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.
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:
rr
, the relative risk associated with the new treatment.cost_zido
and cost_lami
, the drug costs.dr
, the discount rate.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
)
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")