Deterministic Sensitivity Analysis

2016-11-11

Introduction

The objective of deterministic sensitivity analysis is to assess how model results are sensitive to parameter values. Parameter values are changed through upper and lower bounds, and the results are reported.

Sensitivity analysis is distinct from probabilistic uncertainty analysis: whereas in PSA the objective is to estimate the effect of global uncertainty on model results, in DSA the objective is to assess the sensitivity of results to variations of individual parameters. Both analyses are complementary.

Define the analysis

This example uses the HIV drug model defined in vignette("e-probabilistic", "heemod"). See this vignette for an explanation of the model. Note that as in PSA, parameters need to be defined in define_parameters() in order to be modified in a DSA.

In this example we will study the sensitivity of cost to 4 parameters:

Upper and lower values for the paramters are given to define_dsa().

se <- define_dsa(
  rr, .4, .6,
  
  cost_zido, 1500, 3000,
  cost_lami, 1500, 3000,
  
  dr, .04, .08
)

We then run the sensitivity analysis with run_dsa(), using res_mod the result from run_model() as input.

res <- run_dsa(
  model = res_mod,
  sensitivity = se
)

Interpretation

All the results can be displayed in a table.

res
## A sensitivity analysis on 4 parameters.
## 
## Parameters:
##   -rr
##   -cost_zido
##   -cost_lami
##   -dr
## 
## Original results:
## 
## 2 strategies run for 20 cycles.
## 
## Initial state counts:
## 
##      N
## A 1000
## B    0
## C    0
## D    0
## 
## Counting method: 'life-table'.
## 
##      cost_health cost_drugs cost_total life_year
## mono    46725886   19279596   48417031  8463.387
## comb    71019861   61962911   85148060 14198.651
## 
## Efficiency frontier:
## 
## mono -> comb
## 
## Differences:
## 
##      Cost Diff. Effect Diff.     ICER Ref.
## comb   36731.03     5.735263 6404.419 mono
## 
## Sensitivity analysis:
## 
##                         cost_health cost_drugs cost_total life_year
## cost_lami = 1500 (mono) 46725886    19279596   48417031    8463.387
## cost_lami = 1500 (comb) 71019861    53642502   79593035   14198.651
## cost_lami = 3000 (mono) 46725886    19279596   48417031    8463.387
## cost_lami = 3000 (comb) 71019861    74940478   93812382   14198.651
## cost_zido = 1500 (mono) 46725886    12695081   43363208    8463.387
## cost_zido = 1500 (comb) 71019861    50916361   77772959   14198.651
## cost_zido = 3000 (mono) 46725886    25390162   53107083    8463.387
## cost_zido = 3000 (comb) 71019861    72214337   91992306   14198.651
## dr = 0.04 (mono)        46725886    19279596   53238469    8463.387
## dr = 0.04 (comb)        71019861    61962911   97480846   14198.651
## dr = 0.08 (mono)        46725886    19279596   44351921    8463.387
## dr = 0.08 (comb)        71019861    61962911   75259528   14198.651
## rr = 0.4 (mono)         46725886    19279596   48417031    8463.387
## rr = 0.4 (comb)         74749377    69178956   89573275   15852.190
## rr = 0.6 (mono)         46725886    19279596   48417031    8463.387
## rr = 0.6 (comb)         66652719    56216918   80800674   12881.970
##                         Cost     Effect    ICER     Cost Diff.
## cost_lami = 1500 (mono) 48417031  8463.387 -        -         
## cost_lami = 1500 (comb) 79593035 14198.651 5435.845 31176.00  
## cost_lami = 3000 (mono) 48417031  8463.387 -        -         
## cost_lami = 3000 (comb) 93812382 14198.651 7915.129 45395.35  
## cost_zido = 1500 (mono) 43363208  8463.387 -        -         
## cost_zido = 1500 (comb) 77772959 14198.651 5999.681 34409.75  
## cost_zido = 3000 (mono) 53107083  8463.387 -        -         
## cost_zido = 3000 (comb) 91992306 14198.651 6780.024 38885.22  
## dr = 0.04 (mono)        53238469  8463.387 -        -         
## dr = 0.04 (comb)        97480846 14198.651 7714.097 44242.38  
## dr = 0.08 (mono)        44351921  8463.387 -        -         
## dr = 0.08 (comb)        75259528 14198.651 5389.047 30907.61  
## rr = 0.4 (mono)         48417031  8463.387 -        -         
## rr = 0.4 (comb)         89573275 15852.190 5570.083 41156.24  
## rr = 0.6 (mono)         48417031  8463.387 -        -         
## rr = 0.6 (comb)         80800674 12881.970 7328.966 32383.64  
##                         Effect Diff. Ref.
## cost_lami = 1500 (mono) -            -   
## cost_lami = 1500 (comb) 5.735263     mono
## cost_lami = 3000 (mono) -            -   
## cost_lami = 3000 (comb) 5.735263     mono
## cost_zido = 1500 (mono) -            -   
## cost_zido = 1500 (comb) 5.735263     mono
## cost_zido = 3000 (mono) -            -   
## cost_zido = 3000 (comb) 5.735263     mono
## dr = 0.04 (mono)        -            -   
## dr = 0.04 (comb)        5.735263     mono
## dr = 0.08 (mono)        -            -   
## dr = 0.08 (comb)        5.735263     mono
## rr = 0.4 (mono)         -            -   
## rr = 0.4 (comb)         7.388802     mono
## rr = 0.6 (mono)         -            -   
## rr = 0.6 (comb)         4.418583     mono

Two distinct plot types are available. The basic plot (type = "simple") displays cost variations for each model, around the base cost.

As expected mono model costs are not senstive to cost_lami, since this drug was not given to this group. Similarly it is not sensitive to rr, because this parameters only modifies transition probabilities in the other model.

plot(res,
     model = "mono",
     result = "cost",
     type = "simple")

On the other hand the comb model cost is sensitive to all 4 parameters.

plot(res,
     model = "comb",
     result = "cost",
     type = "simple")

And its effectiveness is sensitive to rr

plot(res, 
     model = "comb",
     result = "effect",
     type = "simple")

The difference plot (type = "difference") displays the difference between the specified model comb and the reference model mono.

plot(res,
     model = "comb",
     result = "cost",
     type = "difference")

plot(res,
     model = "comb",
     result = "icer",
     type = "difference")