# 3.6 PATIENT FLOW ------------------------------------------------------
# Now that we have all of the disease evidence and modeled outcomes available,
# we can compute the disease model. In the deterministic case, this will simply
# be a trace for both the PS and Markov models.
i$R_table_eff_data_settings <- data.table(i$R_table_eff_data_settings)
p$releff$excel_table <- i$R_table_eff_data_settingsEconomic modelling
This page runs the economic model.
Final pre-processing steps
A table with some settings is add to p.
View
p$releff$excel_table
kable(head(p$releff$excel_table))| Population | Population.name | Treatment.line | Molecule | Treatment.name | Include.in.this.analysis. | End.point | End.point.name | Effectiveness.data.source | Trial.name.if.effectiveness.source.is.trial | Origin.population | Origin.line | Origin.treatment | Origin.trial | Origin.endpoint | Curve.fit..for.survival.analysis. | HR.to.apply | HR.95..CI..LCL. | HR.95..CI..UCL. | Trial |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Poor/intermediate risk | 1 | 0 | nivolumab_monotherapy | No | 0 | Overall survival | 0 | 0 | 1 | 1 | 7 | 2 | 0 | Exponential | 0.000 | 0.0 | 0.000 | NA |
| 1 | Poor/intermediate risk | 1 | 1 | cabozantinib_plus_nivolumab | Yes | 0 | Overall survival | FP_NMA | 0 | 1 | 1 | 7 | 2 | 0 | Exponential | 0.000 | 0.0 | 0.000 | NA |
| 1 | Poor/intermediate risk | 1 | 2 | nivolumab_plus_ipilimumab | Yes | 0 | Overall survival | FP_NMA | 0 | 1 | 1 | 7 | 2 | 0 | Exponential | 0.000 | 0.0 | 0.000 | NA |
| 1 | Poor/intermediate risk | 1 | 3 | lenvatinib_plus_pembrolizumab | Yes | 0 | Overall survival | Apply HR to | 0 | 1 | 1 | 1 | 2 | 0 | NA | 1.134 | 0.8 | 1.619 | NA |
| 1 | Poor/intermediate risk | 1 | 4 | avelumab_plus_axitinib | No | 0 | Overall survival | PH_NMA | 0 | 1 | 1 | 7 | 2 | 0 | Exponential | 0.000 | 0.0 | 0.000 | NA |
| 1 | Poor/intermediate risk | 1 | 5 | pazopanib | Yes | 0 | Overall survival | Assume equal to | 0 | 1 | 1 | 7 | 2 | 0 | Exponential | 0.000 | 0.0 | 0.000 | NA |
The script also confirms that the specified model structure is a valid option (from i$dd_model_struct, and again a bit later from p$basic$structure).
View default model structure
i$dd_model_struct[1] "State transition"p$basic$structure[1] "State transition"The comments in the code provide some description of the modelling, which is a survival analysis using either a state transition (markov) model or partitioned state survival model.
if(!str_trim(i$dd_model_struct) %in% c("State transition", "Partitioned survival")) stop(
"The model structure is not one of the available options. These are 'State transition' and 'Partitioned survival'. Either code or the excel file are out of date or wrongly set up"
)
# The process of computing patient flow is as follows:
#
# - Create an empty object for housing the patient flow (a list)
# - Populate the trace with either disease modelling approach
# - Record metadata on the approach, as this determines what the trace looks like
# - Compute costs based on time in state
# - Compute QALYs based on time in state
# - Compute AEs based on time in state
# - Costs
# - QALYs
# - Return the populated pf list
#
pf <- list()
res <- list()
# 3.6.1 Run the model -----------------------------------------------------
# Running the model can mean two different structures, a markov model which
# we refer to as state transition or a partitioned survival approach. These
# both work using the same parameters object p. There is only one function
# to compute patient flow, f_pf_computePF. This takes several different arguments
# but the main one is p, or the parameters object to power the model with.
# Everything within f_pf_computePF uses objects which are within p, such that
# a copy of p could be saved as a file and as long as all functions have been
# defined and packages loaded the model can be run directly from there.
# The only structures allowed are state transition and partitioned survival. error
# if it is not one of those:
stopifnot(p$basic$structure %in% c("State transition","Partitioned survival"))This code then checks whether the decision problem is “cabozantinib plus nivolumab” - in which case, the first three populations are relevant, as the final three populations can’t receive this treatment.
