Date: 2025-06-16

# Tabular Input

#### 2025-06-16

In most of the `heemod` vignettes models are defined through `R` code. But models with large numbers of states and transition probabilities might be unwieldy to input at the keyboard, and could be conveniently specified by file inputs.

This vignette demonstrates how to make and use files to input models to `heemod`. The files can then be used to run a suite of analyses (including deterministic and probabilistic sensitivity analyses, acceptability curve calculation, etc.) and optionally save results to a folder.

## Introduction

The inputs for state definition, transition matrices, model options, etc. (referenced as tabular inputs) must be provided via `csv`, `xls` or `xlsx` files.1 Columns starting by `.comment` are ignored, as well as blank rows.

These inputs must be provided in separate files. The path to these files is specified in a reference file, that acts as an ‘umbrella’ file atop of the other inputs. The reference file default name is `REFERENCE.csv`.

Warning for users of the `xls` format:
The `xls` files are read with the `readxl` package. As of version 0.1.1 if a column contains strings and numeric values the numeric values are rounded to 6 decimal places. We therefore recommend to use solely the `csv` or `xlsx` format.

## Reference file

This file contains two mandatory columns `data` and `file`, as well as optional columns with comments, which will be ignored. The `data` column must contain the following keywords:

1. `state`: file containing model states.
2. `tm`: file containing transition probabilities.
3. `parameters`: file containing model parameters.

Optionally, the following rows can be provided:

4. `options`: file specifying model options.
5. `demographics`: file describing of the population to run the models on.
6. `data`: a directory containing additional tables to be loaded; these can be `.csv`, `.xls` or `.xlsx`.
7. `output`: a directory to save the output graphics.
8. `source`: a directory in which `R` source files used in the analysis can be placed, and will be sourced when the model is run. The global environment is not modified.

data | file
--- | ---
state | THR_states.csv
tm | THR_transition_probs.csv
parameters | THR_parameters.csv
demographics | THR_demographic_table.csv
data | input_dataframes
output | output
options | THR_options.csv

All the files and directories must be in the reference file directory. Files or directories located elsewhere must be given by absolute path and marked by a `TRUE` value in an optional `absolute_path` column.

## States file

A state file contains 2 mandatory columns: `.model` and `.state`, corresponding to strategy and state names respectively. The other columns correspond to the state values.

Discounting rates can be specified in `.discount.*` columns, where `*` stands for the name of the value to discount. Values are always discounted at the same rate in all states.2

Values specified for only one strategy will be carried over to others. Only values that differ from one strategy to another must be specified separately for each strategy.

.model | .state | cost | qaly | .discount.qaly
--- | --- | --- | --- | ---
standard | PrimaryTHR | 0 | 0.00 | 0.015
standard | SuccessfulPrimary | 0 | 0.85 |
standard | RevisionTHR | 5294 | 0.30 |
standard | SuccessfulRevision | 0 | 0.75 |
standard | Death | 0 | 0.00 |
new | PrimaryTHR | 0 | 0.00 | 0.015

State values that do not change between models need only be specified once (such as all states except `PrimaryTHR` in the `new` model) and will automatically be repeated between models.

## Transition probabilities

A transition probabilities file contains 4 columns:

- `.model`: strategy name.
- `from`: initial state.
- `to`: end state.
- `prob`: transition probability from initial state to end state.

.model | from | to | prob
--- | --- | --- | ---
standard | PrimaryTHR | SuccessfulPrimary | C
standard | PrimaryTHR | Death | 0.02
standard | SuccessfulPrimary | SuccessfulPrimary | C
standard | SuccessfulPrimary | RevisionTHR | pHRFailStandard
standard | SuccessfulPrimary | Death | mr
standard | RevisionTHR | SuccessfulRevision | C
standard | RevisionTHR | Death | 0.02+mr
standard | SuccessfulRevision | SuccessfulRevision | C
standard | SuccessfulRevision | RevisionTHR | 0.04
standard | SuccessfulRevision | Death | mr
standard | Death | Death | 1
new | SuccessfulPrimary | RevisionTHR | pHRFailNew

A probability can be defined by any expression: a number, `C`, a different parameter name (specified in the parameter file), or a function call.

