Title: | Bayesian Modeling via Frequentist Goodness-of-Fit |
---|---|
Description: | A Bayesian data modeling scheme that performs four interconnected tasks: (i) characterizes the uncertainty of the elicited parametric prior; (ii) provides exploratory diagnostic for checking prior-data conflict; (iii) computes the final statistical prior density estimate; and (iv) executes macro- and micro-inference. Primary reference is Mukhopadhyay, S. and Fletcher, D. 2018 paper "Generalized Empirical Bayes via Frequentist Goodness of Fit" (<https://www.nature.com/articles/s41598-018-28130-5 >). |
Authors: | Subhadeep Mukhopadhyay, Douglas Fletcher |
Maintainer: | Doug Fletcher <[email protected]> |
License: | GPL-2 |
Version: | 5.2 |
Built: | 2024-10-31 06:53:00 UTC |
Source: | CRAN |
A Bayesian data modeling scheme that performs four interconnected tasks: (i) characterizes the uncertainty of the elicited parametric prior; (ii) provides exploratory diagnostic for checking prior-data conflict; (iii) computes the final statistical prior density estimate; and (iv) executes macro- and micro-inference.
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
Results from an inter-laboratory study involving measurements for the level of arsenic in oyster tissue.
y
is the mean level of arsenic from a lab and se
is the standard error of the measurement.
data("arsenic")
data("arsenic")
A data frame of for
.
y
mean level of arsenic in the tissue measured by the lab
se
the standard error of the measurement by lab
Wille, S. and Berman, S., 1995. "Ninth round intercomparison for trace metals in marine sediments and biological tissues," NRC/NOAA.
The number of claims on an automobile insurance policy made by individuals during a single year.
data("AutoIns")
data("AutoIns")
A vector of length 9461.
value
number of auto insurance claims by the person
Efron, B. and Hastie, T., 2016. Computer Age Statistical Inference (Vol. 5). Cambridge University Press.
Results of a study that followed pre-school children in north-east Thailand from June 1982 through September 1985. Researchers recorded the number of times a child became ill during every 2-week period.
data("ChildIll")
data("ChildIll")
A vector of length .
value
number of times the child became ill during the study
Bohning, D., 2000. Computer-assisted Analysis of Mixtures and Applications: Meta-analysis, Disease Mapping, and Others (Vol. 81). CRC press.
The number of times Alexander Corbet captured a species of butterfly during a two-year period in Malaysia.
data("CorbBfly")
data("CorbBfly")
A vector of length .
value
number of times Corbet captured the species
Fisher, R.A., Corbet, A.S. and Williams, C.B., 1943. "The relation between the number of species and the number of individuals in a random sample of an animal population." The Journal of Animal Ecology, pp.42-58.
Efron, B. and Hastie, T., 2016. Computer Age Statistical Inference (Vol. 5). Cambridge University Press.
A function that calculates the full entropy of a DS(G,m) prior. For DS(G,m) with , also returns the excess entropy
LP.
DS.entropy(DS.GF.obj)
DS.entropy(DS.GF.obj)
DS.GF.obj |
Object resulting from running DS.prior function on a data set. |
ent |
The total entropy of the DS(G,m) prior where |
qLP |
The excess entropy when |
Doug Fletcher
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial") DS.entropy(rat.ds)
data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial") DS.entropy(rat.ds)
A function that generates the finite Bayes prior and posterior distribution, along with the Bayesian credible interval for the posterior mean.
DS.Finite.Bayes(DS.GF.obj, y.0, n.0 = NULL, cred.interval = 0.9, iters = 25)
DS.Finite.Bayes(DS.GF.obj, y.0, n.0 = NULL, cred.interval = 0.9, iters = 25)
DS.GF.obj |
Object from |
y.0 |
For Binomial family, number of success |
n.0 |
For the Binomial family, the total number of trials for the new study. In the Normal family, |
cred.interval |
The desired probability for the credible interval of the posterior mean; the default is 0.90 ( |
iters |
Integer value of total number of iterations. |
prior.fit |
Fitted values for the estimated parametric, DS, and finite Bayes prior distributions. |
post.fit |
Dataframe with |
interval |
The |
post.vec |
Vector containing the PEB posterior mean ( |
Doug Fletcher, Subhadeep Mukhopadhyay
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
Efron, B., 2018. "Bayes, Oracle Bayes, and Empirical Bayes," Technical Report.
