## Introduction

This page compares the computational performance of hesim against other R packages that have been used to develop health economic models for health technology assessment. We provide benchmarks for both a semi-Markov model and a time-inhomogeneous Markov model.

The following R packages and scripts are used. The file benchmarks.R contains the code used to run the models.

library("data.table")
library("flexsurv")
library("ggplot2")
library("heemod")
library("hesim")
library("kableExtra")
library("mstate")
source("benchmarks.R")

## Semi-Markov models

Williams et al. (2016) adapted the mstate package to simulate parametric semi-Markov multi-state models. Here, we use simulate a 6-state model for leukemia patients following bone marrow transplantation with both hesim and mstate. Since a semi-Markov process is assumed, an individual-level simulation is used. Additional details were previously provided in a blog post.

We fit a parametric Weibull model, but note that computational performance does not differ substantially across parametric distributions. We also checked the performance of a spline model, which can be used to model very flexible baseline hazards, but is slower because the quantile function must be computed numerically and hesim, by default, uses inverse transform sampling to randomly sample from survival splines. To facilitate direct comparison with the Weibull model, we used a parameterization of the spline equivalent to a Weibull distribution. When using mstate, multi-state models are simulated using a cumulative hazard function estimated on a discrete grid, so a time step must be defined. We used a step size of 1/52 (i.e., one week) so that each time step was a week long. This produced reasonably accurate state probability estimates that were similar to those performed in continuous time with hesim (see plot below).

DIST = "weibull"
STEP = 1/52

We began by simulating “deterministic” models assuming no parameter uncertainty. Comparisons of state probabilities simulated using 5,000 patients with hesim and mstate are shown in the plot.

smb1 <-  benchmark_semi_markov(n_patients = 1000, uncertainty = "none", dist = DIST,
step = STEP)
smb2 <-  benchmark_semi_markov(n_patients = 5000, uncertainty = "none", dist = DIST,
step = STEP)
smb2\$plot

We then performed probabilistic sensitivity analysis (PSA) and varied both the number of patients simulated and the number of draws of the parameters. Run times are reported in the table below. hesim is considerably faster and the speed advantage is most notable when a PSA is performed. Although slower than the Weibull model, the spline model is still fast, meaning that flexible baseline hazards can be modeled if required with only a small negative impact on performance.

smb <- list(
smb1,
smb2,
benchmark_semi_markov(n_patients = 1000, uncertainty = "normal",
n_samples = 100, dist = DIST,
step = STEP),
benchmark_semi_markov(n_patients = 1000, uncertainty = "normal",
n_samples = 1000, dist = DIST,
step = STEP)
)
semi_markov_table(smb)
Run time
# of patients # of PSA samples mstate hesim (parametric) hesim (spline)
1000 1 11 seconds 0.062 seconds 0.061 seconds
5000 1 1.4 minutes 0.11 seconds 0.24 seconds
1000 100 22 minutes 0.63 seconds 2.9 seconds
1000 1000 3.6 hours 6 seconds 29 seconds

## Markov models

heemod is a general purpose R package for simulating Markov cohort models. We simulated the 5-state time inhomogeneous Markov model of total hip replacement from the Decision Modeling for Health Economic Evaluation textbook with hesim and heemod. Vignettes for this example are available in both packages ( hesim, heemod).

Cohort models were simulated with both packages and an individual-level model was also simulated with hesim. A single representative patient was used in the cohort model and 1000 patients were simulated in the individual-level model. The cohort models were simulated for 60 years using cycle lengths of 1 year.

mb <- list(
benchmark_markov(n_samples = 10, n_patients = 1000),
benchmark_markov(n_samples = 100, n_patients = 1000),
benchmark_markov(n_samples = 1000, n_patients = 1000)
)
markov_table(mb)
# of patients
Run time
# of PSA samples Cohort Individual heemod hesim (cohort) hesim (individual)
10 1 1000 1.5 seconds 0.097 seconds 0.21 seconds
100 1 1000 12 seconds 0.12 seconds 1.1 seconds
1000 1 1000 2 minutes 1.2 seconds 11 seconds

## Computing environment

sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Mojave 10.14.6
##
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
## [1] mstate_0.3.1      kableExtra_1.2.1  hesim_0.5.0.9999  heemod_0.13.0
## [5] ggplot2_3.3.3     flexsurv_1.1.1    survival_3.2-7    data.table_1.13.6
## [9] knitr_1.30
##
## loaded via a namespace (and not attached):
##  [1] deSolve_1.28       tidyselect_1.1.0   xfun_0.18          purrr_0.3.4
##  [5] splines_4.0.3      lattice_0.20-41    colorspace_2.0-0   vctrs_0.3.6
##  [9] generics_0.1.0     htmltools_0.5.0    viridisLite_0.3.0  rlang_0.4.10
## [13] pillar_1.4.7       glue_1.4.2         withr_2.3.0        RColorBrewer_1.1-2
## [17] pryr_0.1.4         muhaz_1.2.6.1      lifecycle_0.2.0    plyr_1.8.6
## [21] stringr_1.4.0      munsell_0.5.0      gtable_0.3.0       rvest_0.3.6
## [25] mvtnorm_1.1-1      mvnfast_0.2.5      codetools_0.2-16   evaluate_0.14
## [29] memoise_1.1.0      highr_0.8          Rcpp_1.0.5         scales_1.1.1
## [33] webshot_0.5.2      digest_0.6.27      stringi_1.5.3      dplyr_1.0.2
## [37] grid_4.0.3         quadprog_1.5-8     tools_4.0.3        magrittr_2.0.1
## [41] lazyeval_0.2.2     tibble_3.0.4       crayon_1.3.4       tidyr_1.1.2
## [45] pkgconfig_2.0.3    ellipsis_0.3.1     Matrix_1.2-18      xml2_1.3.2
## [49] rmarkdown_2.4      httr_1.4.2         rstudioapi_0.13    R6_2.5.0
## [53] compiler_4.0.3