Package 'CoMiRe' reference manual

Title:	Convex Mixture Regression
Description:	Posterior inference under the convex mixture regression (CoMiRe) models introduced by Canale, Durante, and Dunson (2018) <doi:10.1111/biom.12917>.
Authors:	Antonio Canale [aut, cre], Daniele Durante [ctb], Arianna Falcioni [aut], Luisa Galtarossa [aut], Tommaso Rigon [ctb]
Maintainer:	Antonio Canale <[email protected]>
License:	GPL-2
Version:	0.8
Built:	2024-12-15 07:38:23 UTC
Source:	CRAN

Convex Mixture Regression

Description

Posterior inference under the convex mixture regression (CoMiRe) models introduced by Canale, Durante, and Dunson (2018) <doi:10.1111/biom.12917>.

Details

The CoMiRe package implements the convex mixture regresion approach of Canale, Durante, and Dunson (2018) and some extensions to deal with binary response variables or to account for the presence of continuous and categorical confunders. Estimation is conducted via Gibbs sampler. Posterior plots for inference and goodness-of-fit tests are also available.

Author(s)

Antonio Canale [aut, cre], Daniele Durante [ctb], Arianna Falcioni [aut], Luisa Galtarossa [aut], Tommaso Rigon [ctb] Maintainer: Antonio Canale <[email protected]>

References

Canale, A., Durante, D., and Dunson, D. (2018), Convex Mixture Regression for Quantitative Risk Assessment, Biometrics, 74, 1331-1340

Additional risk function

Description

Additional risk function estimated from the object fit

Usage

add.risk(y, x, fit, mcmc, a, alpha=0.05, 
x.grid=NULL, y.grid=NULL)
add.risk(y, x, fit, mcmc, a, alpha=0.05, 
x.grid=NULL, y.grid=NULL)

Arguments

`y`	optional numeric vector for the response used in `comire.gibbs`. If `y` is missing, `y.grid` must be provided.
`x`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`.
`fit`	the output of `comire.gibbs`. an object of the class `classCoMiRe`.
`mcmc`	a list giving the MCMC parameters.
`a`	threshold of clinical interest for the response variable
`alpha`	level of the credible bands.
`x.grid`	optional numerical vector giving the actual values of the grid for x for plotting the additional risk function. If $x.gird$ is not provided, standard grids are automatically used.
`y.grid`	optional numerical vector giving the actual values of the grid for y for plotting the additional risk function. If $y.gird$ is not provided, standard grids are automatically used.

Value

A list of arguments for generating posterior output. It contains:

mcmc.risk a matrix containing in the lines the MCMC chains, after thinning, of the additional risk function over x.grid, in the columns.
summary.risk a data frame with four variables: the posterior means of the additional risk function over x.grid, the respective $\alpha/2$ and $1-\alpha/2$ quantiles, and x.grid.

Author(s)

Antonio Canale, Arianna Falcioni

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", x = dde, xlim = c(0,150))
                    

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
 
risk.data <- add.risk(y = gestage, x = dde, fit = fit1, mcmc = mcmc, 
a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", x = dde, xlim = c(0,150))


}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", x = dde, xlim = c(0,150))
                    

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
 
risk.data <- add.risk(y = gestage, x = dde, fit = fit1, mcmc = mcmc, 
a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", x = dde, xlim = c(0,150))


}

classCoMiRe class constructor

Description

A constructor for the classCoMiRe class. The class classCoMiRe is a named list containing the output of the posterior estimation of CoMiRe model implemented in comire.gibbs

Usage

as.classCoMiRe(call = NULL, out = NULL, z = NULL, z.val = NULL, f0 = NULL, f1 = NULL, 
nrep, nb, bin = FALSE, univariate = TRUE)
as.classCoMiRe(call = NULL, out = NULL, z = NULL, z.val = NULL, f0 = NULL, f1 = NULL, 
nrep, nb, bin = FALSE, univariate = TRUE)

Arguments

`call`	a formula for `comire.gibbs`.
`out`	an output of `comire.gibbs`.
`z`	optional numeric vector or matrix for the confounding covariates.
`z.val`	optional numeric vector containing a fixed value of interest for each of the confounding covariates to be used for the plots. Default value is `mean(z)` for numeric covariates or the mode for factorial covariates.
`f0`, `f1`	optional matrices containing simulated values of the mixture densities at low and high dose exposure; default values are simulated with `comire.gibbs`. It is possible to change these for differente fixed values of `z`: see `predict_new_z` function.
`nrep`	integer giving the total number of iterations used in `comire.gibbs`.
`nb`	integer giving the number of burn-in iterations used in `comire.gibbs`.
`bin`	logical. It is `TRUE` if y is drawn for a binomial distribution.
`univariate`	logical. It is `TRUE` if the model is univariate.

