Description Usage Arguments Value Author(s) References See Also Examples

Determines effective sample size of a parametric prior distribution in Bayesian conjugate models (beta-binomial, gamma-exponential, gamma-Poisson, dirichlet-multinomial, normal-normal, inverse-chi-squared-normal, inverse-gamma-normal), Bayesian linear and logistic regression models, Bayesian continual reassessment method (CRM), and Bayesian time to event model.

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`model` |
Model specifications. Options are: 'betaBin' for beta-binomial model; 'gammaEx' for gamma-exponential model; 'gammaPois' for gamma-Poisson model; 'dirMult' for dirichlet-multinomial model; 'normNorm' for normal-normal model; 'invChisqNorm' for scaled-inverse-chi-squared-normal model; or 'invGammaNorm' for inverse-gamma-normal models. For non-conjugate models, options are: 'linreg' for linear regression model; and 'logistic' for logistic regression models. In addition, the continual reassessment method (CRM) can be specified as: model = 'crm', or as 'tite.crm' for the time-to-event CRM (TITE CRM). Finally, time to event models can be specified as model = 'surv' |

`label` |
Optional labeling for hyperparameters. Please see examples for sample usage. |

`prior` |
Prior distribution specification specified as a list. Options are 'beta', 'gamma', 'dirichlet', 'norm' (for normal prior), 'scaled-inverse-chisquared', and 'inverse-gamma'. |

`m` |
A positive integer specified as an maximum value in which ESS is searched. |

`nsim` |
Number of simulations for numerical approximation (specified only for model = 'linreg' or model = 'logistic'). |

`ncov` |
(Required for linear or logistic regression model) Number of covariates |

`svec1` |
(Required for linear or logistic regression model) Specification of first subvector for calculating ESS |

`svec2` |
(Required for linear or logistic regression model) Specification of second subvector for calculating ESS |

`PI` |
(Required for CRM) A vector of the true toxicity probabilites associated with the doses. |

`betaSD` |
(Required for CRM) Standard deviation of the normal prior of the model parameter. |

`target` |
(Required for CRM) The target dose limiting toxicity (DLT) rate. |

`obswin` |
(Further required for TITE (time-to-event) CRM) The observation window with respect to which the maximum tolerated dose (MTD) is defined. Default is obswin=30. |

`rate` |
(Further required for TITE (time-to-event) CRM) Patient arrival rate: Expected number of arrivals per observation window. Example: obswin=6 and rate=3 means expecting 3 patients arrive in 6 time units. Default is rate=2. |

`accrual` |
(Further required for TITE (time-to-event) CRM) Patient accrual scheme. Default is accrual="poisson". Alternatively use accrual="fixed" whereby inter-patient arrival is fixed. |

`shapeParam` |
(Required for time to event model) Shape parameter of the inverse gamma prior |

`scaleParam` |
(Required for time to event model) Scale parameter of the inverse gamma prior |

`fast` |
Accelerate ESS computation for linear or logistic regression models with C++ code? Default is fast=TRUE. |

`ESS` |
Returns ESS |

`ESSsubvec1` |
(For linear or logistic regression model) ESS for the first sub-vector |

`ESSsubvec2` |
(For linear or logistic regression model) ESS for the second sub-vector |

Jaejoon Song <jjsong2@mdanderson.org>, Satoshi Morita <smorita@kuhp.kyoto-u.ac.jp>, J. Jack Lee <jjlee@mdanderson.org>

Morita, S., Thall, P. F., and Muller, P. (2008). Determining the effective sample size of a parametric prior. Biometrics, 64, 595-602.

Morita, S., Thall, P. F., and Muller, P. (2010). Evaluating the impact of prior assumptions in Bayesian biostatistics. Stat Biosci, 2, 1-17.

O'Quigley J., Pepe M., Fisher, L. (1990).Continual reassessment method: A practical design for phase I clinical trials in cancer. Biometrics, 46, 33-48.

Thall, P. F., Wooten, L. H., Tannir, N. M. (2005). Monitoring event times in early phase clinical trials: some practical issues. Clinical Trials, 2, 467-478.