View default decision problem
p$basic$decision_problem[1] "cabo+nivo"# Check the decision problem. If it's cabo+nivo only the first 3 overall
# populations are relevant as one cannot get cabo+nivo in pops 4-6
if(p$basic$decision_problem == "cabo+nivo") {
p$basic$pops_to_run <- 1:3
} else {
p$basic$pops_to_run <- NULL
}The objects p and i, which contain the parameters used to run the model, can be save as .rds files to make it easier to re-run the model.
# populate the pf object irrespective of model structure or overall populations
# to include.
#
# Note that if you put n_cores as NULL or 1 then the model will run in sequence.
# For QC, you can easily just save i and p as a file so all you need to do is
# load libraries to repeat the results and QC things:
saveRDS(p, file.path(s_path,"standalone scripts/QC/p.rds"))
saveRDS(i, file.path(s_path, "standalone scripts/QC/i.rds"))
#
# If you run the model using scenario 1 (rather than base case scenario 0)
# It will be a partitioned survival model. in that case it's a good idea to
# save a backup of p and i under a different name so that you have an input
# set for the paritioned survival model to hand at any time.
#
# saveRDS(p,"./2_Scripts/standalone scripts/QC/p_PS.rds")
# saveRDS(i,"./2_Scripts/standalone scripts/QC/i_PS.rds")
# p <- readRDS("./2_Scripts/standalone scripts/QC/p.rds")
# i <- readRDS("./2_Scripts/standalone scripts/QC/i.rds")Run the model
The survival analysis run using f_pf_computePF(). This function can take a while to run. For the purposes of this walkthrough, the code has been modified using if(FALSE){} to prevent the function from running and, instead, a set of pre-run model results are loaded.
Further info about pre-run model results
The model result file is very large and, as such, cannot be easily synced with GitHub. Therefore, in order to run this script on a new machine (as described in the walkthrough README), you will need to run Model_Structure.R (or the walkthrough .qmd file) to generate the file.
The function f_pf_compute_PF() will use either:
f_pf_computePF_mk()(if state transition model, i.e. Markov model)f_pf_computePF_ps()(if partitioned survival model)
The purpose of this is to model how patients move through different health states/treatments, from which we can find outputs like costs and utilities.
State transition model. Steps include:
- Getting relevant population data and creating
sequence_listwith the allowed treatment sequences for a given population - Creating
util_gpop_mat- a matrix of health state utility values that account for ageing - Transition probabilities (
TPs) are calculated for each sequence, then used to construct Markov traces (TRACE) (ie. matrix of state vectors across all model cycles) - These are used to calculate costs through the treatment sequence (
pf_costs) (e.g. cost per cyclecpc, costs on initiationcoi, and costs on deathcod), QALYspf_qalys) and adverse events (pf_ae)
Partitioned survival model. Steps include:
- Getting relevant population data and creating the utility matrix
util_gpop_mat - Using
f_pf_partSA_state_res(), simulates patient states (e.g. PFS) across time horizon for each treatment sequence, returns the costs (costs) and QALYs (qalys)
# Make this NA to run single core:
if(FALSE){
tick <- Sys.time()
pf <- f_pf_computePF(
p = p,
struct = p$basic$structure,
verbose = FALSE,
plots = FALSE,
just_pop = p$basic$pops_to_run,
just_nlines = NULL,
just_seq = NULL
)
print(Sys.time() - tick)
}
# if (is.na(keep_free_cores)) {
# plan(sequential)
# } else {
# plan(multisession(workers = max(availableCores()-keep_free_cores,1)))
# }
# Save result
# computepf_file = file.path(d_path, "computepf_example.rds")
# saveRDS(pf, file=computepf_file)
# Load result
computepf_file = file.path(d_path, "computepf_example.rds")
pf <- readRDS(computepf_file)Analyse the model results
The model results are compiled using f_res_compute_results() which will then use either:
f_res_compute_results_mk()for the state transition modelf_res_compute_results_ps()for the partitioned survival model
These each in turn utilities various other functions to summarise the model results. There are various functions, depending on the level of detail desired in the plots. This is set to either 4 or 5, depending on whether it is scenario 0.
