`BCEs0` is a R library specifically designed to run a full Bayesian cost-effectiveness analysis of individual data in the presence of structural zero costs for some subjects. The framework assumes that data are available for n_{0} and n_{1} subjects, that are respectively given some treatment t_{0} and t_{1}. Typically, costs and clinical benefits should be modelled assuming some form of correlation. But in the case of structural zeros, the model gets even more complicated, since the population average costs need to be computed accounting for the fact that there are two "components" in the population - one made by the individuals who actually accrue some positive cost and the other by the subjects that have no cost.
The package implements the framework developed here (the published paper is freely available under Open Access agreement, while a working paper with a slightly different version of the model is available from here). Basically, there are three modules; the first one (the green square in the graph below) is a pattern mixture model (in the language of missing data) for the chance of each subject being associated with zero costs. The indicator i-th subject in treatment group t is observed to have 0 costs, and 0 otherwise. The probability is modelled as a function of an overall average value β_{0t} and β_{1t} (and possibly some covariates). The second module (in the red rectangle) is a marginal model for the costs, whose parameters depend on the value taken by dWhen the indicator is 1, then we imply a degenerate distribution on the costs (which ensures that the average cost is estimated to be identically 0). When it is 0, then we imply a non-degenerate distribution (eg a Gamma or a log-Normal). In fact, the population average cost μ_{it}. is obtained as a mixture of the two components ψ_{ct}_{t}_{0} (coming from the non-degenerate distribution) and ψ_{t}_{1}=0, with weights equal to the estimated probability associated with each of the two classes. Finally, the third module (in the blue square) is the conditional model for the measure of effectiveness given the costs. This is defined in terms of a generalised linear regression on the conditional mean ψ_{t}_{0,}ψ_{t}_{1}_{ }which can be re-scaled to obtain the population average for the measure of effectiveness μ._{et}A discussion of the main changes from version 1.0 to 1.1 is here, in the blog. The package has a main function `bces0` which takes as arguments: a named list with arguments`data` `e0` `,` `e1` (the individual values of the measure of effectiveness under either treatment)`c0` `,` `c1` (the individual values of the costs under either treatment)`H.psi` (a vector including the upper limit for the default Uniform prior for the mean of the cost non-degenerate distribution. The first value is used for*t*=0, while the second is used for*t*=1)`H.zeta` (a vector including the upper limit for the default Uniform prior for the standard deviation of the cost non-degenerate distribution. The first value is used for*t*=0, while the second is used for*t*=1)`X0` (an optional matrix including some individually measured covariates under treatment*t*=0 to be used in the pattern-mixture model - if available)`X1` (an optional matrix including some individually measured covariates under treatment*t*=1 to be used in the pattern-mixture model - if available): a string specifying the assumed distribution for the cost variable. Possible choices are`dist.c` - "
`gamma` " (Gamma distribution - generally used to model costs) - "
`logn` " (log-Normal distribution - also generally used to model costs) - "
`norm` " (Normal distribution - not recommended usually, but could be useful if the original cost variable has been pre-processed and transformed in some suitable scale to induce at least approximate normality) : a string specifying the assumed distribution for the effectiveness variable. Possible choices are`dist.e` - "
`beta` " (Beta distribution - can be used to model effectiveness measures defined in [0;1],*eg*QALYs measured in a one-year horizon) - "
`gamma` " (Gamma distribution - can be used to model effectiveness measures defined as positive quantities,*eg*QALYs over a long period of time) - "
`bern` " (Bernoulli distribution - can be used to model effectiveness measures defined as binary variables,*eg*dead/alive) - "
`norm` " (Normal distribution - again not recommended, usually, but could be useful if the original effectiveness variable has been pre-processed and transformed in some suitable scale to induce at least approximate normality) : The values for the parameters`w,W` *w*and*W*which are used to induce a degenerate distribution for the component with null costs. The default choice is*w*=*W*=0.000001. These have no real impact on the model convergence and economic results (provided that they induce a suitable degenerate prior with mean and sd close enough to 0), but may have an impact on measures of model fit (eg DIC), which may be used for model averaging and structural probabilistic sensitivity analysis: the number of MCMC iterations to be run (default value = 10000)`n.iter` : the number of MCMC iterations to be discarded in the burn-in period (default value = 5000)`n.burnin` : the number of Markov chains to be used in the process`n.chains` : a logical value (default TRUE) to indicate whether a robust (Cauchy) specification should be used for the regression coefficients in the pattern model. If FALSE, then a minimally informative Normal distribution is applied`robust` : a string with the name of the .txt to which the JAGS code representing the assumptions specified by the user is written. The default choice is model.txt in the current working directory`model.file`
bces0 will write a JAGS model encoding the distributional assumptions specified by the user for the costs and effectiveness measure and save it into a file model.txt. This can be then used as a "template" and can be modified to account for more complex models (eg including structured effects or different distributional assumptions). If no covariates are specified in data, then only the intercepts β The model file is saved in the current working directory and can then be edited to specify different models/assumptions (
eg including individual structured effects or different prior distributions. A R style manual for the package, describing the main characteristics of the package, can be found here. A video of a presentation I gave at the University of Las Palmas (Gran Canaria, Spain) is here.BCEs0 is now available from CRAN - to install type `install.packages("BCEs0")` in your R terminal. MORE DESCRIPTION, EXAMPLES AND INSTRUCTIONS TO COME! Version 1.1 is the current one. |