Constructing an economic model
An economic model consists of a disease model, a utility model, and a set of cost models for each cost category. The utility and cost models are always hesim::StateVals objects, whereas the disease models vary by economic model. The disease model is used to simulate survival curves in a PSM and health state transitions in a cDTSTM and iCTSTM.
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Economic model
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Disease model
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Utility model
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Cost model(s)
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hesim::CohortDtstm
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hesim::CohortDtstmTrans
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hesim::StateVals
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hesim::StateVals
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hesim::Psm
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hesim::PsmCurves
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hesim::StateVals
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hesim::StateVals
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hesim::IndivCtstm
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hesim::IndivCtstmTrans
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hesim::StateVals
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hesim::StateVals
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Since economic models in hesim are inherently Bayesian, we must specify the number of parameter samples we will use for the PSA before constructing the model.
Disease model
Models are constructed as a function of parameters (or model fits) and in regression models, input data. The input data must be objects of class expanded_hesim_data, which are data tables containing the covariates for the statistical model. In our multi-state model, each row is a unique treatment strategy, patient, and health-state transition. The ID variables (strategy_id, patient_id, and transition_id) are stored as attributes of the dataset.
An expanded_hesim_data object can be created directly or by expanding an object of class hesim_data using expand.hesim_data(). Here, we will use the latter approach,
transmod_data <- expand(hesim_dat,
by = c("strategies", "patients", "transitions"))
head(transmod_data)
## strategy_id patient_id transition_id age female from to from_name
## 1: 1 1 1 39.24173 0 1 2 Healthy
## 2: 1 1 2 39.24173 0 1 3 Healthy
## 3: 1 1 3 39.24173 0 2 1 Sick
## 4: 1 1 4 39.24173 0 2 3 Sick
## 5: 1 2 1 41.72205 1 1 2 Healthy
## 6: 1 2 2 41.72205 1 1 3 Healthy
## to_name trans
## 1: Sick 1
## 2: Dead 2
## 3: Healthy 3
## 4: Dead 4
## 5: Sick 1
## 6: Dead 2
attr(transmod_data, "id_vars")
## [1] "strategy_id" "patient_id" "transition_id"
We can now construct the health state transition model, which creates an IndivCtstmTrans object that can be used to simulate health state transitions.
transmod <- create_IndivCtstmTrans(fit_wei, transmod_data,
trans_mat = tmat, n = n_samples)
class(transmod)
## [1] "IndivCtstmTrans" "CtstmTrans" "R6"
Cost and utility models
Since we are using predicted means for costs and utilities, we do not need to specify input data. Instead, we can construct the cost and utility models directly from the stateval_tbl objects.
# Utility
utilitymod <- create_StateVals(utility_tbl, n = n_samples)
# Costs
drugcostmod <- create_StateVals(drugcost_tbl, n = n_samples)
medcostmod <- create_StateVals(medcost_tbl, n = n_samples)
costmods <- list(drugs = drugcostmod,
medical = medcostmod)
Combining the disease progression, cost, and utility models
Once the disease, utility, and cost model have been constructed, we combine them to create the full economic model.
ictstm <- IndivCtstm$new(trans_model = transmod,
utility_model = utilitymod,
cost_models = costmods)
Simulating outcomes
Each economic model contains methods (i.e., functions) for simulating disease progression, costs, and QALYs. These methods are listed in the table below.
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Economic model (R6 class)
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Disease progression
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QALYs
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Costs
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hesim::CohortDtstm
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$sim_stateprobs()
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$sim_qalys()
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$sim_costs()
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hesim::Psm
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$sim_survival() and $sim_stateprobs()
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$sim_qalys()
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$sim_costs()
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hesim::IndivCtstm
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$sim_disease() and $sim_stateprobs()
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$sim_qalys()
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$sim_costs()
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Although all models simulate state probabilities, they do so in different ways. The cDTSTM uses discrete time Markov chains, the PSM calculates differences in probabilities from simulated survival curves, and the iCTSTM aggregates individual trajectories simulated using random number generation. The individual-level simulation is advantageous because it can be used for semi-Markov processes where transition rates depend on time since entering a health state (rather than time since the start of the model).
In the cohort models, costs and QALYs are computed as a function of the state probabilities whereas in individual-level models they are based on the simulated individual trajectories. Like the disease model, the individual-level simulation is more flexible because costs and QALYs can depend on time since entering the health state.
We illustrate with the iCTSTM. First we simulate disease progression for each patient.
ictstm$sim_disease()
head(ictstm$disprog_)
## sample strategy_id patient_id grp_id from to final time_start time_stop
## 1: 1 1 1 1 1 2 0 0.000000 3.086192
## 2: 1 1 1 1 2 1 0 3.086192 5.108223
## 3: 1 1 1 1 1 2 0 5.108223 16.289004
## 4: 1 1 1 1 2 1 0 16.289004 16.339959
## 5: 1 1 1 1 1 2 0 16.339959 19.802941
## 6: 1 1 1 1 2 1 0 19.802941 20.945194
The disease trajectory can be summarized with $sim_stateprobs().
ictstm$sim_stateprobs(t = c(0:10))
head(ictstm$stateprobs_)
## sample strategy_id grp_id state_id t prob
## 1: 1 1 1 1 0 1.000
## 2: 1 1 1 1 1 0.849
## 3: 1 1 1 1 2 0.772
## 4: 1 1 1 1 3 0.690
## 5: 1 1 1 1 4 0.644
## 6: 1 1 1 1 5 0.616
We can then compute costs and QALYs (using a discount rate of 3 percent).
# QALYs
ictstm$sim_qalys(dr = .03)
head(ictstm$qalys_)
## sample strategy_id grp_id state_id dr qalys lys
## 1: 1 1 1 1 0.03 8.1605070 9.761295
## 2: 1 1 1 2 0.03 1.8982012 2.123352
## 3: 1 2 1 1 0.03 8.2143181 9.825662
## 4: 1 2 1 2 0.03 0.9982393 1.116643
## 5: 2 1 1 1 0.03 3.4363922 9.710236
## 6: 2 1 1 2 0.03 2.2454015 2.245998
# Costs
ictstm$sim_costs(dr = .03)
head(ictstm$costs_)
## sample strategy_id grp_id state_id dr category costs
## 1: 1 1 1 1 0.03 drugs 48806.48
## 2: 1 1 1 2 0.03 drugs 10616.76
## 3: 1 2 1 1 0.03 drugs 98256.62
## 4: 1 2 1 2 0.03 drugs 11166.43
## 5: 2 1 1 1 0.03 drugs 48551.18
## 6: 2 1 1 2 0.03 drugs 11229.99