The summary functions include:
f_pf_mk_summary()to getundiscanddiscresults (undiscounted and discounted)f_res_mk_incremental()to getincrementalf_res_wa_model()to getweighted_modeldiscounted or undiscounted, summarised usingf_res_sum_weighted_model()f_pf_wa_sr_plots()to getweighted_trace_plots
And more! As summarised in code comments below, the outcomes of this from each detail level are:
- Top line results by sequence and weighted average results (costs, QALYs, LYs)
- Include incremental analysis (from
f_res_mk_incremental()) - Include weighted average pairwise comparisons
- Include incremental analysis by sequence
- Include trace plots
Except for the partitioned survival, 4 is breakdown tables and 4 is state residency plots.
# 3.6.2 Compiling model results -------------------------------------------
# Depending on which model structure is used to compute patient flow, the results
# are processed in different ways. The below function simply routes the pf object
# to the appropriate function to process the results, and returns an object
# res containing the results:
Scenario_number <- i$R_Scenario_num
if(Scenario_number == 0) {detail_level <- 5} else {detail_level <- 4}
# Detail level guide:
# State transition
# 1 is top line results by sequence (costs, QALYs, LYs) and weighted average results
# 2 is just the top line table and non-dominated weighted average incremental results
# 3 includes weighted average pairwise comparisons
# 4 includes incremental analysis by sequence
# 5 includes trace plots
# PartSA analysis
# 1 is top line results for the PartSA analysis (costs, QALYs, LYs)
# 2 is incremental analysis as well
# 3 includes breakdown tables as well
# 4 includes state residency plots
res <- f_res_compute_results(
pf = pf,
structure = p$basic$structure,
p = p,
detail_level = detail_level,
vs_mol = 1,
no_active_lines = i$R_max_trt_lines
)
View
res
A few examples of results from res are shown below…
kable(head(res$undisc$pop_1$ly$breakdown, 3))| trt_n | trt | L1_on | L1_off | BSC | L2_on | L2_off | L3_on | L3_off | L4_on | L4_off |
|---|---|---|---|---|---|---|---|---|---|---|
| 1→999 | Cabozantinib plus nivolumab→Placebo / BSC | 1.945363 | 0.1088617 | 0.3625033 | NA | NA | NA | NA | NA | NA |
| 5→999 | Pazopanib→Placebo / BSC | 1.144445 | 0.1148029 | 0.3673995 | NA | NA | NA | NA | NA | NA |
| 7→999 | Sunitinib→Placebo / BSC | 1.144445 | 0.1148029 | 0.3673995 | NA | NA | NA | NA | NA | NA |
kable(head(res$incremental$pop_1$expanded_results, 3))| trt_n | trt | costs | qalys | ly | L1 | str_dom | extdom | ic | iq | il | ICER | r |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7→999 | Sunitinib→Placebo / BSC | 22826.06 | 1.085297 | 1.626648 | 7|999 | FALSE | FALSE | 0.000 | 0.0000000 | 0.000000 | 0.00 | 1 |
| 5→999 | Pazopanib→Placebo / BSC | 24690.10 | 1.085678 | 1.626648 | 5|999 | FALSE | TRUE | NA | NA | NA | NA | 2 |
| 7→10→999 | Sunitinib→Everolimus→Placebo / BSC | 31562.18 | 1.399302 | 2.169939 | 7|10|999 | FALSE | FALSE | 8736.118 | 0.3140051 | 0.543291 | 27821.58 | 3 |
res$weighted_trace_plots$pop_1$plots$L1_1
res$wa_summarised$pop_1$costs[1] 268538.83 80398.95 100004.76 77049.92res$pairwise_vs_mol$pop_1$qalys[1] 2.253814 1.712196 1.674692 1.684174Severity modifier
A severity modifier is implemented for the state transition model (and not for the partitioned survival model). These are used to weight QALYs for conditions with a high degree of severity.