## Not run: ### Finite Bayes: Rat with theta_71 (y_71 = 4, n_71 = 14) data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start. family = "Binomial") rat.FB <- DS.FiniteBayes(rat.ds, y.0 = 4, n.0 = 14) plot(rat.FB) ## End(Not run)
## Not run: ### Finite Bayes: Rat with theta_71 (y_71 = 4, n_71 = 14) data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start. family = "Binomial") rat.FB <- DS.FiniteBayes(rat.ds, y.0 = 4, n.0 = 14) plot(rat.FB) ## End(Not run)
A function that generates macro-estimates with their uncertainty (standard error).
DS.macro.inf(DS.GF.obj, num.modes = 1, method = c("mean", "mode"), iters = 25, exposure = NULL)
DS.macro.inf(DS.GF.obj, num.modes = 1, method = c("mean", "mode"), iters = 25, exposure = NULL)
DS.GF.obj |
Object from |
num.modes |
The number of modes indicated by |
method |
Returns mean or mode(s) (based on user choice) along with the associated standard error(s). |
iters |
Integer value of total number of iterations. |
exposure |
In the case where |
DS.GF.macro.obj |
Object of class |
model.modes |
For |
mode.sd |
For |
boot.modes |
For |
model.mean |
For |
mean.sd |
For |
boot.mean |
For |
prior.fit |
Fitted values of estimated prior imported from the |
Doug Fletcher, Subhadeep Mukhopadhyay
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
## Not run: ### MacroInference: Mode data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start. family = "Binomial") rat.ds.macro <- DS.macro.inf(rat.ds, num.modes = 2, method = "mode", iters = 5) rat.ds.macro plot(rat.ds.macro) ### MacroInference: Mean data(ulcer) ulcer.start <- gMLE.nn(ulcer$y, ulcer$se)$estimate ulcer.ds <- DS.prior(ulcer, max.m = 4, ulcer.start) ulcer.ds.macro <- DS.macro.inf(ulcer.ds, num.modes = 1, method = "mean", iters = 5) ulcer.ds.macro plot(ulcer.ds.macro) ## End(Not run)
## Not run: ### MacroInference: Mode data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start. family = "Binomial") rat.ds.macro <- DS.macro.inf(rat.ds, num.modes = 2, method = "mode", iters = 5) rat.ds.macro plot(rat.ds.macro) ### MacroInference: Mean data(ulcer) ulcer.start <- gMLE.nn(ulcer$y, ulcer$se)$estimate ulcer.ds <- DS.prior(ulcer, max.m = 4, ulcer.start) ulcer.ds.macro <- DS.macro.inf(ulcer.ds, num.modes = 1, method = "mean", iters = 5) ulcer.ds.macro plot(ulcer.ds.macro) ## End(Not run)
Provides DS nonparametric adaptive Bayes and parametric estimate for a specific observation .
DS.micro.inf(DS.GF.obj, y.0, n.0, e.0 = NULL)
DS.micro.inf(DS.GF.obj, y.0, n.0, e.0 = NULL)
DS.GF.obj |
Object resulting from running DS.prior function on a data set. |
y.0 |
For Binomial family, number of success |
n.0 |
For the Binomial family, the total number of trials for the new study. In the Normal family, |
e.0 |
In the case of the Poisson family with exposure, represents the exposure value for a given count value |
Returns an object of class DS.GF.micro
that can be used in conjunction with plot command to display the DS posterior distribution for the new study.
