Heterogeneity & Demographic Analysis

2016-11-21

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:

tab_indiv
## # A tibble: 100 × 2
##      age   sex
##    <dbl> <int>
## 1     48     0
## 2     41     0
## 3     60     0
## 4     43     1
## 5     68     0
## 6     45     1
## 7     51     0
## 8     58     0
## 9     52     0
## 10    45     1
## # ... 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.

summary(res_h)
## 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 690.819781
## standard - Effect         14.30828698   25.5696426  27.7806580  27.036103
## standard - Cost Diff.               -            -           -          -
## standard - Effect Diff.             -            -           -          -
## standard - Icer                     -            -           -          -
## np1 - Cost               615.48340627  635.5509751 640.1676766 659.957450
## np1 - Effect              14.43982318   25.8971558  27.9754765  27.302218
## np1 - Cost Diff.        -167.83433856 -110.7286273  18.1782873 -30.862331
## np1 - Effect Diff.         0.09203743    0.1948185   0.2214442   0.266115
## np1 - Icer              -355.65308588 -316.4394659  82.0897023 -13.482389
##                             3rd Qu.        Max.
## standard - Cost         802.3426777 882.1752204
## standard - Effect        29.0749005  31.3071020
## standard - Cost Diff.             -           -
## standard - Effect Diff.           -           -
## standard - Icer                   -           -
## np1 - Cost              691.6140504 714.3408818
## np1 - Effect             29.5008365  31.6126413
## np1 - Cost Diff.         30.5446941  84.5375046
## np1 - Effect Diff.        0.3499204   0.4719046
## np1 - Icer              156.7853582 918.5122572
## 
## * 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'.
## 
## Values:
## 
##           utility     cost
## standard 27036.10 690819.8
## np1      27302.22 659957.4
## 
## Efficiency frontier:
## 
## np1
## 
## Differences:
## 
##     Cost Diff. Effect Diff.      ICER     Ref.
## np1  -30.86233     0.266115 -115.9737 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.

tab_indiv_w
## # A tibble: 100 × 3
##      age   sex   .weights
##    <dbl> <int>      <dbl>
## 1     66     0 0.55272818
## 2     61     1 0.40775074
## 3     75     1 0.76490015
## 4     47     0 0.06054413
## 5     59     1 0.51861366
## 6     55     0 0.57235881
## 7     49     1 0.42416105
## 8     39     0 0.93200582
## 9     63     0 0.47428143
## 10    50     1 0.10827813
## # ... with 90 more rows
res_w <- update(res_mod, newdata = tab_indiv_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. 
## 0.005555 0.393600 0.567400 0.561800 0.794400 0.981100 
## 
## Total weight: 56.17992
## 
## * Values distribution:
## 
##                                  Min.      1st Qu.      Median        Mean
## standard - Cost          530.94590166  605.0062810 629.7415598 695.4517627
## standard - Effect         17.56922957   25.5696426  27.3769142  26.2696949
## standard - Cost Diff.               -            -           -           -
## standard - Effect Diff.             -            -           -           -
## standard - Icer                     -            -           -           -
## np1 - Cost               615.48340627  635.5509751 642.5234906 661.3131936
## np1 - Effect              17.66126700   25.8299343  27.7656911  26.5352387
## np1 - Cost Diff.        -155.93829747 -110.7286273  13.9560193 -34.1385691
## np1 - Effect Diff.         0.09203743    0.1948185   0.2261571   0.2655438
## np1 - Icer              -349.93447295 -316.4394659  74.4349668 -13.4798285
##                             3rd Qu.        Max.
## standard - Cost         802.3426777 871.8854128
## standard - Effect        29.0570960  31.7692206
## standard - Cost Diff.             -           -
## standard - Effect Diff.           -           -
## standard - Icer                   -           -
## np1 - Cost              691.6140504 711.4055539
## np1 - Effect             29.3493218  32.0078346
## np1 - Cost Diff.         30.5446941  84.5375046
## np1 - Effect Diff.        0.3499204   0.4556047
## np1 - Icer              156.7853582 918.5122572
## 
## * 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'.
## 
## Values:
## 
##           utility     cost
## standard 26269.69 695451.8
## np1      26535.24 661313.2
## 
## Efficiency frontier:
## 
## np1
## 
## Differences:
## 
##     Cost Diff. Effect Diff.     ICER     Ref.
## np1  -34.13857    0.2655438 -128.561 standard

Parallel computing

Updating can be significantly sped up by using parallel computing. This can be done in the following way:

Results may vary depending on the machine, but we found speed gains to be quite limited beyond 4 cores.