pscEst {psc} | R Documentation |
Function for performing estimation procedures in 'pscfit'
Description
Function for performing estimation procedures in 'pscfit'
Usage
pscEst(CFM, DC_clean, nsim, start, start.se, trt)
Arguments
CFM |
a model object supplied to pscfit |
DC_clean |
a cleaned dataset ontained using dataComb(). |
nsim |
the number of MCMC simulations to run |
start |
the stating value for |
start.se |
the stating value for |
trt |
an optional vector denoting treatment allocations where mulitple treatment comparisons are bieng made |
Details
Define the set of model parameters B
to contain \Gamma
which summarize
the parameters of the CFM. Prior distributions are defined for B using a
multivariate normal distribution \pi (B) \sim MVN(\mu ,\Sigma)
where \mu|
is the vector of coefficient estimates from the validated model and \Sigma
is the variance-covariance matrix. This information is taken directly from the
outputs of the parametric model and no further elicitation is required.
The prior distirbution for the efficacy parameter (\pi{(\beta)}
) is set
as an uniformative N(0,1000)
.
Ultimately the aim is to estimate the posterior distribution for \beta
conditional
on the distribution of B and the observed data. A full form for the posterior
distribution is then given as
P(\beta \vert B,D) \propto L(D \vert B,\beta) \pi(B) \pi(\beta)
Please see 'pscfit' for more details on liklihood formation.
For each iteration of the MCMC procedure, the following algorithm is performed
Set and indicator s=1, and define an initial state based on prior hyperparameters for
\pi(B)
and\pi(\beta)
such thatb_s = \mu and \tau_s=0
Update
s = s+1
and draw model parametersb_s
from\pi(B)
and an draw a proposal estimate of\beta
from some target distributionEstimate
\Gamma_(i,S)=\nu^T x_i
where\nu
is the subset of parameters fromb_s
which relate to the model covariates and define 2 new likelihood functions\Theta_(s,1)=L(D \vert B=b_s,\beta=\tau_(s-1) )
&\Theta_(s,2)= L(D \vert B=b_s,\beta=\tau_s)
Draw a single value
\psi
from a Uniform (0,1) distribution and estimate the condition\omega= \Theta_(s,1)/\Theta_(s,2)
. If\omega > \psi
then accept\tau_s
as belonging to the posterior distributionP(\beta \vert B,D)
otherwise retain\tau_(s-1)
Repeat steps 2 – 4 for the required number of iterations
The result of the algorithm is a posterior distribution for the log hazard ratio,
\beta
, captures the variability in B through the defined priors \pi{(\beta)}
.
Value
A matrix containing the draws form the posterior distribution