DS.mean |
Posterior mean for |
DS.mode |
Posterior mode for |
PEB.mean |
Posterior mean for |
PEB.mode |
Posterior mode for |
post.vec |
Vector containing |
study |
User-provided |
post.fit |
Dataframe with |
Doug Fletcher, Subhadeep Mukhopadhyay
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
### MicroInference for Naval Shipyard Data: sample where y = 0 and n = 5 data(ship) ship.ds <- DS.prior(ship, max.m = 2, c(.5,.5), family = "Binomial") ship.ds.micro <- DS.micro.inf(ship.ds, y.0 = 0, n.0 = 5) ship.ds.micro plot(ship.ds.micro)
### MicroInference for Naval Shipyard Data: sample where y = 0 and n = 5 data(ship) ship.ds <- DS.prior(ship, max.m = 2, c(.5,.5), family = "Binomial") ship.ds.micro <- DS.micro.inf(ship.ds, y.0 = 0, n.0 = 5) ship.ds.micro plot(ship.ds.micro)
A function that determines the posterior expectations and posterior modes for a set of observed data.
DS.posterior.reduce(DS.GF.obj, exposure)
DS.posterior.reduce(DS.GF.obj, exposure)
DS.GF.obj |
Object resulting from running DS.prior function on a data set. |
exposure |
In the case of the Poisson family with exposure, represents the exposure values for the count data. |
Returns matrix with the columns indicating PEB mean, DS mean, PEB mode, and DS modes for
observations in the data set.
Doug Fletcher
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial") DS.posterior.reduce(rat.ds)
data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial") DS.posterior.reduce(rat.ds)
A function that generates the uncertainty diagnostic function (U-function
) and estimates DS prior model.
DS.prior(input, max.m = 8, g.par, family = c("Normal","Binomial", "Poisson"), LP.type = c("L2", "MaxEnt"), smooth.crit = "BIC", iters = 200, B = 1000, max.theta = NULL)
DS.prior(input, max.m = 8, g.par, family = c("Normal","Binomial", "Poisson"), LP.type = c("L2", "MaxEnt"), smooth.crit = "BIC", iters = 200, B = 1000, max.theta = NULL)
input |
For |
max.m |
The truncation point |
g.par |
Vector with estimated parameters for specified conjugate prior distribution |
family |
The distribution of |
LP.type |
User selects either |
smooth.crit |
User selects either |
iters |
Integer value that gives the maximum number of iterations allowed for convergence; default is 200. |
B |
Integer value for number of grid points used for distribution output; default is 1000. |
max.theta |
For |
Function can take and will return the Bayes estimate with given starting parameters. Returns an object of class
DS.GF.obj
; this object can be used with plot command to plot the U-function (Ufunc
), Deviance Plots (mDev
), and DS-G comparison (DS_G
).
LP.par |
|
g.par |
Parameters for |
LP.max.uns |
Vector of all LP-Fourier coefficients prior to smoothing, where the length is the same as |
LP.max.smt |
Vector of all smoothed LP-Fourier coefficients, where the length is the same as |
prior.fit |
Fitted values for the estimated prior. |
UF.data |
Dataframe that contains values required for plotting the U-function. |
dev.df |
Dataframe that contains deviance values for values of |
m.val |
The value of |
sm.crit |
Smoothing criteria; either |
fam |
The user-selected family. |
LP.type |
User-selected representation of |
obs.data |
Observed data provided by user for |
Doug Fletcher, Subhadeep Mukhopadhyay
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
Mukhopadhyay, S., 2017. "Large-Scale Mode Identification and Data-Driven Sciences," Electronic Journal of Statistics, 11(1), pp.215-240.
data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial") rat.ds plot(rat.ds, plot.type = "Ufunc") plot(rat.ds, plot.type = "DSg") plot(rat.ds, plot.type = "mDev")
data(rat) rat.start <- gMLE.bb(rat$y, rat$n)$estimate rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial") rat.ds plot(rat.ds, plot.type = "Ufunc") plot(rat.ds, plot.type = "DSg") plot(rat.ds, plot.type = "mDev")
Generates samples of size from DS
prior distribution.