Author(s)

Antonio Canale, Arianna Falcioni

$\beta(x)$ plot

Description

Posterior mean (continuous lines) and pointwise credible bands (shaded areas) for $\beta(x)$ .

Usage

betaplot(x, fit, x.grid = NULL, xlim = c(0, max(x)), xlab = "x")
betaplot(x, fit, x.grid = NULL, xlim = c(0, max(x)), xlab = "x")

Arguments

`x`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`.
`fit`	the output of `comire.gibbs` opportunely trasformed in `classCoMiRe` class.
`x.grid`	optional numerical vector giving the actual values of the grid for x for plotting $\beta(x)$ . If `x.gird` is not provided, standard grids are automatically used.
`xlim`	numeric vectors of length 2, giving the x coordinates ranges for the plot.
`xlab`	the title of the x axis.

Author(s)

Antonio Canale

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
betaplot(x=dde, fit=fit.dummy, x.grid=seq(0,180, length=100), xlim=c(0,150))


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)

                         
betaplot(x=dde, fit=fit1, x.grid=seq(0,180, length=100), xlim=c(0,150))


}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
betaplot(x=dde, fit=fit.dummy, x.grid=seq(0,180, length=100), xlim=c(0,150))


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)

                         
betaplot(x=dde, fit=fit1, x.grid=seq(0,180, length=100), xlim=c(0,150))


}

Benchmark dose

Description

Benchmark dose associated to a particular risk

Usage

BMD(level, risk, x, alpha=0.05)
BMD(level, risk, x, alpha=0.05)

Arguments

`level`	dose level of interest.
`risk`	`summary.risk$mcmc.risk` from the output of `add.risk` function.
`x`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`.
`alpha`	level of the credible bands.

Value

A dataframe containing as variables:

q the dose level of interest.
BMD the benchmark dose.
low lower credible limit.
upp upper credible limit.
BMDL a more conservative benchmark dose.

Author(s)

Antonio Canale

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       
                     

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)


risk.data <- add.risk(y = gestage, x = dde, fit = fit, mcmc = mcmc,
a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       


}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       
                     

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)


risk.data <- add.risk(y = gestage, x = dde, fit = fit, mcmc = mcmc,
a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       


}

Benchmark dose plot

Description

Posterior mean (continuous lines) and pointwise credible bands (shaded areas) for the benchmark dose in function of the increase in risk.

Usage

bmd.plot(bmd.data)
bmd.plot(bmd.data)

Arguments

bmd.data

output of BMD function.

Author(s)

Antonio Canale

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit, mcmc = mcmc, 
a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       


}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit, mcmc = mcmc, 
a = 37, x.grid = seq(0, max(dde), length = 100))
bmd.data <- BMD(seq(0,.20, length=50), risk.data$mcmc.risk, 
x=seq(0,max(dde), length=100), alpha=0.05)
bmd.plot(bmd.data)       


}

Gibbs sampler for CoMiRe model

Description

Posterior inference via Gibbs sampler for CoMiRe model

Usage

comire.gibbs(y, x, z = NULL, family = 'continuous', 
       grid = NULL, mcmc, prior, 
       state = NULL, seed, max.x = max(x), z.val = NULL, verbose = TRUE)
comire.gibbs(y, x, z = NULL, family = 'continuous', 
       grid = NULL, mcmc, prior, 
       state = NULL, seed, max.x = max(x), z.val = NULL, verbose = TRUE)

