hesim
This article provides an overview of the hesim
package and a quick example. The other articles provide more in depth examples.
hesim
supports three types of health economic models: (i) cohort discrete time state transition models (cDTSTMs), (ii) Nstate partitioned survival models (PSMs), and (iii) individuallevel continuous time state transition models (iCTSTMs). cDTSTMs are Markov cohort models and can be timehomogeneous or timeinhomogeneous. iCTSTMs are individuallevel simulations that can encompass both Markov and semiMarkov processes. All models are implemented as R6 classes and have methods for simulating disease progression, QALYs, and costs.
Economic model  R6 class 

Nstate partitioned survival model (PSM) 
hesim::Psm

Cohort discrete time state transition model (cDTSTM) 
hesim::CohortDtstm

Individuallevel continuous time state transition model (iCTSTM) 
hesim::IndivCtstm

Each economic model consists of submodels for disease progression, utility, and costs (usually for multiple cost categories). As shown in the figure, a typical analysis proceeds in a 3steps:
The entire analysis is inherently Bayesian, as uncertainty in the parameters from the statistical models is propagated throughout the economic model and decision analysis with probabilistic sensitivity analysis (PSA). Furthermore, since the statistical and economic models are integrated, patient heterogeneity can be easily introduced with patient level covariates.
Before beginning an analysis, it is necessary to define the treatment strategies of interest, the target population, and the model structure. This can be done in hesim
by creating a hesim_data
object with the function hesim_data()
. Integer valued identification (ID) variables are used to uniquely identify strategies (strategy_id
), patients (patient_id
), nondeath healthstates (state_id
), and (if applicable) healthstate transitions (transition_id
). Subgroups can optionally be identified with grp_id
.
Let’s consider an example where we use an iCTSTM to evaluate two competing treatment strategies, the standard of care (SOC) and a New treatment. We will consider a generic model of disease progression with three health states (stage 1, stage 2, and death) with four transitions (stage 1 > stage 2, stage 2 > stage 1, stage 1 > death, and stage 2 > death). Since we are using an individuallevel model, we must simulate a target population that is sufficiently large so that uncertainty reflects uncertainty in the model parameters, rather than variability across simulated individuals. For the sake of illustration, we will create subgroups stratified by sex.
library("hesim")
library("data.table")
# Treatment strategies
strategies < data.table(strategy_id = c(1, 2),
strategy_name = c("SOC", "New"))
# Patients
n_patients < 1000
patients < data.table(patient_id = 1:n_patients,
age = rnorm(n_patients, mean = 45, sd = 7),
female = rbinom(n_patients, size = 1, prob = .51))
patients[, grp_id := ifelse(female == 1, 1, 2)]
patients[, grp_name := ifelse(female == 1, "Female", "Male")]
# (Nondeath) health states
states < data.table(state_id = c(1, 2),
state_name = c("Stage 1", "Stage 2"))
# Transitions
tmat < rbind(c(NA, 1, 2),
c(3, NA, 4),
c(NA, NA, NA))
colnames(tmat) < rownames(tmat) < c("Stage 1", "Stage 2", "Death")
transitions < create_trans_dt(tmat)
transitions[, trans := factor(transition_id)]
# Combining
hesim_dat < hesim_data(strategies = strategies,
patients = patients,
states = states,
transitions = transitions)
print(hesim_dat)
## $strategies
## strategy_id strategy_name
## 1: 1 SOC
## 2: 2 New
##
## $patients
## patient_id age female grp_id grp_name
## 1: 1 52.48267 1 1 Female
## 2: 2 48.72248 0 2 Male
## 3: 3 41.00760 1 1 Female
## 4: 4 44.27358 0 2 Male
## 5: 5 37.84868 1 1 Female
## 
## 996: 996 45.33566 0 2 Male
## 997: 997 41.75346 1 1 Female
## 998: 998 40.94714 0 2 Male
## 999: 999 46.93467 1 1 Female
## 1000: 1000 53.92943 0 2 Male
##
## $states
## state_id state_name
## 1: 1 Stage 1
## 2: 2 Stage 2
##
## $transitions
## transition_id from to from_name to_name trans
## 1: 1 1 2 Stage 1 Stage 2 1
## 2: 2 1 3 Stage 1 Death 2
## 3: 3 2 1 Stage 2 Stage 1 3
## 4: 4 2 3 Stage 2 Death 4
##
## attr(,"class")
## [1] "hesim_data"
When presenting results, it may be preferable to have more informative labels that the ID variables. These can be generated from a hesim_data
object using get_labels()
.
## $strategy_id
## SOC New
## 1 2
##
## $grp_id
## Female Male
## 1 2
##
## $state_id
## Stage 1 Stage 2 Death
## 1 2 3
Each submodel contains fields for the model parameters and the input data. Models can be parameterized by either fitting statistical models using R
, inputting values directly, or from a combination of the two. There are two types of parameter objects, standard parameter objects prefixed by “params” and “transformed” parameter objects prefixed by “tparams”. The former contain the underlying parameters of a statistical model and are used alongside the input data to make predictions. The latter contain parameters more immediate to prediction that have already been transformed as function of the input data. The regression coefficients of a logistic regression are an example of a parameter objects while the predicted probabilities are examples of a transformed parameter object.
As shown in the table below, the statistical model used to parameterize the disease model varies by the type of economic model. For example, multinomial logistic regressions can be used to parameterize a cDTSTM, a set of N1 independent survival models are used to parameterize an Nstate partitioned survival model, and multistate models can be used to parameterize an iCTSTM.
Economic model (R6 class)  Statistical model  Parameter object  Model object 