https://biostatistics.mdanderson.org/SoftwareDownload/

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library(BayesESS)
# Calculating ESS for a beta-binomial model with
# beta(1,2) prior
ess(model='betaBin',prior=c('beta',1,2))
# Calculating ESS for a gamma-exponential model with
# gamma(2,4) prior
ess(model='gammaEx',prior=c('gamma',2,4))
# Calculating ESS for a gamma-Poisson model with
# gamma(2,4) prior
ess(model='gammaPois',prior=c('gamma',2,4))
# Calculating ESS for a dirichlet-multinomial model with
# dirichlet(10,15,20) prior
ess(model='dirMult',prior=c('dirichlet',10,15,20))
# Calculating ESS for a scaled-inverse-chi-squared-normal model
# when mean is known and variance is unknown
# with scaled-inverse-chi-squared(nu_0=10,sigma^2_0=1) prior for variance
# ESS for such model can be found analytically
ess(model='invChisqNorm',prior=c(10,1))
# Calculating ESS for a normal-normal model
# when mean is unknown and variance is known
# with normal(mu_0=10,sigma^2=1,n_0=30) prior (i.e. known variance is sigma^2=1)
# ESS for such model can be found analytically (ESS = n_0)
ess(model='normNorm',prior=c('norm',10,1,30))
# Calculating ESS for a scaled-inverse-chi-squared-normal model
# when mean and variance are both unknown
# with scaled-inverse-chi-squared(nu_0=10,sigma^2_0=1) prior for variance
# and normal(mu_0=1,sigma^2/phi=sigma^2/30) prior for mean
# Smaller nsim = 1000 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
## Not run:
ess(model='invChisqNorm',prior=c(10,1,1,30),m=20,nsim=1000)
## End(Not run)
# Calculating ESS for a inverse-gamma-normal model
# when mean is known and variance is unknown
# with inverse-gamma(alpha=5,beta=5) prior
# Note: the inverse-gamma(nu_0/2,nu_0*sigma^2_0/2) prior is
# equivalent to scaled-inverse-chi-squared(nu_0,sigma^2_0)
# ESS for such model can be found analytically
ess(model='invGammaNorm',prior=c(5,5))
# Calculating ESS for a inverse-gamma-normal model
# when mean and variance are both unknown
# with inverse-gamma(alpha=5,beta=5) prior
# and normal(mu_0=1,sigma^2/phi=sigma^2/30) prior for mean
# Note: the inverse-gamma(nu_0/2,nu_0*sigma^2_0/2) prior is
# equivalent to scaled-inverse-chi-squared(nu_0,sigma^2_0)
# Smaller nsim = 1000 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
## Not run:
ess(model='invGammaNorm',prior=c(5,5,1,30),m=20,nsim=1000)
## End(Not run)
# Calculating ESS for a linear regression model with
# three covariates, with priors specified as
# beta0 ~ N(0,1); beta1 ~ N(0,.1); beta2 ~ N(0,.2); beta3 ~ N(0,.3); tau ~ Gamma(1,1);
# Smaller nsim = 50 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
# The value of nsim as low as 1,000 may be used to reduce runtime.
## Not run:
ess(model='linreg',label=c('beta0','beta1','beta2','beta3','tau'),
prior=list(c('norm',0,1),c('norm',0,.1),c('norm',0,.2),c('norm',0,.3),c('gamma',1,1)),
ncov=3,m=50,nsim=50,svec1=c(0,1,1,1,0),svec2=c(0,0,0,0,1))
## End(Not run)
# Calculating ESS for a linear regression model with
# two covariates, with priors specified as
# beta0 ~ N(0,1); beta1 ~ N(0,.1); beta2 ~ N(0,.2); tau ~ Gamma(1,1);
# Smaller nsim = 50 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
# The value of nsim as low as 1,000 may be used to reduce runtime.
## Not run:
ess(model='linreg',label=c('beta0','beta1','beta2','tau'),
prior=list(c('norm',0,1),c('norm',0,.1),c('norm',0,.2),c('gamma',1,1)),
ncov=2,m=50,nsim=50,svec1=c(0,1,1,0),svec2=c(0,0,0,1))
## End(Not run)
# Calculating ESS for a logistic regression model with
# three covariates, with priors specified as
# beta0 ~ N(0,1); beta1 ~ N(0,1); beta2 ~ N(0,1); beta3 ~ N(0,1)
# Smaller nsim = 50 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
# The value of nsim as low as 1,000 may be used to reduce runtime.
## Not run:
ess(model='logistic',label=c('beta0','beta1','beta2','beta3'),
prior=list(c('norm',0,1),c('norm',0,1),c('norm',0,1),c('norm',0,1)),
ncov=3,m=50,nsim=50,svec1=c(1,0,0,0),svec2=c(0,1,1,1))
## End(Not run)
# Calculating ESS for a continual reassessment method (CRM)
# with true toxicity probabilites PI=c(.02,.06,.10,.18,.30)
# prior is specified as N(0,2.5) with target DLT = 0.2
# Smaller nsim = 50 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
# The value of nsim as low as 1,000 may be used to reduce runtime.
## Not run:
ess(model='crm',prior=c(.02,.06,.10,.18,.30),
m=7,nsim=50,
PI=c(.02,.06,.10,.18,.30),
betaSD=sqrt(2.5),target=0.2)
## End(Not run)
# Calculating ESS for a TITE CRM
# with true toxicity probabilites PI=c(.02,.06,.10,.18,.30)
# prior is specified as N(0,1.5) with target DLT = 0.2
# Smaller nsim = 50 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
# The value of nsim as low as 1,000 may be used to reduce runtime.
## Not run:
ess(model='tite.crm',prior=c(.02,.06,.10,.18,.30),
m=7,nsim=50,
PI=c(.02,.06,.10,.18,.30),
betaSD=sqrt(1.5),target=0.2,obswin=30,rate=2,
accrual="poisson")
## End(Not run)
# Calculating ESS for a time to event model
# prior is specified as inverse-gamma(5.348,30.161)
# Smaller nsim = 50 is specified for illustration purposes
# The user can use nsim = 10,000 to carry out the most accurate ESS computations.
# The value of nsim as low as 1,000 may be used to reduce runtime.
## Not run:
ess(model='surv',shapeParam=5.348,scaleParam=30.161,m=7,nsim=50)
## End(Not run)
``` |

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