Arguments

`y`	numeric vector for the response: when `family="continuous"` `y` must be a numeric vector; if `family="binary"` `y` must assume values `0` or `1`.
`x`	numeric vector for the covariate relative to the dose of exposure.
`z`	numeric vector for the confunders; a vector if there is only one confounder or a matrix for two or more confunders
`family`	type of `y`. This can be `"continuous"` or `"binary"`. Default `"continuous"`.
`grid`	a list giving the parameters for plotting the posterior mean density and the posterior mean $\beta(x)$ over finite grids if `family="continuous"` and `z=NULL`. It must include the following values: `grids`, logical value (if `TRUE` the provided grids are used, otherwise standard grids are automatically used); `xgrid` and `ygrid`, numerical vectors with the actual values of the grid for y and x.
`mcmc`	a list giving the MCMC parameters. It must include the following integers: `nb` giving the number of burn-in iterations, `nrep` giving the total number of iterations, `thin` giving the thinning interval, `ndisplay` giving the multiple of iterations to be displayed on screen while the algorithm is running (a message will be printed every `ndisplay` iterations).
`prior`	a list containing the values of the hyperparameters. If `family = "continuous"`, it must include the following values: `mu.theta`, the prior mean $\mu_\theta$ for each location parameter $\theta_{0h}$ and $\theta_1$ , `k.theta`, the prior variance $k_\theta$ for each location paramter $\theta_{0h}$ and $\theta_1$ , `mu.gamma` (if `p` confounding covariates are included in the model) a `p`-dimentional vector of prior means $\mu_\gamma$ of the parameters $\gamma$ corresponding to the confounders, `k.gamma`, the prior variance $k_\gamma$ for parameter corresponding to the confounding covariate (if `p=1`) or `sigma.gamma` (if `p>1`), that is the covariance matrix $\Sigma_\gamma$ for the parameters corresponding to the `p` confounding covariates; this must be a symmetric positive definite matrix. `eta`, numeric vector of size `J` for the Dirichlet prior on the beta basis weights, `alpha`, prior for the mixture weights, `a` and `b`, prior scale and shape parameter for the gamma distribution of each precision parameter, `J`, parameter controlling the number of elements of the I-spline basis, `H`, total number of components in the mixture at $x_0$ . If `family="binary"` it must include the following values: `eta`, numeric vector of size `J` for the Dirichlet prior on the beta basis weights, `a.pi0` and `b.pi0`, the prior parameters of the prior beta distribution for $\pi_0$ , `J`, parameter controlling the number of elements of the Ispline basis.
`state`	if `family="continuous"`, a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis or if we want to start the MCMC algorithm from some particular value of the parameters.
`seed`	seed for random initialization.
`max.x`	maximum value allowed for `x`.
`z.val`	optional numeric vector containing a fixed value of interest for each of the confounding covariates to be used for the plots. Default value is `mean(z)` for numeric covariates or the mode for factorial covariates.
`verbose`	logical, if `TRUE` a message on the status of the MCMC algorithm is printed to the console. Default is `TRUE`.

Details

The function fit a convex mixture regression (CoMiRe) model (Canale, Durante, Dunson, 2018) via Gibbs sampler. For continuous outcome $y \in \mathcal{Y}$ , adverse esposure level $x \in \mathcal{X}$ and no confunding variables, one can set family = 'continuous' and z = NULL and fit model
$f_x(y) = \{1-\beta(x)\} \sum_{h=1}^{H}\nu_{0h} \phi(y; \theta_{0h}, \tau_{0h}^{-1}) + \beta(x) \phi(y; \theta_{\infty}, \tau_{\infty}^{-1})$ ;

where $\beta(x) = \sum_{j=1}^{J} \omega_j \psi_j(x), x\ge0,$ is a a monotone nondecreasing interpolation function, constrained between 0 and 1 and $\psi_1,...,\psi_J$ are monotone nondecreasing I-splines basis.
If $p \ge 1$ confounding covariates $z \in \mathcal{Z}$ are available, passing the argument z the function fits model

$f(y; x,z) = \{1-\beta(x)\} f_0(y;z) + \beta(x) f_\infty(y;z)$ ;

where:
$f_0(y;z)= \sum_{h=1}^{H} \nu_{0h} \phi(y;\theta_{0h}+z^\mathsf{T}\gamma,\tau_{0h}^{-1})$ , and $f_\infty(y;z)= \phi(y;\theta_\infty+ z^\mathsf{T}\gamma,\tau_{\infty}^{-1})$ .

Finally, if $y$ is a binary response, one can set family = 'binary' and fit model

$p_x(y) = (\pi_x)^y (1 - \pi_x)^{1-y}$ ;

where $\pi_x = P(Y=1 | x)$ is $\pi_x = \{1-\beta(x)\} \pi_0 + \beta(x) \pi_\infty$ .