hesim::CohortDtstm

Custom 
hesim::tparams_transprobs

msm::msm

Multinomial logistic regressions 
hesim::params_mlogit_list

hesim::multinom_list


hesim::Psm

Independent survival models 
hesim::params_surv_list

hesim::flexsurvreg_list

hesim::IndivCtstm

Multistate model (joint likelihood) 
hesim::params_surv

flexsurv::flexsurvreg

Multistate model (transitionspecific) 
hesim::params_surv_list

hesim::flexsurvreg_list

The parameters of a survival model are stored in a params_surv
object and a params_surv_list
can be used to store the parameters of multiple survival models. The latter is useful for storing the parameters of a multistate model or the independent survival models required for a PSM. The parameters of a multinomial logistic regression are stored in a params_mlogit
object and can be created by fitting a model for each row in a transition probability matrix with nnet::multinom()
. tparams_transprobs
objects are examples of transformed parameter objects that store transition probability matrices. They can be predicted from a fitted multistate model using the msm
package or constructed “by hand” in a custom manner.
We illustrate an example of a statistical model of disease progression fit with R
by estimating a multistate model with a joint likelihood using flexsurv::flexsurvreg()
.
State values (i.e., utilities and costs) do not depend on the choice of disease model. They can currently either be modeled using a linear model or with predicted means.
Statistical model  Parameter object  Model object 

Predicted means 
hesim::tparams_mean

hesim::stateval_tbl

Linear model 
hesim::params_lm

stats::lm

The most straightforward way to construct state values is with stateval_tbl()
, which creates a special object used to assign values (i.e. predicted means) to health states that can vary across PSA samples, treatment strategies, patients, and/or time intervals. State values can be specified either as moments (e.g., mean and standard error) or parameters (e.g., shape and scale of gamma distribution) of a probability distribution, or by presimulating values from a suitable probability distribution (e.g., from a Bayesian model). Here we will use stateval_tbl
objects for utility and two cost categories (drug and medical).
# Utility
utility_tbl < stateval_tbl(
data.table(state_id = states$state_id,
mean = mstate3_exdata$utility$mean,
se = mstate3_exdata$utility$se),
dist = "beta"
)
# Costs
drugcost_tbl < stateval_tbl(
data.table(strategy_id = strategies$strategy_id,
est = mstate3_exdata$costs$drugs$costs),
dist = "fixed"
)
medcost_tbl < stateval_tbl(
data.table(state_id = states$state_id,
mean = mstate3_exdata$costs$medical$mean,
se = mstate3_exdata$costs$medical$se),
dist = "gamma"
)
## state_id mean se
## 1: 1 0.65 0.1732051
## 2: 2 0.85 0.2000000
## strategy_id est
## 1: 1 5000
## 2: 2 10000
## state_id mean se
## 1: 1 1000 10.95445
## 2: 2 1600 14.14214
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.
Economic model  Disease model  Utility model  Cost model(s) 

