Heterogeneity & Demographic Analysis

2016-09-16

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("non-homogeneous", package = "heemod").

Population characteristics

The characteristics of the population are input from a table, with one column per parameter and one row per individul. Those may be per 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:

tab_indiv
## # A tibble: 100 × 2
##      age   sex
##    <dbl> <int>
## 1     68     1
## 2     53     0
## 3     69     1
## 4     51     0
## 5     58     1
## 6     56     0
## 7     62     1
## 8     62     0
## 9     56     1
## 10    59     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_models() in the Time-varying Markov models vignette, can be passed to update() to update the model woth the new data and perform the heterogeneity analysis.

res_h <- update(res_mod, newdata = tab_indiv)
## No weights specified in model update, using equal weights.
## Updating model 'standard'...
## Updating model '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      485852.97365  605006.2810 629468.02596 696751.856036
## standard - Effect     11784.33667   22793.0050  27578.78609  26385.856281
## standard - Δ Cost               -            -            -             -
## standard - Δ Effect             -            -            -             -
## standard - Icer                 -            -            -             -
## np1 - Cost           603342.63272  635550.9751 642202.04577 661671.304738
## np1 - Effect          11828.39436   23084.8338  27870.58379  26653.304443
## np1 - Δ Cost        -164881.37326 -129482.9089  12734.01981 -35080.551298
## np1 - Δ Effect           44.05769     194.8185    229.43277    267.448162
## np1 - Icer             -354.32431    -333.0520     54.54396      4.617731
##                         3rd Qu.        Max.
## standard - Cost     828543.4528 878043.3890
## standard - Effect    29074.9005  31598.6556
## standard - Δ Cost             -           -
## standard - Δ Effect           -           -
## standard - Icer               -           -
## np1 - Cost          699060.5439 713162.0157
## np1 - Effect         29500.8365  31835.3665
## np1 - Δ Cost         30544.6941 117489.6591
## np1 - Δ Effect         388.7769    465.3403
## np1 - Icer             156.7854   2666.7230
## 
## * Combined result:
## 
## 2 Markov models run for 60 cycles.
## 
## Initial states:
## 
##                N
## PrimaryTHR  1000
## SuccessP       0
## RevisionTHR    0
## SuccessR       0
## Death          0
## 
## Counting method: 'end'.
## 
##           utility     cost
## standard 26385.86 696751.9
## np1      26653.30 661671.3
## 
## Efficiency frontier:
## 
## standard np1
## 
## Model difference:
## 
##          Cost    Effect      ICER
## np1 -35.08055 0.2674482 -131.1677

The variation of the incremental differences in cost, effect or ICER can then be plotted.

plot(res_h, type = "icer", model = "np1", binwidth = 500)

plot(res_h, type = "effect", model = "np1", binwidth = 50)

plot(res_h, type = "cost", model = "np1", binwidth = 25000)

The results from the combined model can be plotted similarly to the results from run_models().

plot(res_h, type = "counts", model = "np1")

Weigthed 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     64     1 0.34386349
## 2     70     1 0.98740624
## 3     63     0 0.32383772
## 4     71     1 0.04471101
## 5     55     0 0.85404708
## 6     74     0 0.98496043
## 7     56     0 0.96513131
## 8     52     0 0.11708605
## 9     68     1 0.72040239
## 10    49     1 0.38014489
## # ... with 90 more rows
res_w <- update(res_mod, newdata = tab_indiv_w)
## Updating model 'standard'...
## Updating model 'np1'...
res_w
## An analysis re-run on 100 parameter sets.
## 
## * Weigths distribution:
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01639 0.32490 0.57520 0.55100 0.81200 0.99650 
## 
## Total weight: 55.10398
## 
## * Values distribution:
## 
##                              Min.      1st Qu.       Median        Mean
## standard - Cost      451929.91015  613836.4635 633614.16232 688839.6225
## standard - Effect      7472.56790   22521.1145  25657.74359  25035.5850
## standard - Δ Cost               -            -            -           -
## standard - Δ Effect             -            -            -           -
## standard - Icer                 -            -            -           -
## np1 - Cost           594291.10290  637950.8204 644063.94579 659497.1486
## np1 - Effect           7490.09703   22739.4487  25919.56300  25289.2626
## np1 - Δ Cost        -160479.85885 -110728.6273  14550.96853 -29342.4739
## np1 - Δ Effect           17.52913     208.5430    221.44419    253.6775
## np1 - Icer             -352.23489    -316.4395     63.42149    258.2954
##                         3rd Qu.        Max.
## standard - Cost     802342.6777 871885.4128
## standard - Effect    29062.6841  30944.2824
## standard - Δ Cost             -           -
## standard - Δ Effect           -           -
## standard - Icer               -           -
## np1 - Cost          691614.0504 711405.5539
## np1 - Effect         29396.8763  31173.7151
## np1 - Δ Cost         24114.3568 143644.1681
## np1 - Δ Effect         349.9204    455.6047
## np1 - Icer             115.6325  13472.7451
## 
## * Combined result:
## 
## 2 Markov models run for 60 cycles.
## 
## Initial states:
## 
##                N
## PrimaryTHR  1000
## SuccessP       0
## RevisionTHR    0
## SuccessR       0
## Death          0
## 
## Counting method: 'end'.
## 
##           utility     cost
## standard 25035.59 688839.6
## np1      25289.26 659497.1
## 
## Efficiency frontier:
## 
## standard np1
## 
## Model difference:
## 
##          Cost    Effect      ICER
## np1 -29.34247 0.2536775 -115.6684