Value

An object of the class classCoMiRe, i.e. a list of arguments for generating posterior output. It contains:

callthe model formula
post.means a list containing the posterior mean density beta over the grid, of all the mixture parameters and, if family = "continuous" and z = NULL, of $f_0$ and $f_{inf}$ over the y.grid.
ci a list containing the 95% credible intervals for all the quantities stored in post.means.
mcmc a list containing all the MCMC chains.
z the same of the input
z.val the same of the input
f0,f1 MCMC replicates of the density in the two extremes (only if family = 'continuous')
nrep,nb the same values of the list mcmc in the input arguments
bin logical, equal to TRUE if family = 'binary'
univariate logical, equal to TRUE if z is null or a vector

Author(s)

Antonio Canale [aut, cre], Daniele Durante [ctb], Arianna Falcioni [aut], Luisa Galtarossa [aut], Tommaso Rigon [ctb]

References

Canale, A., Durante, D., and Dunson, D. (2018), Convex Mixture Regression for Quantitative Risk Assessment, Biometrics, 74, 1331-1340

Galtarossa, L., Canale, A., (2019), A Convex Mixture Model for Binomial Regression, Book of Short Papers SIS 2019

Examples

{

data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 


prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
summary(fit.dummy)
 


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4) 

## 1. binary case ##

prior <- list(pi0=mean(gestage), eta=rep(1, J)/J, 
             a.pi0=27, b.pi0=360, J=J)
             
fit_binary<- comire.gibbs(premature, dde, family="binary", 
                          mcmc=mcmc, prior=prior, seed=5, max.x=180)
                          
                          
## 2. continuous case ##

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)


## 2.2 One confunder ##

mage_std <- scale(mage, center = TRUE, scale = TRUE) 

prior <- list(mu.theta=mean(gestage), k.theta=10, mu.gamma=0, k.gamma=10, 
              eta=rep(1, J)/J, alpha=1/H, a=2, b=2, H=H, J=J)
              
fit2 <- comire.gibbs(gestage, dde, mage_std, family="continuous", 
              mcmc=mcmc, prior=prior, seed=5, max.x=180)


## 2.3 More confunders ##

Z <- cbind(mage, mbmi, sei)
Z <- scale(Z, center = TRUE, scale = TRUE)
Z <- as.matrix(cbind(Z, CPP$smoke))
colnames(Z) <- c("age", "BMI", "sei", "smoke")

mod <- lm(gestage ~ dde + Z)
prior <- list(mu.theta = mod$coefficients[1], k.theta = 10,
              mu.gamma = mod$coefficients[-c(1, 2)], sigma.gamma = diag(rep(10, 4)),
              eta = rep(1, J)/J, alpha = 1/H, a = 2, b = 2, H = H, J = J)
              
fit3 <- comire.gibbs(y = gestage, x = dde, z = Z, family = "continuous", mcmc = mcmc, 
                     prior = prior, seed = 5)

 
}



{

data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 


prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
summary(fit.dummy)
 


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4) 

## 1. binary case ##

prior <- list(pi0=mean(gestage), eta=rep(1, J)/J, 
             a.pi0=27, b.pi0=360, J=J)
             
fit_binary<- comire.gibbs(premature, dde, family="binary", 
                          mcmc=mcmc, prior=prior, seed=5, max.x=180)
                          
                          
## 2. continuous case ##

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)


## 2.2 One confunder ##

mage_std <- scale(mage, center = TRUE, scale = TRUE) 

prior <- list(mu.theta=mean(gestage), k.theta=10, mu.gamma=0, k.gamma=10, 
              eta=rep(1, J)/J, alpha=1/H, a=2, b=2, H=H, J=J)
              
fit2 <- comire.gibbs(gestage, dde, mage_std, family="continuous", 
              mcmc=mcmc, prior=prior, seed=5, max.x=180)


## 2.3 More confunders ##

Z <- cbind(mage, mbmi, sei)
Z <- scale(Z, center = TRUE, scale = TRUE)
Z <- as.matrix(cbind(Z, CPP$smoke))
colnames(Z) <- c("age", "BMI", "sei", "smoke")

mod <- lm(gestage ~ dde + Z)
prior <- list(mu.theta = mod$coefficients[1], k.theta = 10,
              mu.gamma = mod$coefficients[-c(1, 2)], sigma.gamma = diag(rep(10, 4)),
              eta = rep(1, J)/J, alpha = 1/H, a = 2, b = 2, H = H, J = J)
              
fit3 <- comire.gibbs(y = gestage, x = dde, z = Z, family = "continuous", mcmc = mcmc, 
                     prior = prior, seed = 5)

 
}

Posterior mean density plot for dose intervals

Description

Pointwise posterior mean (continuous blue lines), and credible bands (shaded blue areas) for f (y | x, z) calculated in x.val under the the model fitted in fit.