DS.sampler(k, g.par, LP.par, con.prior, LP.type, B) DS.sampler.post(k, g.par, LP.par, y.0, n.0, con.prior, LP.type, B)
DS.sampler(k, g.par, LP.par, con.prior, LP.type, B) DS.sampler.post(k, g.par, LP.par, y.0, n.0, con.prior, LP.type, B)
k |
Total number of samples requested. |
g.par |
Estimated parameters for specified conjugate prior distribution (i.e beta prior: |
LP.par |
LP coefficients for DS prior. |
con.prior |
The distribution type of conjugate prior |
LP.type |
The type of LP means, either |
y.0 |
Depending on |
n.0 |
Depending on |
B |
The number of grid points, default is 250. |
DS.sampler.post
uses the same type of sampling as DS.sampler
to generate random values from a DS posterior distribution.
Vector of length containing sampled values from DS prior or DS posterior.
Doug Fletcher, Subhadeep Mukhopadhyay
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
Mukhopadhyay, S., 2017. "Large-Scale Mode Identification and Data-Driven Sciences," Electronic Journal of Statistics, 11(1), pp.215-240.
##Extracted parameters from rat.ds object rat.g.par <- c(2.3, 14.1) rat.LP.par <- c(0, 0, -0.5) samps.prior <- DS.sampler(25, rat.g.par, rat.LP.par, con.prior = "Beta") hist(samps.prior,15) ##Posterior for rat data samps.post <- DS.sampler.post(25, rat.g.par, rat.LP.par, y.0 = 4, n.0 = 14, con.prior = "Beta") hist(samps.post, 15)
##Extracted parameters from rat.ds object rat.g.par <- c(2.3, 14.1) rat.LP.par <- c(0, 0, -0.5) samps.prior <- DS.sampler(25, rat.g.par, rat.LP.par, con.prior = "Beta") hist(samps.prior,15) ##Posterior for rat data samps.post <- DS.sampler.post(25, rat.g.par, rat.LP.par, y.0 = 4, n.0 = 14, con.prior = "Beta") hist(samps.post, 15)
The observed rotation velocities and their uncertainties of Low Surface Brightness (LSB) galaxies, along with the physical radius of the galaxy.
data("galaxy")
data("galaxy")
A data frame of for
.
y
actual observed (smoothed) velocity
se
uncertainty of observed velocity
X
physical radius of the galaxy
De Blok, W.J.G., McGaugh, S.S., and Rubin, V. C., 2001. "High-resolution rotation curves of low surface brightness galaxies. II. Mass models," The Astronomical Journal, 122(5), p. 2396.
Determines the LP basis for a given parametric prior distribution.
gLP.basis(x, g.par, m, con.prior, ind)
gLP.basis(x, g.par, m, con.prior, ind)
x |
|
g.par |
Estimated parameters for specified prior distribution (i.e beta prior: |
m |
Number of LP-Polynomial basis. |
con.prior |
Specified conjugate prior distribution for basis functions. Options are |
ind |
Default is NULL which returns matrix with |
Matrix with m
columns of values for the LP-Basis functions evaluated at x
-values.
Subhadeep Mukhopadhyay, Doug Fletcher
Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.
Mukhopadhyay, S., 2017. "Large-Scale Mode Identification and Data-Driven Sciences," Electronic Journal of Statistics, 11(1), pp.215-240.
Mukhopadhyay, S. and Parzen, E., 2014. "LP Approach to Statistical Modeling," arXiv: 1405.2601.
Computes type-II Maximum likelihood estimates and
for Beta prior
Beta
.
