain probability. Real scalars.
p1
Probability we must show poi prevalence is below / above the thresholds
pi.thresh or tau.thresh or within specified bounds. Real scalar.
psi
(Inversely related to) the variability of the subject-level prevalences
in diseased clusters. Real scalar.
omegaparm
Prior parameters for the beta-distributed input omega, which
is the probability that the disease is in the region. Real vector (2 x 1).
gamparm
Prior parameters for the beta-distributed input gam, which
is the subzone-level prevalence (or the prevalence among subzones). Real
vector (2 x 1).
tauparm
Prior parameters for the beta-distributed input tau, which is the
cluster-level prevalence (or the prevalence among clusters). Real vector (2 x 1).
etaparm
Prior parameters for the beta-distributed input eta, which is the
sensitivity of the diagnostic test. Real vector (2 x 1).
thetaparm
Prior parameters for the beta-distributed input theta, which is
the specificity of the diagnostic test. Real vector (2 x 1).
burnin
Number of MCMC iterations to discard from the beginning of the chain.
Integer scalar.
Details
Note that this function performs in the same manner as EpiBayes_s except
it doesn't store the posterior distributions of all of the parameters in the model
and hence is a bit quicker to run.
This model is a Bayesian hierarchical model that serves two main purposes:
Simulation model: can simulate data under user-specified conditions
and run replicated data sets under the Bayesian model to observed the behavior
of the system under random realizations of simulated data.
Posterior inference model: can use actual observed data from the field,
run it through the Bayesian model, and make inference on parameter(s) of
interest using the posterior distribution(s).
The posterior distributions are avaialable for a particular parameter, say tau, by
typing name_of_your_model$taumat.
Note: be careful about the size of the taumat matrix you are calling. The
last index of any of the variables from above is the MCMC replications and so we
would typically always omit the last index when looking at any particular variable.
If we want to look at the posterior distribution of the cluster level
prevalence (tau) for the first replication in the first subzone, we
will note that taumat is a matrix with the first dimension indexed by
replication, the second dimension indexed by subzone, and the third dimension
indexed by MCMC replications. Then, we will type something like
name_of_your_model$taumat[1, 1, ] to visually
inspect the posterior distribution in the form of a vector. For the second
replication in the fourth subzone, we can type
name_of_your_model$taumat[2, 4, ], and so forth.
Then, we can make histograms of these distributions if we so desire by the
following code:
hist(name_of_your_model$taumat[1, 1, ], col = "cyan");box("plot").
To observe a trace plot, we can type:
plot(name_of_your_model$taumat[1, 1, ], type = "l")
for all of the MCMC replications and we can look
at the trace plot after a burnin of 1000 iterations by typing:
plot(name_of_your_model$taumat[1, 1, -c(1:1000)], type ="l").
Value
This function is the 'no storage' model meaning it does not return as many values as the
'storage' model, EpiBayes_s. It returns enough to perform inference
but not to perform diagnostics for the model fit nor MCMC convergence.
If this is the first time running the model, we recommend that the user utilizes
the function EpiBayes_ns and diagnose issues before continuing with
this 'no storage' model.
Nevertheless, below are the outputs of this model.
p2.tilde Real scalar Proportion of simulated data sets that result in the probability of poi prevalence below poi.thresh with probability p1
p4.tilde Real scalar Proportion of simulated data sets that result in the probability of poi prevalence above poi.thresh with probability p1
p6.tilde Real scalar Proportion of simulated data sets that result in the probability of poi prevalence between poi.lb and poi.ub with probability p1
taumat Real array (reps x H x MCMCreps) Posterior distributions of the cluster-level prevalence for all simulated data sets (i.e., reps)
gammat Real matrix (reps x MCMCreps) Posterior distribution of the subzone-level prevalence
ForOthers Various other data not intended to be used by the user, but used to pass information on to the plot, summary, and print methods
The posterior distribution output, say taumat, can be manipulated after it is
returned with the coda package after it is converted to an mcmc object.
Parameter Meanings
Below we describe the meanings of the parameters in epidemiological language for ease
of implementation and elicitation of inputs to this function.