Usage

fit.pdf.mcmc(y, x, fit, mcmc, J=10, H = 10, alpha = 0.05, 
max.x = max(x), x.val, y.grid = NULL, xlim = c(0, max(x)), 
ylim = c(0, 1), xlab = NULL)
fit.pdf.mcmc(y, x, fit, mcmc, J=10, H = 10, alpha = 0.05, 
max.x = max(x), x.val, y.grid = NULL, xlim = c(0, max(x)), 
ylim = c(0, 1), xlab = NULL)

Arguments

`y`	optional numeric vector for the response used in `comire.gibbs`. If `y` is missing, `y.grid` must be provided.
`x`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`.
`fit`	the output of `comire.gibbs` opportunely trasformed in `classCoMiRe` class.
`mcmc`	a list giving the MCMC parameters.
`J`	parameter controlling the number of elements of the I-spline basis
`H`	total number of components in the mixture at $x_0$ .
`alpha`	level of the credible bands.
`max.x`	maximum value allowed for x.
`x.val`	central points of each dose interval to be used in the posterior estimation of the probability density function.
`y.grid`	optional numerical vector giving the actual values of the grid for y for plotting the posterior mean density. If `y.grid` is not provided, standard grids are automatically used.
`xlim`, `ylim`	numeric vectors of length 2, giving the x and y coordinates ranges for the plot.
`xlab`	the title of the x axis.

Author(s)

Antonio Canale, Arianna Falcioni

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
fit.pdf.mcmc(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, J = 10, H = 10, 
                         alpha = 0.05, max.x = max(dde), x.val = 125, 
                         xlim = c(25,48), ylim = c(0,0.25),
                         xlab = "Gest. age. for DDE = 125")
                         

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
          
fit.pdf.mcmc(y = gestage, x = dde, fit = fit1, mcmc = mcmc, J = 10, H = 10, 
                         alpha = 0.05, max.x = max(dde), x.val = 125, 
                         xlim = c(25,48), ylim = c(0,0.25),
                         xlab = "Gest. age. for DDE = 125")
                         

}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
fit.pdf.mcmc(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, J = 10, H = 10, 
                         alpha = 0.05, max.x = max(dde), x.val = 125, 
                         xlim = c(25,48), ylim = c(0,0.25),
                         xlab = "Gest. age. for DDE = 125")
                         

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
          
fit.pdf.mcmc(y = gestage, x = dde, fit = fit1, mcmc = mcmc, J = 10, H = 10, 
                         alpha = 0.05, max.x = max(dde), x.val = 125, 
                         xlim = c(25,48), ylim = c(0,0.25),
                         xlab = "Gest. age. for DDE = 125")
                         

}

CoMiRe plot

Description

An S3 plot method for an object of classCoMiRe class.

Usage

## S3 method for class 'classCoMiRe'
plot(
  x,
  y,
  xobs,
  mcmc,
  J = 10,
  H = 10,
  a = NULL,
  max.x = max(xobs),
  bandwidth = 20,
  x.grid = NULL,
  xlim = c(0, max(xobs)),
  ylim = c(0, 1),
  xlab = "x",
  alpha = 0.05,
  risk = TRUE,
  bmd = TRUE,
  level,
  oneevery = 20,
  ...
)
## S3 method for class 'classCoMiRe'
plot(
  x,
  y,
  xobs,
  mcmc,
  J = 10,
  H = 10,
  a = NULL,
  max.x = max(xobs),
  bandwidth = 20,
  x.grid = NULL,
  xlim = c(0, max(xobs)),
  ylim = c(0, 1),
  xlab = "x",
  alpha = 0.05,
  risk = TRUE,
  bmd = TRUE,
  level,
  oneevery = 20,
  ...
)