gMLE.bb(success, trials, start = NULL, optim.method = "default", lower = 0, upper = Inf)
gMLE.bb(success, trials, start = NULL, optim.method = "default", lower = 0, upper = Inf)
success |
Vector containing the number of successes. |
trials |
Vector containing the total number of trials that correspond to the successes. |
start |
initial parameters; default is NULL which allows function to determine MoM estimates as initial parameters. |
optim.method |
optimization method in |
lower |
lower bound for parameters; default is 0. |
upper |
upper bound for parameters; default is infinity. |
estimate |
MLE estimate for beta parameters. |
convergence |
Convergence code from |
loglik |
Loglikelihood that corresponds with MLE estimated parameters. |
initial |
Initial parameters, either user-defined or determined from method of moments. |
hessian |
Estimated Hessian matrix at the given solution. |
Aleksandar Bradic
https://github.com/SupplyFrame/EmpiricalBayesR/blob/master/EmpiricalBayesEstimation.R
data(rat) ### MLE estimate of alpha and beta rat.mle <- gMLE.bb(rat$y, rat$N)$estimate rat.mle ### MoM estimate of alpha and beta rat.mom <- gMLE.bb(rat$y, rat$N)$initial rat.mom
data(rat) ### MLE estimate of alpha and beta rat.mle <- gMLE.bb(rat$y, rat$N)$estimate rat.mle ### MoM estimate of alpha and beta rat.mom <- gMLE.bb(rat$y, rat$N)$initial rat.mom
Computes type-II Maximum likelihood estimates and
for Normal prior
Normal
.
gMLE.nn(value, se, fixed = FALSE, method = c("DL","SJ","REML","MoM"))
gMLE.nn(value, se, fixed = FALSE, method = c("DL","SJ","REML","MoM"))
value |
Vector of values. |
se |
Standard error for each value. |
fixed |
When |
method |
Determines the method to find |
estimate |
Vector with both estimated |
mu.hat |
Estimated |
tau.sq |
Estimated |
method |
User-selected method. |
Doug Fletcher
Marin-Martinez, F. and Sanchez-Meca, J., 2010. "Weighting by inverse variance or by sample size in random-effects meta-analysis," Educational and Psychological Measurement, 70(1), pp. 56-73.
Brown, L.D., 2008. "In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies," The Annals of Applied Statistics, pp. 113-152.
Sidik, K. and Jonkman, J.N., 2005. "Simple heterogeneity variance estimation for meta-analysis," Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(2), pp. 367-384.
data(ulcer) ### MLE estimate of alpha and beta ulcer.mle <- gMLE.nn(ulcer$y, ulcer$se, method = "DL")$estimate ulcer.mle ulcer.reml <- gMLE.nn(ulcer$y, ulcer$se, method = "REML")$estimate ulcer.reml
data(ulcer) ### MLE estimate of alpha and beta ulcer.mle <- gMLE.nn(ulcer$y, ulcer$se, method = "DL")$estimate ulcer.mle ulcer.reml <- gMLE.nn(ulcer$y, ulcer$se, method = "REML")$estimate ulcer.reml
Computes Type-II Maximum likelihood estimates and
for gamma prior
Gamma
.
gMLE.pg(cnt.vec, exposure = NULL, start.par = c(1,1))
gMLE.pg(cnt.vec, exposure = NULL, start.par = c(1,1))
cnt.vec |
Vector containing Poisson counts. |
exposure |
Vector containing exposures for each count. The default is no exposure, thus |
start.par |
Initial values that will pass to |
Returns a vector where the first component is and the second component is the scale parameter
for the gamma distribution:
Doug Fletcher
Koenker, R. and Gu, J., 2017. "REBayes: An R Package for Empirical Bayes Mixture Methods," Journal of Statistical Software, Articles, 82(8), pp. 1-26.
### without exposure data(ChildIll) ill.start <- gMLE.pg(ChildIll) ill.start ### with exposure data(NorbergIns) X <- NorbergIns$deaths E <- NorbergIns$exposure/344 norb.start <- gMLE.pg(X, exposure = E) norb.start
### without exposure data(ChildIll) ill.start <- gMLE.pg(ChildIll) ill.start ### with exposure data(NorbergIns) X <- NorbergIns$deaths E <- NorbergIns$exposure/344 norb.start <- gMLE.pg(X, exposure = E) norb.start
The number of claims on a life insurance policy for each of
Norwegian occupational categories and the total number of years the workers in each category were exposed to risk (
).
data("NorbergIns")
data("NorbergIns")
A data frame of the occupational group number (group
), the number of deaths (deaths
), and the years of exposure (exposure
) for .
group
Occupational group number
deaths
The number of deaths in the occupational group resulting in a claim on a life insurance policy.
exposure
The total number of years of exposure to risk for those who passed.
