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
:
## # A tibble: 100 × 2
## age sex
## <dbl> <int>
## 1 75 1
## 2 67 0
## 3 58 0
## 4 63 0
## 5 55 1
## 6 60 1
## 7 68 0
## 8 63 1
## 9 66 0
## 10 76 1
## # ℹ 90 more rows
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'...
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 470.23578695 613.9316623 700.278258 704.5466169
## standard - Effect 5.05860925 24.2050060 27.255222 25.9194304
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 599.19333183 637.9767000 662.750240 663.8741848
## np1 - Effect 5.07524179 24.4874532 27.540020 26.1897501
## np1 - Cost Diff. -165.40882382 -105.3260667 -37.528018 -40.6724321
## np1 - Effect Diff. 0.01663254 0.1948185 0.230908 0.2703197
## np1 - Icer -354.56585682 -309.9367104 -177.278286 10.1345801
## 3rd Qu. Max.
## standard - Cost 794.8012271 878.7813785
## standard - Effect 29.2164282 31.5292548
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 689.4751604 713.3725547
## np1 - Effect 29.4828147 31.7651919
## np1 - Cost Diff. 24.0450377 128.9575449
## np1 - Effect Diff. 0.3391523 0.4665109
## np1 - Icer 115.2176112 7753.3265967
##
## * 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 25919.43 704546.6
## np1 26189.75 663874.2
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -40.67243 0.2703197 -150.4605 standard
The 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()
.
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 57 0 0.467
## 2 54 0 0.783
## 3 62 1 0.638
## 4 63 0 0.776
## 5 68 1 0.864
## 6 60 0 0.336
## 7 54 0 0.102
## 8 64 0 0.380
## 9 63 0 0.908
## 10 47 1 0.541
## # ℹ 90 more rows
## Updating strategy 'standard'...
## Updating strategy 'np1'...
## An analysis re-run on 100 parameter sets.
##
## * Weigths distribution:
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.002444 0.208542 0.520190 0.507997 0.792633 0.996271
##
## Total weight: 50.79967
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 470.23578695 605.0062810 633.703456 691.7877979
## standard - Effect 5.05860925 24.4991251 26.729786 25.4356749
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 599.19333183 635.5509751 643.518623 660.3053583
## np1 - Effect 5.07524179 24.8264025 27.104563 25.6940475
## np1 - Cost Diff. -163.38052116 -102.7776207 9.607599 -31.4824396
## np1 - Effect Diff. 0.01663254 0.1948185 0.220806 0.2583727
## np1 - Icer -353.62679735 -307.3529333 54.342778 212.4876176
## 3rd Qu. Max.
## standard - Cost 786.6690449 875.943516
## standard - Effect 29.0596426 31.808168
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 687.1659033 712.562995
## np1 - Effect 29.2683350 32.047217
## np1 - Cost Diff. 30.5446941 128.957545
## np1 - Effect Diff. 0.3272774 0.462014
## 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 25435.67 691787.8
## np1 25694.05 660305.4
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -31.48244 0.2583727 -121.849 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.