Arguments

`x`	the output of `comire.gibbs`, an object of the `classCoMiRe` class.
`y`	numeric vector for the response used in `comire.gibbs`.
`xobs`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`.
`mcmc`	a list giving the MCMC parameters.
`J`	parameter controlling the number of elements of the I-spline basis
`H`	total number of components in the mixture at $x_0$ .
`a`	optional threshold of clinical interest for the response variable.
`max.x`	maximum value allowed for x.
`bandwidth`	the kernel bandwidth smoothing parameter for the `post.pred.check` plot.
`x.grid`	optional numerical vector giving the actual values of the grid for x for plotting the additional risk function. If $x.gird$ is not provided, standard grids are automatically used.
`xlim`, `ylim`	numeric vectors of length 2, giving the x and y coordinates ranges for the plot.
`xlab`	the title of the x axis.
`alpha`	level of the credible bands, default 0.05
`risk`	if `TRUE` the additional risk plot via `riskplot` is computed.
`bmd`	if `TRUE` the benchmark dose plot via `bmd.plot` is computed.
`level`	if `bmd=TRUE`, dose levels of interest for BMD plot.
`oneevery`	integer number representing how many MCMC draws to plot in the posterior predictive check. It draws one sample every `oneevery`.
`...`	additional arguments to be passed.

Details

The output is a list of ggplot2 plots containing the result of the betaplot function and, if the threshold a is provided, of post.pred.check, riskplot, bmd.plot.

Value

If a=NULL returns only betaplot otherwise, if risk=FALSE and bmd=FALSE returns a list containing betaplot (which is automatically plotted) and post.pred.check plot. Finally, if a is provided, risk=TRUE and bmd=TRUE returns a list with betaplot, post.pred.check, riskplot and bmd.plot.

Author(s)

Antonio Canale, Arianna Falcioni

Posterior predictive check plot

Description

A plot for an object of classCoMiRe class. The plot is a goodness-of-fit assessment of CoMiRe model. Since Version 0.8 if z is provided into the fit object, an error message is returned. If family = 'continuous', a smoothed empirical estimate of F(a|x) = pr(y < a | x) is computed from the observed data (black line) and from some of the data sets simulated from the posterior predictive distribution in the fit object (grey lines). If family = 'binary', a smoothed empirical estimate of the proportion of events (black line) and of the smoothed empirical proportion of data simulated from the posterior predictive distribution in the fit object (grey lines). In the x axis are reported the observed exposures.

Usage

post.pred.check(y, x, fit, mcmc, J=10, H=10, a, max.x=max(x), 
xlim=c(0, max(x)), bandwidth = 20, oneevery = 20)
post.pred.check(y, x, fit, mcmc, J=10, H=10, a, max.x=max(x), 
xlim=c(0, max(x)), bandwidth = 20, oneevery = 20)

Arguments

`y`	numeric vector for the response used in `comire.gibbs`
`x`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`
`fit`	the output of `comire.gibbs` opportunely trasformed in `classCoMiRe` class
`mcmc`	a list giving the MCMC parameters
`J`	parameter controlling the number of elements of the I-spline basis
`H`	total number of components in the mixture at $x_0$
`a`	threshold of clinical interest to compute the F(a\|x,z)
`max.x`	maximum value allowed for x
`xlim`	numeric vectors of length 2, giving the x coordinates ranges for the plot
`bandwidth`	the kernel bandwidth smoothing parameter
`oneevery`	integer number representing how many MCMC draws to plot in the posterior predictive check. It draws one sample every `oneevery`.

Author(s)

Antonio Canale, Arianna Falcioni

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
post.pred.check(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, J = 10, H = 10, a = 37, 
                max.x = max(dde), xlim = c(0,150), oneevery = 4)
                

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)

post.pred.check(y = gestage, x = dde, fit = fit1, mcmc = mcmc, J = 10, H = 10, a = 37, 
                max.x = max(dde), xlim = c(0,150))


}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
post.pred.check(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, J = 10, H = 10, a = 37, 
                max.x = max(dde), xlim = c(0,150), oneevery = 4)
                

## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit1 <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)

post.pred.check(y = gestage, x = dde, fit = fit1, mcmc = mcmc, J = 10, H = 10, a = 37, 
                max.x = max(dde), xlim = c(0,150))


}

comire.gibbs for different fixed values of z

Description

This function computes the predicted values of the density al low dose f_0 and of the density at high dose f_{inf}, for fixed values of the confounders z.

Usage

predict_new_z(fit, y, z.val)
predict_new_z(fit, y, z.val)

Arguments

`fit`	the output of `comire.gibbs` opportunely trasformed in `classCoMiRe` class
`y`	numeric vector for the response used in `comire.gibbs`
`z.val`	optional numeric vector containing a fixed value of interest for each of the confounding covariates to be used for the plots. Default value is `mean(z)` for numeric covariates or the mode for factorial covariates.

