Heterogeneity & Demographic Analysis
2022-03-16
Introduction
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").
Population characteristics
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:
## # A tibble: 100 x 2
## age sex
## <dbl> <int>
## 1 32 1
## 2 56 1
## 3 53 1
## 4 65 1
## 5 38 0
## 6 66 1
## 7 59 0
## 8 48 1
## 9 60 0
## 10 62 0
## # ... with 90 more rows
library(ggplot2)
ggplot(tab_indiv, aes(x = age)) +
geom_histogram(binwidth = 2)
Running the analysis
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 update, using equal weights.
## Updating strategy 'standard'...
## Updating strategy 'np1'...
Interpreting results
The summary() method reports summary statistics for cost, effect and ICER, as well as the result from the combined model.
## An analysis re-run on 100 parameter sets.
##
## * Unweighted analysis.
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 530.94590166 605.0062810 621.9893893 685.2381026
## standard - Effect 9.32287610 25.6577436 27.7806580 27.0726753
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 615.48340627 635.5509751 640.1676766 658.3659693
## np1 - Effect 9.38064927 25.8299343 27.9754765 27.3341846
## np1 - Cost Diff. -167.83433856 -110.7286273 18.1782873 -26.8721332
## np1 - Effect Diff. 0.05777317 0.1948185 0.2214442 0.2615092
## np1 - Icer -355.65308588 -316.4394659 82.0897023 4.2323184
## 3rd Qu. Max.
## standard - Cost 802.3426777 882.1752204
## standard - Effect 30.2219909 31.5986556
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 691.6140504 714.3408818
## np1 - Effect 30.4434351 31.8353665
## np1 - Cost Diff. 30.5446941 84.5375046
## np1 - Effect Diff. 0.3499204 0.4719046
## np1 - Icer 156.7853582 1275.2350079
##
## * Combined result:
##
## 2 strategies run for 60 cycles.
##
## Initial state counts:
##
## PrimaryTHR = 1000L
## SuccessP = 0L
## RevisionTHR = 0L
## SuccessR = 0L
## Death = 0L
##
## Counting method: 'beginning'.
##
## Values:
##
## utility cost
## standard 27072.68 685238.1
## np1 27334.18 658366.0
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -26.87213 0.2615092 -102.7579 standard
The variation of cost or effect can then be plotted.
plot(res_h, result = "effect", binwidth = 5)
plot(res_h, result = "cost", binwidth = 50)
plot(res_h, result = "icer", type = "difference",
binwidth = 500)
plot(res_h, result = "effect", type = "difference",
binwidth = .1)
plot(res_h, result = "cost", type = "difference",
binwidth = 30)
The results from the combined model can be plotted similarly to the results from run_model().
plot(res_h, type = "counts")
Weighted results
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.
## # A tibble: 100 x 3
## age sex .weights
## <dbl> <int> <dbl>
## 1 65 1 0.543
## 2 56 0 0.257
## 3 63 1 0.784
## 4 71 0 0.240
## 5 53 1 0.872
## 6 68 0 0.558
## 7 72 0 0.239
## 8 42 1 0.674
## 9 68 1 0.908
## 10 64 0 0.391
## # ... with 90 more rows
res_w <- update(res_mod, newdata = tab_indiv_w)
## Updating strategy 'standard'...
## Updating strategy 'np1'...
## An analysis re-run on 100 parameter sets.
##
## * Weigths distribution:
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02336 0.35455 0.58339 0.56491 0.78636 0.99446
##
## Total weight: 56.4915
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 489.70561885 605.0062810 629.9316751 701.6031159
## standard - Effect 6.14259603 25.5696426 27.3769142 26.1663890
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 604.44079805 635.5509751 643.0316939 663.0711056
## np1 - Effect 6.16727815 25.8299343 27.7656911 26.4375563
## np1 - Cost Diff. -169.74573893 -129.4829089 13.1000189 -38.5320103
## np1 - Effect Diff. 0.02468212 0.1948185 0.2214442 0.2711673
## np1 - Icer -356.48325605 -333.0519971 82.0897023 -3.7874031
## 3rd Qu. Max.
## standard - Cost 828.5434528 884.8498736
## standard - Effect 29.0459530 31.5986556
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 699.0605439 715.1041347
## np1 - Effect 29.2544960 31.8353665
## np1 - Cost Diff. 30.5446941 114.7351792
## np1 - Effect Diff. 0.3887769 0.4761675
## np1 - Icer 156.7853582 4648.5141231
##
## * Combined result:
##
## 2 strategies run for 60 cycles.
##
## Initial state counts:
##
## PrimaryTHR = 1000L
## SuccessP = 0L
## RevisionTHR = 0L
## SuccessR = 0L
## Death = 0L
##
## Counting method: 'beginning'.
##
## Values:
##
## utility cost
## standard 26166.39 701603.1
## np1 26437.56 663071.1
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -38.53201 0.2711673 -142.0968 standard
Parallel computing
Updating can be significantly sped up by using parallel computing. This can be done in the following way:
- Define a cluster with the
use_cluster() functions (i.e. use_cluster(4) to use 4 cores).
- Run the analysis as usual.
- To stop using parallel computing use the
close_cluster() function.
Results may vary depending on the machine, but we found speed gains to be quite limited beyond 4 cores.