Heterogeneity analysis is a way to explore how the results of a model can vary depending on the characteristics of individuals in a population, and demographic analysis estimates the average values of a model over an entire population.
In practice these two analyses naturally complement each other: heterogeneity analysis runs the model on multiple sets of parameters (reflecting differents characteristics found in the target population), and demographic analysis combines the results.
For this example we will use the result from the assessment of a new total hip replacement previously described in vignette("d-non-homogeneous", "heemod")
.
The characteristics of the population are input from a table, with one column per parameter and one row per individual. Those may be for example the characteristics of the indiviuals included in the original trial data.
For this example we will use the characteristics of 100 individuals, with varying sex and age, specified in the data frame tab_indiv
:
tab_indiv
## # A tibble: 100 × 2
## age sex
## <dbl> <int>
## 1 70 1
## 2 58 1
## 3 71 0
## 4 72 1
## 5 69 0
## 6 60 1
## 7 58 1
## 8 59 1
## 9 62 0
## 10 51 0
## # ... with 90 more rows
library(ggplot2)
ggplot(tab_indiv, aes(x = age)) +
geom_histogram(binwidth = 2)
res_mod
, the result we obtained from run_model()
in the Time-varying Markov models vignette, can be passed to update()
to update the model with the new data and perform the heterogeneity analysis.
res_h <- update(res_mod, newdata = tab_indiv)
## No weights specified in model update, using equal weights.
## Updating model 'standard'...
## Updating model 'np1'...
The summary()
method reports summary statistics for cost, effect and ICER, as well as the result from the combined model.
summary(res_h)
## An analysis re-run on 100 parameter sets.
##
## * Unweighted analysis.
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 489705.61885 613836.464 700765.4220 707842.23619
## standard - Effect 6142.59603 25569.643 27376.9142 26462.35137
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 604440.79805 637950.820 662887.3683 664792.10704
## np1 - Effect 6167.27815 25829.934 27765.6911 26738.92591
## np1 - Cost Diff. -160479.85885 -129482.909 -37878.0537 -43050.12914
## np1 - Effect Diff. 24.68212 208.543 231.4481 276.57455
## np1 - Icer -352.23489 -333.052 -178.4235 -34.15831
## 3rd Qu. Max.
## standard - Cost 828543.4528 871885.4128
## standard - Effect 29074.9005 31598.6556
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 699060.5439 711405.5539
## np1 - Effect 29500.8365 31835.3665
## np1 - Cost Diff. 24114.3568 114735.1792
## np1 - Effect Diff. 388.7769 455.6047
## np1 - Icer 115.6325 4648.5141
##
## * Combined result:
##
## 2 strategies run for 60 cycles.
##
## Initial state counts:
##
## N
## PrimaryTHR 1000
## SuccessP 0
## RevisionTHR 0
## SuccessR 0
## Death 0
##
## Counting method: 'end'.
##
## utility cost
## standard 26462.35 707842.2
## np1 26738.93 664792.1
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -43.05013 0.2765745 -155.6547 standard
The variation of the incremental differences in cost, effect or ICER can then be plotted.
plot(res_h, type = "icer", model = "np1", binwidth = 500)
plot(res_h, type = "effect", model = "np1", binwidth = 50)
plot(res_h, type = "cost", model = "np1", binwidth = 25000)
The results from the combined model can be plotted similarly to the results from run_model()
.
plot(res_h, type = "counts", model = "np1")
Weights can be used in the analysis by including an optional column .weights
in the new data to specify the respective weights of each strata in the target population.
tab_indiv_w
## # A tibble: 100 × 3
## age sex .weights
## <dbl> <int> <dbl>
## 1 57 0 0.56670097
## 2 55 0 0.09616077
## 3 66 1 0.56064040
## 4 57 1 0.19279303
## 5 66 0 0.72781279
## 6 55 0 0.46064354
## 7 47 0 0.89288972
## 8 46 0 0.91552882
## 9 66 0 0.64694395
## 10 59 1 0.97023568
## # ... with 90 more rows
res_w <- update(res_mod, newdata = tab_indiv_w)
## Updating model 'standard'...
## Updating model 'np1'...
res_w
## An analysis re-run on 100 parameter sets.
##
## * Weigths distribution:
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01712 0.27250 0.54770 0.51340 0.73020 0.99800
##
## Total weight: 51.33572
##
## * Values distribution:
##
## Min. 1st Qu. Median
## standard - Cost 546153.34802 605006.2810 629545.85355
## standard - Effect 14308.28698 24414.3654 27376.91420
## standard - Cost Diff. - - -
## standard - Effect Diff. - - -
## standard - Icer - - -
## np1 - Cost 619827.71155 635550.9751 642341.30954
## np1 - Effect 14439.82318 24687.7787 27765.69106
## np1 - Cost Diff. -167834.33856 -118531.7322 14550.96853
## np1 - Effect Diff. 92.03743 194.8185 229.43277
## np1 - Icer -355.65309 -323.3515 63.42149
## Mean 3rd Qu. Max.
## standard - Cost 698290.32147 828543.4528 882175.2204
## standard - Effect 26266.52731 29074.9005 31404.9817
## standard - Cost Diff. - - -
## standard - Effect Diff. - - -
## standard - Icer - - -
## np1 - Cost 662109.02565 699060.5439 714340.8818
## np1 - Effect 26534.54165 29500.8365 31687.4141
## np1 - Cost Diff. -36181.29581 30544.6941 95600.1249
## np1 - Effect Diff. 268.01434 388.7769 471.9046
## np1 - Icer -21.39138 156.7854 1742.3821
##
## * Combined result:
##
## 2 strategies run for 60 cycles.
##
## Initial state counts:
##
## N
## PrimaryTHR 1000
## SuccessP 0
## RevisionTHR 0
## SuccessR 0
## Death 0
##
## Counting method: 'end'.
##
## utility cost
## standard 26266.53 698290.3
## np1 26534.54 662109.0
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -36.1813 0.2680143 -134.9976 standard
Updating can be significantly sped up by using parallel computing. This can be done in the following way:
use_cluster()
functions (i.e. use_cluster(4)
to use 4 cores).close_cluster()
function.Results may vary depending on the machine, but we found speed gains to be quite limited beyond 4 cores.