Value

An object of class classCoMiRe.

Author(s)

Antonio Canale, Arianna Falcioni

CoMiRe print

Description

The print.classCoMiRe method prints the type of a classCoMiRe object.

Usage

## S3 method for class 'classCoMiRe'
print(x, ...)
## S3 method for class 'classCoMiRe'
print(x, ...)

Arguments

`x`	an object of class `classCoMiRe`;
`...`	additional arguments.

Author(s)

Antonio Canale, Arianna Falcioni

Additional risk function plot

Description

Posterior mean (continuous lines) and pointwise credible bands (shaded areas) for $Ra(x, a)$ .

Usage

riskplot(risk.data, xlab = NULL, x = NULL, ylim=c(0,1), xlim=c(0, max(x)))
riskplot(risk.data, xlab = NULL, x = NULL, ylim=c(0,1), xlim=c(0, max(x)))

Arguments

`risk.data`	output of `add.risk` function.
`xlab`	the title of the x axis.
`x`	numeric vector for the covariate relative to the dose of exposure used in `comire.gibbs`.
`xlim`, `ylim`	numeric vectors of length 2, giving the x and y coordinates ranges for the plot.

Author(s)

Antonio Canale

Examples

{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", x = dde, xlim = c(0,150))


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
 
risk.data <- add.risk(y = gestage, x = dde, fit = fit, mcmc = mcmc, 
a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", 
x = dde, xlim = c(0,150))


}
{
data(CPP)
attach(CPP)

n <- NROW(CPP)
J <- H <- 10

premature <- as.numeric(gestage<=37)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## too few iterations to be meaningful. see below for safer and more comprehensive results

mcmc <- list(nrep=10, nb=2, thin=1, ndisplay=4) 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit.dummy <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=1, max.x=180)
                     
risk.data <- add.risk(y = gestage, x = dde, fit = fit.dummy, mcmc = mcmc, 
    a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", x = dde, xlim = c(0,150))


## safer procedure with more iterations (it may take some time)

mcmc <- list(nrep=5000, nb=2000, thin=5, ndisplay=4)

## Fit the model for continuous y 

prior <- list(mu.theta=mean(gestage), k.theta=10, eta=rep(1, J)/J, 
              alpha=rep(1,H)/H, a=2, b=2, J=J, H=H)
              
fit <- comire.gibbs(gestage, dde, family="continuous", 
                     mcmc=mcmc, prior=prior, seed=5, max.x=180)
 
risk.data <- add.risk(y = gestage, x = dde, fit = fit, mcmc = mcmc, 
a = 37, x.grid = seq(0, max(dde), length = 100))
riskplot(risk.data$summary.risk, xlab="DDE", 
x = dde, xlim = c(0,150))


}

CoMiRe summary

Description

The summary.classCoMiRe method provides summary information on classCoMiRe objects.

Usage

## S3 method for class 'classCoMiRe'
summary(object, ...)
## S3 method for class 'classCoMiRe'
summary(object, ...)

Arguments

`object`	an object of class `classCoMiRe`;
`...`	additional arguments

Author(s)

Antonio Canale Arianna Falcioni

Package 'CoMiRe'

Help Index

Convex Mixture Regression

Description

Details

Author(s)

References

Additional risk function

Description

Usage

Arguments

Value

Author(s)

Examples

classCoMiRe class constructor

Description

Usage

Arguments

Author(s)

β(x)\beta(x)β(x) plot

Description

Usage

Arguments

Author(s)

Examples

Benchmark dose

Description

Usage

Arguments

Value

Author(s)

Examples

Benchmark dose plot

Description

Usage

Arguments

Author(s)

Examples

Gibbs sampler for CoMiRe model

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Posterior mean density plot for dose intervals

Description

Usage

Arguments

Author(s)

Examples

CoMiRe plot

Description

Usage

Arguments

Details

Value

Author(s)

Posterior predictive check plot

Description

Usage

Arguments

Author(s)

Examples

comire.gibbs for different fixed values of z

Description

Usage

Arguments

Value

Author(s)

CoMiRe print

Description

Usage

Arguments

Author(s)

Additional risk function plot

Description

Usage

$\beta(x)$ plot