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

"q", Transition intensity (in the same format)

"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). The same format as logq and q with two indices.

"loghr". Covariate effect on intensities of transition from states given a Markov model. 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".

"logtaf". Covariate effect on the sojourn time in states given a semi-Markov model with a phase-type approximation. This is specified with only one index, indicating the state, e.g. "loghr(age,2)". Note this is interpreted as a log hazard ratio for times to transitions on the latent space, but for the sojourn time on the observable space, this is a "time acceleration factor", such that an coefficent of log(2) increases the risk of the next transition through halving the expected sojourn time.

"hr". Hazard ratio.

"loe" Log odds of error (relative to no misclassification). "loe(1,2)" indicates the log odds of misclassification in state 2 for true state 1, relative to no misclassifiation.

"logshape" "logscale" Log shape or scale parameter for the sojourn distribution in a phase-type approximation model. The index indicates the state, e.g. logshape(2) and logscale(2) indicate the log shape and scale parameter for the sojourn distribution in state 2.

"logoddsnext". Log odds of transition to a destination state in a phase-type approximation model with competing destination states. These parameters are only used in phase-type approximation models where there are multiple potential states that an individual could transition to immediately on leaving the state that has a phase-type approximation sojourn distribution. These parameters are defined with two indices. For example, logoddsnext(1,2) is the log odds of transition to state 2 on leaving state 1. The odds is the probability of transition to state 2 divided by the probability of transition to the first out of the set of potential destination states.

Covariate effects on competing transitions out of semi-Markov states are specified with logrrnext. For example, "logrrnext(age,2,3)" for the effect of age on the relative rate of transition from state 2 to state 3, relative to the rate of transition from state 2 to the first competing destination state. These parameters are not applicable to semi-Markov states with only one potential next destination state.

In general, 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. This is only used for the parameters that have direct normal priors, that is logq, loghr, logtaf, logshape, logscale, loe, logoddsnext. That is, excluding time, q and hr, whose priors are defined by transformations of a normal distribution.

sd

Prior standard deviation (only for parameters with direct normal priors)

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 (e.g. "logq" if "time" was provided, or "loghr" if "hr" was provided)

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 ratio)

Two quantiles (out of the median, lower or upper) should be provided. If all 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")
summary(mod)
#> # A tibble: 4 × 7
#>   name   from    to    posterior  mode prior_string                    prior
#>   <chr> <int> <int>   <rvar[1d]> <dbl> <chr>                      <rvar[1d]>
#> 1 q         1     2  0.62 ± 0.23 0.578 0.14 (0.018, 1.0e+00)    0.23 ± 0.3  
#> 2 q         2     1  3.63 ± 1.33 3.41  0.10 (0.001, 1.0e+01)    1.44 ± 9.4  
#> 3 mst       1    NA  1.83 ± 0.68 1.73  10.0 (0.1, 998)        143.84 ± 942.0
#> 4 mst       2    NA  0.31 ± 0.11 0.293 7.4 (1.0, 55)           12.41 ± 16.2