Heterogeneity & Demographic Analysis

2016-10-28

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:

tab_indiv
## # A tibble: 100 × 2
##      age   sex
##    <dbl> <int>
## 1     67     1
## 2     40     1
## 3     50     0
## 4     44     0
## 5     67     1
## 6     60     1
## 7     61     0
## 8     47     0
## 9     63     1
## 10    58     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 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 629699.85051 694099.0410
## standard - Effect      9322.87610   22793.0050  27376.91420  25384.5899
## standard - Δ Cost               -            -            -           -
## standard - Δ Effect             -            -            -           -
## standard - Icer                 -            -            -           -
## np1 - Cost           603342.63272  635550.9751 642616.86984 660984.1287
## np1 - Effect           9380.64927   23084.8338  27765.69106  25645.0357
## np1 - Δ Cost        -164881.37326 -110728.6273  13100.01886 -33114.9123
## np1 - Δ Effect           44.05769     194.8185    221.44419    260.4458
## np1 - Icer             -354.32431    -316.4395     63.42149     49.3021
##                         3rd Qu.        Max.
## standard - Cost     802342.6777 878043.3890
## standard - Effect    29074.9005  31307.1020
## standard - Δ Cost             -           -
## standard - Δ Effect           -           -
## standard - Icer               -           -
## np1 - Cost          691614.0504 713162.0157
## np1 - Effect         29500.8365  31540.5654
## np1 - Δ Cost         30544.6941 117489.6591
## np1 - Δ Effect         349.9204    465.3403
## np1 - Icer             156.7854   2666.7230
## 
## * 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'.
## 
##           utility     cost
## standard 25384.59 694099.0
## np1      25645.04 660984.1
## 
## Efficiency frontier:
## 
## standard -> np1
## 
## Model difference:
## 
##          Cost    Effect      ICER
## np1 -33.11491 0.2604458 -127.1471

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_model().

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

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     58     1 0.257142175
## 2     59     1 0.233707460
## 3     37     0 0.502128315
## 4     50     1 0.413410924
## 5     78     0 0.653694508
## 6     58     0 0.848250724
## 7     39     0 0.005358921
## 8     80     1 0.142529890
## 9     70     1 0.312865614
## 10    54     0 0.951281772
## # ... 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. 
## 0.005359 0.224100 0.491500 0.481700 0.696400 0.961000 
## 
## Total weight: 48.16557
## 
## * Values distribution:
## 
##                              Min.      1st Qu.       Median        Mean
## standard - Cost      485852.97365  613836.4635 700765.42198 697054.7275
## standard - Effect      9322.87610   22793.0050  27376.91420  25584.0926
## standard - Δ Cost               -            -            -           -
## standard - Δ Effect             -            -            -           -
## standard - Icer                 -            -            -           -
## np1 - Cost           603342.63272  637950.8204 662887.36828 661804.4659
## np1 - Effect           9380.64927   23084.8338  27765.69106  25848.0165
## np1 - Δ Cost        -155938.29747 -110728.6273  -9727.98242 -35250.2617
## np1 - Δ Effect           44.05769     208.5430    221.44419    263.9238
## np1 - Icer             -349.93447    -316.4395    -48.98015    183.6297
##                         3rd Qu.        Max.
## standard - Cost     812146.4091 865532.3779
## standard - Effect    29963.9255  31769.2206
## standard - Δ Cost             -           -
## standard - Δ Effect           -           -
## standard - Icer               -           -
## np1 - Cost          694400.3581 709594.0804
## np1 - Effect         30409.5470  32007.8346
## np1 - Δ Cost         24114.3568 143644.1681
## np1 - Δ Effect         364.4596    445.6214
## np1 - Icer             115.6325  13472.7451
## 
## * 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'.
## 
##           utility     cost
## standard 25584.09 697054.7
## np1      25848.02 661804.5
## 
## Efficiency frontier:
## 
## standard -> np1
## 
## Model difference:
## 
##          Cost    Effect      ICER
## np1 -35.25026 0.2639238 -133.5622