Parameter (3-level) Description (2-level) Description
omega Probability of disease being in the region. Not used.
gam Subzone-level (between-subzone) prevalence. Probability of disease being in the region.
z.gam Subzone-level (between-subzone) prevalence latent indicator variable. Not used.
tau Cluster-level (between-cluster) prevalence. Same as (3-level).
z.tau Cluster-level (between-cluster) prevalence latent indicator variable. Same as (3-level).
pi Subject-level (within-cluster) prevalence. Same as (3-level).
z.pi Subject-level (within-cluster) prevalence latent indicator variable. Same as (3-level).
mu Mean prevalence among infected clusters. Same as (3-level).
psi (Related to) variability of prevalence among infected clusters (inversely related so higher psi -> lower variance of prevalences among diseased clusters). Same as (3-level).
eta Diagnostic test sensitivity. Same as (3-level).
theta Diagnostic test specificity. Same as (3-level).
c1 Latent count of true positive diagnostic test results. Same as (3-level).
c2 Latent count of true negative diagnostic test results. Same as (3-level).
Note that in the code, each of these variables are denoted, for example,
taumat instead of plain tau to denote that that variable is a
matrix (or, more generally an array) of values.
References
Branscum, A., Johnson, W., and Gardner, I. (2006) Sample size calculations for disease
freedom and prevalence estimation surveys. Statistics in Medicine 25,
2658-2674.
See Also
The function EpiBayes_s stores more output so the user may check
diagnostics, but is understandably slower to execute.
Examples
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testrun_nostorage = EpiBayes_ns(
H = 2,
k = rep(30, 2),
n = rep(rep(150, 30), 2),
seasons = rep(c(1, 2, 3, 4), each = 15),
reps = 10,
MCMCreps = 10,
poi = "tau",
y = NULL,
mumodes = matrix(c(
0.50, 0.70,
0.50, 0.70,
0.02, 0.50,
0.02, 0.50
), 4, 2, byrow = TRUE
),
pi.thresh = 0.05,
tau.thresh = 0.02,
gam.thresh = 0.10,
tau.T = 0,
poi.lb = 0,
poi.ub = 1,
p1 = 0.95,
psi = 4,
omegaparm = c(100, 1),
gamparm = c(100, 1),
tauparm = c(1, 1),
etaparm = c(100, 6),
thetaparm = c(100, 6),
burnin = 1
)
testrun_nostorage
print(testrun_nostorage)
testrun_nostoragesummary = summary(testrun_nostorage, prob = 0.90, n.output = 5)
testrun_nostoragesummary
plot(testrun_nostorage$taumat[1, 1, ], type = "l")
plot(testrun_nostorage$gammat[1, ], type = "l")
## Can't look at any other posterior distributions other than gam and tau
## Not run:
plot(testrun_nostorage$pimat[1, 1, ], type = "l")
plot(testrun_nostorage$omegamat[1, ], type = "l")
## End(Not run)
EpiBayes documentation built on May 30, 2017, 4:01 a.m.
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Description Usage Arguments Details Value Parameter Meanings References See Also Examples
Description
This function is used to model disease (freedom and prevalence estimation) using a Bayesian hierarchical model with one, two, or three levels of sampling. The most general, the three level, would be represented by the hierarchy: (region -> subzone -> cluster -> subject) and the two- and one- level sampling would simply be the same with either subzone removed or subzone and cluster removed, respectively. This function is the 'no storage' model and hence stores only immediately relevant output.