Norberg, R., 1989. "Experience rating in group life insurance," Scandinavian Actuarial Journal, 1989(4), pp. 194-224.
Koenker, R. and Gu, J., 2017. "REBayes: An R Package for Empirical Bayes Mixture Methods," Journal of Statistical Software, Articles, 82(8), pp. 1-26.
Incidence of endometrial stromal polyps in studys of female rats in control group of a 1977 study on the carcinogenic effects of a diabetic drug phenformin. For each of the
groups,
represents the number of rats who developed the tumors out of
total rats in the group.
data("rat")
data("rat")
A data frame of for
.
y
number of female rats in the study who developed polyps/tumors
n
total number of rats in the study
National Cancer Institute (1977), "Bioassay of phenformin for possible carcinogenicity," Technical Report No. 7.
Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., and Rubin, D.B., 2014. Bayesian Data Analysis (Vol. 3). Boca Raton, FL: CRC press.
Tarone, R.E., 1982. "The use of historical control information in testing for a trend in proportions," Biometrics, pp. 215-220.
Data represents results of quality-control inspections executed by Portsmouth Naval Shipyard on lots of welding materials. The data has observations of number of defects
out of the total number of tested
.
data("ship")
data("ship")
A data frame of for
.
y
number of defects found in the inspection
n
total samples tested in the inspection
Martz, H.F. and Lian, M.G., 1974. "Empirical Bayes estimation of the binomial parameter," Biometrika, 61(3), pp. 517-523.
The standardized mean difference and standard errors
for seven randomised studies on the use of topical steroids in treatment of chronic rhinosinusitis with nasal polyps.
data("steroid")
data("steroid")
A data frame of for
.
y
standard mean difference of clinical trials for topical steroids found in the study
se
standard error of the standard mean difference for the study
IntHout, J., Ioannidis, J. P., Rovers, M. M., & Goeman, J. J., 2016. "Plea for routinely presenting prediction intervals in meta-analysis," BMJ open, 6(7), e010247.
Data involves the number of malignant lymph nodes removed during intestinal surgery for cancer patients. For each patient,
is the total number of satellite nodes removed during surgery from a patient and
is the number of malignant nodes.
data("surg")
data("surg")
A data frame of for
.
y
number of malignant lymph nodes removed from the patient
n
total number of lymph nodes removed from the patient
Efron, B., 2016. "Empirical Bayes deconvolution estimates," Biometrika, 103(1), pp. 1-20.
An experiment that requires a common thumbtack to be "flipped" times. Out of these total number of flips,
is the total number of times that the thumbtack landed point up.
data("tacks")
data("tacks")
A data frame of for
.
y
number of times a thumbtack landed point up in the trial
n
total number of flips for the thumbtack in the trial
Beckett, L. and Diaconis, P., 1994. "Spectral analysis for discrete longitudinal data," Advances in Mathematics, 103(1), pp. 107-128.
During several studies of the oral antifungal agent terbinafine, a proportion of the patients in the trial terminated treatment due to some adverse effects. In the data set, is the number of terminated treatments and
is the total number of patients in the in the
trial.
data("terb")
data("terb")
A data frame of for
.
y
number of patients who terminated treatment early in the trial
n
total number of patients in the clinical trial
Young-Xu, Y. and Chan, K.A., 2008. "Pooling overdispersed binomial data to estimate event rate," BMC Medical Research Methodology, 8(1), p. 58.
The data consist of randomized trials between 1980 and 1989 of a surgical treatment for stomach ulcers. Each of the trials has an estimated log-odds ratio that measures the rate of occurrence of recurrent bleeding given the surgical treatment.
data("ulcer")
data("ulcer")
A data frame of se
for
.
y
log-odds of the occurrence of recurrent bleeding in the study
se
standard error of the log-odds for the study
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