hesim::CohortDtstm

hesim::CohortDtstmTrans

hesim::StateVals

hesim::StateVals

hesim::Psm

hesim::PsmCurves

hesim::StateVals

hesim::StateVals

hesim::IndivCtstm

hesim::IndivCtstmTrans

hesim::StateVals

hesim::StateVals

The submodels are constructed from (i) parameter or model objects and (ii) input data (if a transformed parameter object is not used). They can be instantiated using S3
generic methods prefixed by “create
” or with the R6
constructor method $new()
. We illustrate use of the former below.
In all cases, it is necessary to specify the number of parameter samples to use for the PSA.
The disease model is constructed as a function of the fitted multistate model (using the stored regression coefficients) and input data. The input data must be an object of class expanded_hesim_data
, which is a data.table
containing the covariates for the statistical model. In our multistate model, each row is a unique treatment strategy, patient, and healthstate transition.
An expanded_hesim_data
object can be created by expanding an object of class hesim_data
using expand.hesim_data()
.
transmod_data < expand(hesim_dat,
by = c("strategies", "patients", "transitions"))
head(transmod_data)
## strategy_id patient_id transition_id strategy_name age female grp_id
## 1: 1 1 1 SOC 52.48267 1 1
## 2: 1 1 2 SOC 52.48267 1 1
## 3: 1 1 3 SOC 52.48267 1 1
## 4: 1 1 4 SOC 52.48267 1 1
## 5: 1 2 1 SOC 48.72248 0 2
## 6: 1 2 2 SOC 48.72248 0 2
## grp_name from to from_name to_name trans
## 1: Female 1 2 Stage 1 Stage 2 1
## 2: Female 1 3 Stage 1 Death 2
## 3: Female 2 1 Stage 2 Stage 1 3
## 4: Female 2 3 Stage 2 Death 4
## 5: Male 1 2 Stage 1 Stage 2 1
## 6: Male 1 3 Stage 1 Death 2
The disease model is instantiated using the create_IndivCtstmTrans()
generic method. Parameters for the PSA are, by default, drawn from the multivariate normal distribution of the maximum likelihood estimate of the regression coefficients, although we make this explicit with the uncertainty argument.
transmod < create_IndivCtstmTrans(fit_wei, transmod_data,
trans_mat = tmat, n = n_samples,
uncertainty = "normal")
class(transmod)
## [1] "IndivCtstmTrans" "CtstmTrans" "R6"
Since we are using predicted means for utilities and costs, we do not need to specify input data. Instead, we can construct the utility and cost models directly from the stateval_tbl
objects.
# Utility
utilitymod < create_StateVals(utility_tbl, n = n_samples, hesim_data = hesim_dat)
# Costs
drugcostmod < create_StateVals(drugcost_tbl, n = n_samples, hesim_data = hesim_dat)
medcostmod < create_StateVals(medcost_tbl, n = n_samples, hesim_data = hesim_dat)
costmods < list(drugs = drugcostmod,
medical = medcostmod)
Each economic model contains methods (i.e., functions) for simulating disease progression, QALYs, and costs.
Economic model (R6 class)  Disease progression  QALYs  Costs 

hesim::CohortDtstm

$sim_stateprobs()  $sim_qalys()  $sim_costs() 
hesim::Psm

$sim_survival() and $sim_stateprobs()  $sim_qalys()  $sim_costs() 
hesim::IndivCtstm