Usage
1 2 3 4 5 6 | EpiBayes_ns(H, k, n, seasons, reps, MCMCreps, poi = "tau", y = NULL,
mumodes = matrix(c(0.5, 0.7, 0.5, 0.7, 0.02, 0.5, 0.02, 0.5), 4, 2, byrow =
TRUE), pi.thresh = 0.02, tau.thresh = 0.05, gam.thresh = 0.1,
tau.T = 0, poi.lb = 0, poi.ub = 1, p1 = 0.95, psi = 4,
omegaparm = c(100, 1), gamparm = c(100, 1), tauparm = c(1, 1),
etaparm = c(100, 6), thetaparm = c(100, 6), burnin = 1000)
|
Arguments
H |
Number of subzones/states. Should be a 1 if there are only one or two levels of sampling. Integer scalar. |
k |
Number of clusters / farms / ponds / herds. Should be a 1 if there is only one
level of sampling. Integer vector ( |
n |
Number of subjects / animals / mussels / pigs per cluster (can differ among
clusters). Integer vector ( |
seasons |
Numeric season for each cluster in the order: Summer (1), Fall (2),
Winter (3), Spring (4). Integer vector ( |
reps |
Number of (simulated) replicated data sets. Integer scalar. |
MCMCreps |
Number of iterations in the MCMC chain per replicated data set. Integer scalar. |
poi |
The p(arameter) o(f) i(nterest) specifies one of the subzone-level prevalence
( |
y |
An optional input of sums of positive diagnostic testing results if one has a
specific set of diagnostic testing outcomes for every subject (will simulate these
if this is left as |
mumodes |
Modes and (a) 95th percentiles for mode ≤q 0.50 or (b) 5th percentiles for mode > 0.5 for season-specific mean prevalences for diseased clusters in the order: Summer, Fall, Winter, Spring. Real matrix (4 x 2). |
pi.thresh |
Threshold that we must show subject-level prevalence is below to declare disease freedom. Real scalar. |
tau.thresh |
Threshold that we must show cluster-level prevalence is below to declare disease freedom. Real scalar. |
gam.thresh |
Threshold that we must show subzone-level prevalence is below to declare disease freedom. Real scalar. |
tau.T |
Assumed true cluster-level prevalence (used to simulate data to feed into the Bayesian model). Real scalar. |
poi.lb,poi.ub |
Lower and upper bounds for posterior |
p1 |
Probability we must show |
psi |
(Inversely related to) the variability of the subject-level prevalences in diseased clusters. Real scalar. |
omegaparm |
Prior parameters for the beta-distributed input |
gamparm |
Prior parameters for the beta-distributed input |
tauparm |
Prior parameters for the beta-distributed input |
etaparm |
Prior parameters for the beta-distributed input |
thetaparm |
Prior parameters for the beta-distributed input |
burnin |
Number of MCMC iterations to discard from the beginning of the chain. Integer scalar. |
Details
Note that this function performs in the same manner as EpiBayes_s except
it doesn't store the posterior distributions of all of the parameters in the model
and hence is a bit quicker to run.
This model is a Bayesian hierarchical model that serves two main purposes:
Simulation model: can simulate data under user-specified conditions and run replicated data sets under the Bayesian model to observed the behavior of the system under random realizations of simulated data.
Posterior inference model: can use actual observed data from the field, run it through the Bayesian model, and make inference on parameter(s) of interest using the posterior distribution(s).
The posterior distributions are avaialable for a particular parameter, say tau, by
typing name_of_your_model$taumat.
Note: be careful about the size of the taumat matrix you are calling. The
last index of any of the variables from above is the MCMC replications and so we
would typically always omit the last index when looking at any particular variable.
If we want to look at the posterior distribution of the cluster level prevalence (
tau) for the first replication in the first subzone, we will note that taumat is a matrix with the first dimension indexed by replication, the second dimension indexed by subzone, and the third dimension indexed by MCMC replications. Then, we will type something likename_of_your_model$taumat[1, 1, ]to visually inspect the posterior distribution in the form of a vector. For the second replication in the fourth subzone, we can typename_of_your_model$taumat[2, 4, ], and so forth. Then, we can make histograms of these distributions if we so desire by the following code:hist(name_of_your_model$taumat[1, 1, ], col = "cyan");box("plot"). To observe a trace plot, we can type:plot(name_of_your_model$taumat[1, 1, ], type = "l")for all of the MCMC replications and we can look at the trace plot after a burnin of 1000 iterations by typing:plot(name_of_your_model$taumat[1, 1, -c(1:1000)], type ="l").
Value
This function is the 'no storage' model meaning it does not return as many values as the
'storage' model, EpiBayes_s. It returns enough to perform inference
but not to perform diagnostics for the model fit nor MCMC convergence.
If this is the first time running the model, we recommend that the user utilizes
the function EpiBayes_ns and diagnose issues before continuing with
this 'no storage' model.