The result of this section is res$mk$qaly_shortfall_1_to_3 which is a list of three lists, each containing the QALY adjustments for each population.
# 3.6.3 Calculate severity modifier -----------------------------------
# The severity modifier for the weighted average first-line treatment comparison
# uses the best available treatment which is not nivo cabo (molecule 1) for the
# first 3 populations.
#
# This is because this is the best (i.e. most discounted QALYs) available 1L trt
# pathway set.
#
# Calculation is only provided for the state transition model
if (p$basic$structure == "State transition") {
population_numbers <- if(sum(p$basic$pops_to_run == 1:3)>0){1:3} else{1:6}
res$mk$qaly_shortfall_1_to_3 <- lapply(population_numbers, function(npa_pop) {
lu_pop <- p$basic$lookup$pop_map
lu_rpop <- p$basic$lookup$ipd$pop
# npa_pop is overall population, we need to look up risk population from it:
risk_pop_n <- lu_pop[match(npa_pop,lu_pop$Overall.population.number),]$Risk.population.number
risk_pop <- lu_rpop[match(risk_pop_n,lu_rpop$Number),]$Description
i$R_table_ptchar <- as.data.table(i$R_table_ptchar)
if (i$dd_age_sex_source == "Mean") {
# So for this risk population, we need the baseline characteristics:
bl_chars <- i$R_table_ptchar[Population == risk_pop & Treatment.line == 1,]
bl_age <- bl_chars$Starting.age..years..Mean
bl_male <- 1-bl_chars$Starting...female.Mean
} else {
patient_sex_age_IPD <- as.data.table(i$R_table_patientagesex)
patient_sex_age_IPD$Gender <- replace(patient_sex_age_IPD$Gender, patient_sex_age_IPD$Gender=="M","male")
patient_sex_age_IPD$Gender <- replace(patient_sex_age_IPD$Gender, patient_sex_age_IPD$Gender=="F","female")
bl_age <- patient_sex_age_IPD[Line ==1]$Age
bl_male <- patient_sex_age_IPD[Line ==1]$Gender
}
pna_txt <- names(res$wa_summarised)[npa_pop]
tab <- res$wa_summarised[[pna_txt]][L1 != 1,]
met <- tab[which.max(qalys),]
q_met <- met$qalys
comp_no_met <- met$L1
out <- calc_severity_modifier(
age = bl_age,
sex = bl_male,
.patient_level = if(i$dd_age_sex_source == "Mean") {FALSE} else {TRUE},
qalys = q_met,
.i = i,
.p = p
)
out <- cbind(out, SOC = comp_no_met)
return(out)
})
}
How is the severity modifier calculated?
There are first a few processing steps before the function to calculate severity, calc_severity_modifier(). Looking at an example of npa_pop=1, we start with getting the look-up for the population and the population mappings.
npa_pop = 1
lu_pop <- p$basic$lookup$pop_map
lu_rpop <- p$basic$lookup$ipd$pop
lu_poplu_rpopThe risk population can then be identified - in this case “0” or “All risk”.