$sim_disease() and $sim_stateprobs()  $sim_qalys()  $sim_costs() 
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 individuallevel simulation is advantageous because it can be used for semiMarkov processes where transition rates depend on time since entering a health state (rather than time since the start of the model).
The utility and cost models always simulate QALYs and costs from the simulated progression of disease with the methods $sim_qalys()
and $sim_costs()
, respectively. In the cohort models, QALYs and costs are computed as a function of the state probabilities whereas in individuallevel models they are based on the simulated individual trajectories. Like the disease model, the individuallevel simulation is more flexible because QALYs and costs can depend on time since entering the health state.
We illustrate with the iCTSTM. The first step is to simulate disease progression for each patient.
## sample strategy_id patient_id grp_id from to final time_start time_stop
## 1: 1 1 1 1 1 2 0 0.0000000 5.5926021
## 2: 1 1 1 1 2 1 0 5.5926021 11.0755831
## 3: 1 1 1 1 1 2 0 11.0755831 23.0101684
## 4: 1 1 1 1 2 3 1 23.0101684 25.9967803
## 5: 1 1 2 2 1 2 0 0.0000000 0.5628722
## 6: 1 1 2 2 2 1 0 0.5628722 1.9488058
The disease trajectory is summarized with $sim_stateprobs()
.
## sample strategy_id grp_id state_id t prob
## 1: 1 1 1 1 0 0.541
## 2: 1 1 1 1 1 0.452
## 3: 1 1 1 1 2 0.390
## 4: 1 1 1 1 3 0.362
## 5: 1 1 1 1 4 0.331
## 6: 1 1 1 1 5 0.303
Finally, we compute QALYs and costs (using a discount rate of 3 percent).
## sample strategy_id grp_id state_id dr qalys lys
## 1: 1 1 1 1 0.03 1.3231834 4.6109578
## 2: 1 1 1 2 0.03 0.5793097 1.0081329
## 3: 1 1 2 1 0.03 1.1782761 4.1059927
## 4: 1 1 2 2 0.03 0.5821319 1.0130442
## 5: 1 2 1 1 0.03 1.3799400 4.8087399
## 6: 1 2 1 2 0.03 0.4119457 0.7168808
## sample strategy_id grp_id state_id dr category costs
## 1: 1 1 1 1 0.03 drugs 23054.789
## 2: 1 1 1 2 0.03 drugs 5040.665
## 3: 1 1 2 1 0.03 drugs 20529.964
## 4: 1 1 2 2 0.03 drugs 5065.221
## 5: 1 2 1 1 0.03 drugs 48087.399
## 6: 1 2 1 2 0.03 drugs 7168.808
Once output has been simulated with an economic model, a decision analysis can be performed. CEAs can be conducted using other R
packages such as BCEA or directly with hesim
.
To perform a CEA, simulated QALYs and costs are summarized and a ce
object is created, which contains mean QALYs and costs for each sample from the PSA by treatment strategy. QALYs and costs can either be summarized by subgroup (by_grp = TRUE
) or aggregated across all patients (by_grp = FALSE
).
## $costs
## category dr sample strategy_id costs grp_id
## 1: drugs 0.03 1 1 53690.64 1
## 2: drugs 0.03 1 2 106765.41 1
## 3: drugs 0.03 2 1 57245.18 1
## 4: drugs 0.03 2 2 105605.45 1
## 5: drugs 0.03 3 1 54308.02 1
## 
## 5996: total 0.03 998 2 123983.61 1
## 5997: total 0.03 999 1 64882.46 1
## 5998: total 0.03 999 2 120279.42 1
## 5999: total 0.03 1000 1 61244.38 1
## 6000: total 0.03 1000 2 111419.59 1
##
## $qalys
## dr sample strategy_id qalys grp_id
## 1: 0.03 1 1 3.662901 1
## 2: 0.03 1 2 3.482167 1
## 3: 0.03 2 1 7.894164 1
## 4: 0.03 2 2 7.132230 1
## 5: 0.03 3 1 5.476550 1
## 
## 1996: 0.03 998 2 9.744932 1
## 1997: 0.03 999 1 7.286610 1
## 1998: 0.03 999 2 7.432333 1
## 1999: 0.03 1000 1 8.607339 1
## 2000: 0.03 1000 2 8.561227 1
##
## attr(,"class")
## [1] "ce"
The functions cea()
and cea_pw()
are used to perform a CEA. The former simultaneously accounts for all treatment strategies while the latter makes pairwise comparisons between interventions and a chosen comparator.
cea_out < cea(ce, dr_qalys = .03, dr_costs = .03)
cea_pw_out < cea_pw(ce, dr_qalys = .03, dr_costs = .03, comparator = 1)
Summary and plotting functions are available to analyze the output. For instance, we can use plot_ceac()
to quickly plot a costeffectiveness acceptability curve (CEAC), which displays the probability that each treatment strategy is the most costeffective at a given willingness to pay for a QALY. The labels we constructed earlier are used to give the treatment strategies informative names.
This article provided an overview of the hesim
package. We recommend exploring the examples in the other articles to learn more.
cDTSTMs (i.e., Markov cohort models) are probably the most commonly used models in health economics and there are examples demonstrating multiple ways to build them with hesim
. One approach that has not yet been discussed is a functional one that allows users to define a model (with define_model()
) in terms of expressions that transform underlying parameter draws from a PSA into relevant transformed parameters (e.g., transition probability matrices, mean state values) as a function of input data.
Other relevant topics include more through treatments of CEA, multistate modeling, individuallevel simulations based on aggregate data, and partitioned survival analysis. As the examples illustrate, any analysis can be performed either for a single group or in the context of multiple subgroups.