Nevertheless, below are the outputs of this model.
p2.tilde | Real scalar | Proportion of simulated data sets that result in the probability of poi prevalence below poi.thresh with probability p1 |
p4.tilde | Real scalar | Proportion of simulated data sets that result in the probability of poi prevalence above poi.thresh with probability p1 |
p6.tilde | Real scalar | Proportion of simulated data sets that result in the probability of poi prevalence between poi.lb and poi.ub with probability p1 |
taumat | Real array (reps x H x MCMCreps) | Posterior distributions of the cluster-level prevalence for all simulated data sets (i.e., reps) |
gammat | Real matrix (reps x MCMCreps) | Posterior distribution of the subzone-level prevalence |
ForOthers | Various other data not intended to be used by the user, but used to pass information on to the plot, summary, and print methods |
|
The posterior distribution output, say taumat, can be manipulated after it is
returned with the coda package after it is converted to an mcmc object.
Parameter Meanings
Below we describe the meanings of the parameters in epidemiological language for ease of implementation and elicitation of inputs to this function.
| Parameter | (3-level) Description | (2-level) Description |
omega | Probability of disease being in the region. | Not used. |
gam | Subzone-level (between-subzone) prevalence. | Probability of disease being in the region. |
z.gam | Subzone-level (between-subzone) prevalence latent indicator variable. | Not used. |
tau | Cluster-level (between-cluster) prevalence. | Same as (3-level). |
z.tau | Cluster-level (between-cluster) prevalence latent indicator variable. | Same as (3-level). |
pi | Subject-level (within-cluster) prevalence. | Same as (3-level). |
z.pi | Subject-level (within-cluster) prevalence latent indicator variable. | Same as (3-level). |
mu | Mean prevalence among infected clusters. | Same as (3-level). |
psi | (Related to) variability of prevalence among infected clusters (inversely related so higher psi -> lower variance of prevalences among diseased clusters). | Same as (3-level). |
eta | Diagnostic test sensitivity. | Same as (3-level). |
theta | Diagnostic test specificity. | Same as (3-level). |
c1 | Latent count of true positive diagnostic test results. | Same as (3-level). |
c2 | Latent count of true negative diagnostic test results. | Same as (3-level). |
Note that in the code, each of these variables are denoted, for example,
taumat instead of plain tau to denote that that variable is a
matrix (or, more generally an array) of values.
References
Branscum, A., Johnson, W., and Gardner, I. (2006) Sample size calculations for disease freedom and prevalence estimation surveys. Statistics in Medicine 25, 2658-2674.
See Also
The function EpiBayes_s stores more output so the user may check
diagnostics, but is understandably slower to execute.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | testrun_nostorage = EpiBayes_ns(
H = 2,
k = rep(30, 2),
n = rep(rep(150, 30), 2),
seasons = rep(c(1, 2, 3, 4), each = 15),
reps = 10,
MCMCreps = 10,
poi = "tau",
y = NULL,
mumodes = matrix(c(
0.50, 0.70,
0.50, 0.70,
0.02, 0.50,
0.02, 0.50
), 4, 2, byrow = TRUE
),
pi.thresh = 0.05,
tau.thresh = 0.02,
gam.thresh = 0.10,
tau.T = 0,
poi.lb = 0,
poi.ub = 1,
p1 = 0.95,
psi = 4,
omegaparm = c(100, 1),
gamparm = c(100, 1),
tauparm = c(1, 1),
etaparm = c(100, 6),
thetaparm = c(100, 6),
burnin = 1
)
testrun_nostorage
print(testrun_nostorage)
testrun_nostoragesummary = summary(testrun_nostorage, prob = 0.90, n.output = 5)
testrun_nostoragesummary
plot(testrun_nostorage$taumat[1, 1, ], type = "l")
plot(testrun_nostorage$gammat[1, ], type = "l")
## Can't look at any other posterior distributions other than gam and tau
## Not run:
plot(testrun_nostorage$pimat[1, 1, ], type = "l")
plot(testrun_nostorage$omegamat[1, ], type = "l")
## End(Not run)
|
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