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 71 0
## 2 58 1
## 3 58 0
## 4 60 1
## 5 62 0
## 6 69 1
## 7 46 1
## 8 57 1
## 9 79 1
## 10 55 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.
<- update(res_mod, newdata = tab_indiv) res_h
## 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.
summary(res_h)
## An analysis re-run on 100 parameter sets.
##
## * Unweighted analysis.
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 4.254235e+02 611.6289179 629.4680260 694.269716
## standard - Effect 4.554756e+00 25.5696426 27.7806580 26.532292
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 5.872463e+02 637.3508591 642.2020458 660.970037
## np1 - Effect 4.561086e+00 25.8299343 27.9754765 26.799720
## np1 - Cost Diff. -1.648814e+02 -110.7286273 13.1000189 -33.299679
## np1 - Effect Diff. 6.330508e-03 0.1948185 0.2214442 0.267428
## np1 - Icer -3.543243e+02 -316.4394659 63.4214929 261.605811
## 3rd Qu. Max.
## standard - Cost 802.3426777 8.780434e+02
## standard - Effect 29.9639255 3.130710e+01
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 691.6140504 7.131620e+02
## np1 - Effect 30.4095470 3.154057e+01
## np1 - Cost Diff. 25.7219412 1.618227e+02
## np1 - Effect Diff. 0.3499204 4.653403e-01
## np1 - Icer 125.9207494 2.556236e+04
##
## * 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 26532.29 694269.7
## np1 26799.72 660970.0
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -33.29968 0.267428 -124.5183 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")
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 81 1 0.109
## 2 76 0 0.424
## 3 61 0 0.461
## 4 58 1 0.303
## 5 42 1 0.558
## 6 61 0 0.0293
## 7 57 1 0.865
## 8 80 1 0.0892
## 9 83 1 0.172
## 10 54 0 0.0510
## # … with 90 more rows
<- update(res_mod, newdata = tab_indiv_w) res_w
## Updating strategy 'standard'...
## Updating strategy 'np1'...
res_w
## An analysis re-run on 100 parameter sets.
##
## * Weigths distribution:
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02251 0.28270 0.46206 0.49745 0.73346 0.99673
##
## Total weight: 49.74493
##
## * Values distribution:
##
## Min. 1st Qu. Median Mean
## standard - Cost 485.85297365 605.0062810 629.4680260 698.4756444
## standard - Effect 9.32287610 25.5696426 27.7806580 26.6638850
## standard - Cost Diff. - - - -
## standard - Effect Diff. - - - -
## standard - Icer - - - -
## np1 - Cost 603.34263272 635.5509751 642.2020458 662.1621740
## np1 - Effect 9.38064927 25.8299343 27.9754765 26.9353285
## np1 - Cost Diff. -164.88137326 -129.4829089 13.1000189 -36.3134704
## np1 - Effect Diff. 0.04405769 0.1948185 0.2294328 0.2714434
## np1 - Icer -354.32431375 -333.0519971 60.8289935 -4.5262903
## 3rd Qu. Max.
## standard - Cost 828.5434528 878.0433890
## standard - Effect 29.0749005 31.7692206
## standard - Cost Diff. - -
## standard - Effect Diff. - -
## standard - Icer - -
## np1 - Cost 699.0605439 713.1620157
## np1 - Effect 29.5008365 32.0078346
## np1 - Cost Diff. 30.5446941 117.4896591
## np1 - Effect Diff. 0.3887769 0.4653403
## np1 - Icer 156.7853582 2666.7229585
##
## * 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 26663.89 698475.6
## np1 26935.33 662162.2
##
## Efficiency frontier:
##
## np1
##
## Differences:
##
## Cost Diff. Effect Diff. ICER Ref.
## np1 -36.31347 0.2714434 -133.7791 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.