Constructor for a prior distribution in msmbayes

Usage

msmprior(
  par,
  mean = NULL,
  sd = NULL,
  median = NULL,
  lower = NULL,
  upper = NULL
)

Arguments

par

Character string indicating the model parameter to place the prior on

This should start with one of the following:

"logq". Log transition intensity.

"q", Transition intensity

"time". Defined as 1/q. This can be interpreted as the mean time to the next transition to state $s$ for people in state $r$ (from the point of view of someone observing one person at a time, and switching to observing a different person if a competing transition happens).

"loghr". Log hazard ratio

"hr". Hazard ratio

Then for transition intensities, it should two include indices indicating the transition, e.g. "logq(2,3)" for the log transition intensity from state 2 to state 3.

For covariate effects, the covariate name is supplied alongside the transition indices, e.g. "loghr(age,2,3)" for the effect of age on the log hazard ratio of transitioning from state 2 to state 3.

For factor covariates, this should include the level, e.g. "loghr(sexMALE,2,3)" for level "MALE" of factor "sex".

The indices or the covariate name can be omitted to indicate that the same prior will used for all transitions, or/and all covariates. This can be done with or without the brackets, e.g. "logq()" or "logq" are both understood.

mean

Prior mean (only used for logq or loghr)

sd

Prior standard deviation (only used for logq or loghr)

median

Prior median

lower

Prior lower 95% quantile

upper

Prior upper 95% quantile

Value

A list of class "msmprior", with components

par (as supplied by the user)

par_base (either "logq" or "loghr")

covname (name of covariate effect)

ind1, ind2 (as supplied by the user)

mean (of log-normal prior on par_base)

sd (of log-normal prior on par_base)

Details

In msmbayes, a normal prior is used for the log transition intensities (logq) and log hazard ratios (loghr). The goal of this function is to determine the mean and SD of this prior. It can be used in two ways:

(a) directly specifying the prior mean and SD of logq or loghr`

(b) specifying prior quantiles for more interpretable transformations of these. These may include q (the transition intensity) or time (the reciprocal of the intensity, interpreted as a mean time to this transition when observing a sequence of individuals at risk of it). Or hr (hazard ratio2)

Two quantiles out of the median, lower or upper should be provided. If three are provided, then the upper quantile is ignored. These are transformed back to the scale of logq or loghr, and the unique normal prior with these quantiles is deduced.

Examples

priors <- list(
   msmprior("logq(1,2)", median=-2, lower=-4),
   msmprior("q(2,1)",    median=0.1, upper=10)
)
Q <- rbind(c(0,1),c(1,0))
mod <- msmbayes(data=infsim2, state="state", time="months", subject="subject",
                Q=Q,  priors=priors, fit_method="optimize")
#> Initial log joint probability = -185.951 
#>     Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes  
#>       12      -18.3986    0.00174506    0.00118475      0.9593      0.9593       13    
#> Optimization terminated normally:  
#>   Convergence detected: relative gradient magnitude is below tolerance 
#> Finished in  0.3 seconds.
summary(mod)
#> # A tibble: 4 × 6
#>   name   from    to      value prior                 rhat
#>   <chr> <int> <int> <rvar[1d]> <chr>                <dbl>
#> 1 q         1     2  0.58 ± NA "0.14 (0.018, 0.99)"    NA
#> 2 q         2     1  3.41 ± NA "0.10 (0.001, 9.88)"    NA
#> 3 mst       1    NA  1.73 ± NA " 7.4 (1.0,  54)"       NA
#> 4 mst       2    NA  0.29 ± NA "10.0 (0.1, 988)"       NA