Function which allows comparison of a data cohort against a parametric Counter Factual Model (CFM). The function allows models of the type 'flexsurvreg' and 'glm' to be supplied. The function performs by calculating the linear predictor as a combination of the CFM and the dataset supplied and then selects a likelihood based on the type of model specified. Likelihood is estimated using a Baysian MCMC procedure wherebey the parameters of the CFM acts as informative priors.
Arguments
- CFM
An R model object of class 'glm' or 'flexsurvspline'
- DC
A dataset including columns to match to covariates in the model
- nsim
The number of simulations for the MCMC routine
- id
Numeric vector stating which patient(s) from the dataset should be included in the analysis. Defaults to all patients
- trt
An optional vector denoting treatment allocations for multiple treatment comparisons. Defaults to NULL.
Value
a object of class 'psc' with attributes model.type, the cleaned Dataset and the posterior distribution of the fitted model
Attributes include
A 'cleaned' dataset including extracted components of the CFM and the cleaned DC included in the procedure
An object defining the class of model (and therefore the procedure applied - see above)
A matrix containing the draws of the posterior distributions
Details
Model currently supports estimation of more than one treatment (using the 'trt') option and esitmation restricted to sub-groups of the data cohort (using the 'id' option.
the pscfit function compares a dataset ('DC') against a parametric model.
This is done by selecting a likelihood which is identified by the type of CFM that is supplied.
At present, two types of model are supported, a flexible parmaeteric survival model of type 'flexsurvreg'
and a geleneralised linear model of type 'glm'.
Where the CFM is of type 'flexsurvreg' the likeihood supplied is of the form:
$$L(D \vert \Lambda, \Gamma_i) = \prod^{n}_{i=1} f(t_i \vert \Lambda, \Gamma_i)^{c_i} S(t_i|\Lambda, \Gamma_i)^{(1-c_i)}$$
Where \(\Lambda\) defines the cumulative baseline hazard function, \(\Gamma\) is the linear predictor and \(t\) and \(c\) are the event time and indicator variables.
Where the CFM is of the type 'glm' the likelihood supplied is of the form:
$$L(x \vert \Gamma_i) = \prod^{n}_{i=1} b(x \vert \Gamma_i) \exp{\{\Gamma_i^T t(x) - c(\Gamma_i)\} } $$
Where \(b(.)\), \(t(.)\) and \(c(.)\) represent the functions of the exponential family. In both cases, \(\Gamma\) is defined as:
$$\Gamma = \gamma x + \beta$$
Where \(\gamma\) are the model coefficients supplied by the CFM and \(\beta\) is the parameter set to measure the difference between the CFM and the DC.
Estimation is performed using a Bayesian MCMC procedure. Prior distributions for \(\Gamma\) (& \(\Lambda\)) are derived directly from the model coefficients (mean and variance covariance matrix) or the CFM. A bespoke MCMC routine is performed to estimate \(\beta\). Please see '?mcmc' for more detials.
For the standard example where the DC contains information from only a single treatment, trt need not be specified. Where comparisons between the CFM and multiple treatments are require, a covariate of treamtne allocations must be specified sperately (using the 'trt' option).
Examples
library(psc)
e4_data <-psc::e4_data
gemCFM <- psc::gemCFM
psc <- pscfit(gemCFM,e4_data)
#> Warning: 53 rows removed due to missing data in dataset
#>
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summary(psc)
#> Summary:
#>
#> 311 observations selected from the data cohort for comparison
#> CFM of type flexsurvreg identified
#> linear predictor succesfully obtained with median:
#> trt: 1.786
#> Average expected response:
#> trt: 30.077
#> Average observed response: 26.327
#>
#> Counterfactual Model (CFM):
#> A model of class 'flexsurvreg'
#> Fit with 3 internal knots
#>
#> Formula:
#> s.ob ~ t + grade + nodes + lca199
#> <environment: 0x55931a7f64d0>
#>
#> Call:
#> CFM model + beta
#>
#> Coefficients:
#> median 2.5% 97.5% Pr(x<0) Pr(x>0)
#> beta -0.25142 -0.43986 -0.06826 0.99520 0.00480
#> DIC 844.70821 837.88052 857.49216 NA NA