# npa_pop is overall population, we need to look up risk population from it:
risk_pop_n <- lu_pop[match(npa_pop,lu_pop$Overall.population.number),]$Risk.population.number
risk_pop <- lu_rpop[match(risk_pop_n,lu_rpop$Number),]$Description
risk_pop_n[1] 0risk_pop[1] "All"The patient characteristics table from excel is converted into a data table (if not already).
i$R_table_ptchar <- as.data.table(i$R_table_ptchar)
kable(head(i$R_table_ptchar))| Population | Treatment.line | Starting.age..years..Mean | Starting…female.Mean | Starting…PorI.risk.Mean | Body.weight..kg..Mean | Prior.IO…in.12.months.Mean | Starting.age..years..n | Starting…female.n | Starting…PorI.risk.n | Body.weight..kg..n | Starting…PIR.n | Prior.IO…in.12.months.n | Starting.age..years..SE | Starting…female.SE | Starting…PorI.risk.SE | Body.weight..kg..SE | Prior.IO…in.12.months.SE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| All | 1 | 64.40 | 0.2903715 | 0.7755725 | 83.38000 | 0 | 1311 | 1319 | 1310 | 114 | 1310 | 1319 | 0.2856284 | 0.0124989 | 0.0115269 | 1.686593 | 0 |
| Poor / intermediate risk | 1 | 64.20 | 0.2952756 | 1.0000000 | 81.26353 | 0 | 1011 | 1016 | 0 | 114 | 0 | 1319 | 0.3273973 | 0.0143112 | 0.0000000 | 1.686593 | 0 |
| Favourable risk | 1 | 65.40 | 0.2653061 | 0.0000000 | 90.98037 | 0 | 293 | 294 | 0 | 114 | 0 | 1319 | 0.5596696 | 0.0257486 | 0.0000000 | 1.686593 | 0 |
| All | 2 | 63.04 | 0.2848101 | 0.0000000 | 83.38000 | 0 | NA | NA | NA | NA | NA | NA | 0.4186000 | 0.0179527 | 0.0000000 | 1.686593 | 0 |
| All | 3 | 62.62 | 0.2850467 | 0.0000000 | 83.38000 | 0 | NA | NA | NA | NA | NA | NA | 0.7288700 | 0.0308596 | 0.0000000 | 1.686593 | 0 |
| All | 4 | 62.37 | 0.2962963 | 0.0000000 | 83.38000 | 0 | NA | NA | NA | NA | NA | NA | 1.2498500 | 0.0621386 | 0.0000000 | 1.686593 | 0 |
With our source of IPD (as from i$dd_age_sex_source), this code then created lists with the ages and genders of each person in the IPD.
patient_sex_age_IPD <- as.data.table(i$R_table_patientagesex)
patient_sex_age_IPD$Gender <- replace(patient_sex_age_IPD$Gender, patient_sex_age_IPD$Gender=="M","male")
patient_sex_age_IPD$Gender <- replace(patient_sex_age_IPD$Gender, patient_sex_age_IPD$Gender=="F","female")
bl_age <- patient_sex_age_IPD[Line ==1]$Age
bl_male <- patient_sex_age_IPD[Line ==1]$Gender
head(bl_age)[1] 46.36414 74.09583 55.18070 69.14784 78.15880 79.32854head(bl_male)[1] "male" "male" "female" "male" "male" "male" The name of the population is created based on npa_pop.
pna_txt <- names(res$wa_summarised)[npa_pop]
pna_txt[1] "pop_1"The economic model results for that population are identified for treatments except L1 treatment of molecule 1.
tab <- res$wa_summarised[[pna_txt]][L1 != 1,]
kable(tab)| L1 | costs | qalys | ly |
|---|---|---|---|
| 5 | 80398.95 | 1.712196 | 2.836778 |
| 6 | 100004.76 | 1.674692 | 2.764879 |
| 7 | 77049.92 | 1.684174 | 2.780869 |
From that, the treatment with the maximum QALYs is identified, and the QALYs and treatment were extracted
met <- tab[which.max(qalys),]
q_met <- met$qalys
comp_no_met <- met$L1
kable(met)| L1 | costs | qalys | ly |
|---|---|---|---|
| 5 | 80398.95 | 1.712196 | 2.836778 |
These results were then used in the function calc_severity_modifier(). That function uses get_severity_modifier() to find the appropriate severity modifier according to the discounted QALYs for those with the condition and those without.
