Heterogeneity & Demographic Analysis
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 different 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 × 2
## age sex
## <dbl> <int>
## 1 59 1
## 2 56 1
## 3 56 0
## 4 54 1
## 5 50 1
## 6 56 1
## 7 27 0
## 8 55 0
## 9 68 1
## 10 65 1
## # ℹ 90 more rows
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.
## 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 500.08967163 605.0062810 636.5440850 700.1868729
## standard - Effect 13.56976193 24.2050060 26.7297859 26.1336632
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 607.16692250 635.5509751 644.8774403 662.6481086
## np1 - Effect 13.62743581 24.4874532 27.1045630 26.4019315
## np1 - Cost Diff. -165.40882382 -122.7948420 8.3333553 -37.5387642
## np1 - Effect Diff. 0.05767389 0.1948185 0.2284374 0.2682682
## np1 - Icer -354.56585682 -327.6476693 46.0297074 -23.6706472
## 3rd Qu. Max.
## standard - Cost 819.1977737 878.7813785
## standard - Effect 29.0596426 31.8081680
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 696.4029317 713.3725547
## np1 - Effect 29.2683350 32.0472170
## np1 - Cost Diff. 30.5446941 107.0772509
## np1 - Effect Diff. 0.3747771 0.4665109
## np1 - Icer 156.7853582 1856.5985016
##
## * 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 26133.66 700186.9
## np1 26401.93 662648.1
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -37.53876 0.2682682 -139.93 standardThe variation of cost or effect can then be plotted.
The results from the combined model can be plotted similarly to the
results from run_model().
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 × 3
## age sex .weights
## <dbl> <int> <dbl>
## 1 60 1 0.551
## 2 61 1 0.954
## 3 42 0 0.0456
## 4 51 0 0.556
## 5 74 1 0.537
## 6 61 0 0.140
## 7 58 1 0.137
## 8 59 1 0.427
## 9 74 1 0.975
## 10 52 0 0.283
## # ℹ 90 more rows## Updating strategy 'standard'...## Updating strategy 'np1'...## An analysis re-run on 100 parameter sets.
##
## * Weights distribution:
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.006339 0.361987 0.550849 0.543349 0.769366 0.992799
##
## Total weight: 54.33489
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 470.23578695 608.9108842 629.415647 693.4287975
## standard - Effect 5.05860925 24.4991251 26.729786 25.7781948
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 599.19333183 636.6121615 642.187795 660.7307352
## np1 - Effect 5.07524179 24.8264025 27.104563 26.0383842
## np1 - Cost Diff. -166.84613181 -99.5031416 12.772148 -32.6980622
## np1 - Effect Diff. 0.01663254 0.1948185 0.220806 0.2601894
## np1 - Icer -355.21474694 -304.0330575 60.195636 48.9701128
## 3rd Qu. Max.
## standard - Cost 786.6690449 880.792467
## standard - Effect 29.0596426 31.299481
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 687.1659033 713.946335
## np1 - Effect 29.2683350 31.532860
## np1 - Cost Diff. 30.5446941 128.957545
## np1 - Effect Diff. 0.3272774 0.469705
## np1 - Icer 156.7853582 7753.326597
##
## * 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 25778.19 693428.8
## np1 26038.38 660730.7
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -32.69806 0.2601894 -125.6702 standardParallel 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.