This was repeated for the three populations, generating three results lists, which have been combined into the table below:
# The three lists of results, combined into a single table
kable(bind_rows(res$mk$qaly_shortfall_1_to_3))| qaly_soc | qaly_gpop | abs_sf | prop_sf | modifier | SOC |
|---|---|---|---|---|---|
| 1.712196 | 10.38197 | 8.669771 | 0.8350798 | 1 | 5 |
| 2.243521 | 10.38197 | 8.138445 | 0.7839021 | 1 | 5 |
| 2.013113 | 10.38197 | 8.368854 | 0.8060952 | 1 | 3 |
Save the results
This code chunks saves the res list as an .rds file, although that has been disabled for the purpose of this walkthrough.
# 3.6.4 Saving the results ------------------------------------------------------
# the results are in list format so should be saved as an R list file (.rds)
# The naming of the file should reflect the model structure used. The file
# produced has a time stamp to avoid overwriting previous results files.
if(FALSE){
Scenario_name <- i$R_Scenario_name # Use ST for state transition, PS for Partitioned survival, LP for list price, cPAS for cPAS
Scenario_number <- i$R_Scenario_num
Run_date <- date()
if (p$basic$structure == "State transition") {
saveRDS(res, file.path(o_path, paste0(
"ST_Scenario ", Scenario_number,"_",i$dd_drug_price_options,gsub(":","_",Run_date),".rds")))
} else {
saveRDS(res, file.path(o_path, paste0(
"PartSA_Scenario ",Scenario_number,"_",i$dd_drug_price_options,gsub(":","_",Run_date),".rds")))
}
}Creating the report
The function f_res_ProduceWordDoc() produces a word document report. Depending on p$basic$structure, will either use f_res_ProduceWordDoc_ST() (st - state transition) or f_res_ProduceWordDoc_PS() (ps - partitioned survival) to produce the report content. This applies results tables specific to the cabo+nivo population to the word document, in the format required by NICE.
This report is explored in detail on the Report page.
# 3.6.5 Outputting results to Word ------------------------------------------------------
# Outputting the results to word requires a series of functions to produce component
# parts to go in the report, and then consolidating them all into the requested output.
# Get the functions to produce the word document output:
# Produce an automatically generated word document with required results tables
# and automatically name it using the variables that are already inside of
# i and p (including structure, which is located in p$basic$structure. Note
# that this comes from i$dd_model_struct, i.e. named range dd_model_struct from excel.
# please ensure that this is updated for PS model scenarios):
Word_width_inches <- 29.7*0.3937
Run_date <- date()
f_res_ProduceWordDoc(
p = p,
res = res,
Scenario_name = i$R_Scenario_name,
Scenario_number = i$R_Scenario_num,
price_options = i$dd_drug_price_options,
Run_date = Run_date,
word_template_location = file.path(f_path, "reporting/empty results doc.docx"),
Word_width_inches = 29.7*0.3937,
auto_save = FALSE,
verbose = TRUE
)[0;32mWord output for Base case. (scen #0): [0m
[0;31mWord output for Base case. (scen #0): LY breakdown[0m
[0;33mWord output for Base case. (scen #0): QALY breakdown[0m
[0;34mWord output for Base case. (scen #0): Cost breakdown[0m
[0;35mWord output for Base case. (scen #0): Scenario tables[0m
[0;36mWord output for Base case. (scen #0): Severity modifier[0m
[0;37mWord output for Base case. (scen #0): Pairwise results[0m
[0;40mWord output for Base case. (scen #0): Generating word document from results...[0m
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$L1_6rdocx document with 147 element(s)
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1 NA NA NA paragraphFuture plans
The final section of code outlines some of the future plans for this model.
# END OF CODE -------------------------------------------------------
#### Additional changes were originally planned during Phase 2 of this pilot following use for the initial decision problem including
# - Addition of Shiny user interface
# - Genericisation of the code to allow wider use
# - Programming and analysis of model outputs related specifically to sequencing, this may include value of information analyses
# Unfortunately funding for this has not been confirmed currently.
# If you are interested in discussing or funding further development please contact the PenTAG team at pentag@exeter.ac.uk