As with the state file above probabilities specified for only one strategy will be carried over to others. Only probabilities that differ from one strategy to another must be specified separately for each strategy. Unspecified transition probabilities are assumed to be 0.

## Parameters

A parameter file contains 2 mandatory columns: the parameter names `parameter` and the values `value`.

Optional columns can be added to perform deterministic or probabilistic sensitivity analysis (DSA and PSA). `low` and `high` columns specify the lower and upper bounds of parameter values for DSA, while `psa` contains the parameter distribution for PSA.

parameter | value | low | high | psa
--- | --- | --- | --- | ---
lngamma | 0.3740968 | 0.2791966 | 0.468997 | normal(0.27, 0.001)
gamma | exp(lngamma) |  |  |
constant | -5.490935 | -5.906719 | -5.075151 |
agecoef | -0.0367022 | -0.0471246 | -0.0262798 | normal(-0.04, 0.001)
malecoef | 0.768536 | 0.550404 | 0.986668 |
np1 | -1.344474 | -2.109637 | -0.579311 |
rr | exp(np1) | 0.121282 | 0.5602843 | binomial(0.12, 500)
age_init | 60 |  |  |
age | age_init + model_time |  |  |
sex | 0 |  |  |
sex_str | ifelse(sex==1, “Males”, “Females”) |  |  |
mr | look_up(mr_table, age = age, sex = sex_str, bin = TRUE, value = “value”) |  |  |
lambdaStandard | exp(constant + agecoef * age_init + malecoef * sex) |  |  |
lambdaNew | exp(constant + agecoef * age_init + malecoef * sex) * rr |  |  |
pHRFailStandard | 1 - exp(lambdaStandard * ((model_time-1)^gamma - model_time^gamma)) |  |  |
pHRFailNew | 1 - exp(lambdaNew * ((model_time-1)^gamma - model_time^gamma)) |  |  |

A parameter can be specified as any expression: as a number, through a previously defined parameter, with a mathematical formula or a function call.

The `look_up()` function can be used to look up parameter values in external reference tables (see section User-defined data), if a `data` argument is given in the reference file (as for the `mr` parameter in the above example).

## User-defined data

Sometimes external data is required for an analysis (e.g. age-specific mortality rates). A `data` row in the reference file specifies a subdirectory containing data frames to be loaded (saved as `csv`, `xls`, or `xlsx` files). Multiple files can be placed here, and each filename (without the extension) is used as the dataframe name.3

## Model options

Models specified by tabular input will run with defaults options. The following options can be specified in a non-mandatory `options` file:

- `cost`, `effect`: values to be used as cost and effect.
- `init` comma separated starting values.
- `method`: counting method.
- `base`: name of base model.
- `cycles`: run the model for how many cycles?
- `n`: number of resample for PSA.
- `num_core`: number of cluster cores.

option | value
--- | ---
cost | cost
effect | qaly
method | beginning
cycles | 50
n | 10
init | 1000, 0, 0, 0, 0

## Run the analysis

The entire set of analysis specified in the tabular files can be run by the function `run_model_from_tabular()`.

    result <- run_model_tabular(
      location = system.file("tabular/thr", package = "heemod")
    )

    ## Running DSA on strategy 'standard'...

    ## Running DSA on strategy 'new'...

    ## Resampling strategy 'standard'...
    ## Resampling strategy 'standard'...

    ## Resampling strategy 'new'...
    ## Resampling strategy 'new'...

    ## Updating strategy 'standard'...

    ## Updating strategy 'new'...

The results can then be interpreted as usual.

    result$model_runs

    ## 2 strategies run for 50 cycles.
    ##
    ## Initial state counts:
    ##
    ## PrimaryTHR = 1000
    ## SuccessfulPrimary = 0
    ## RevisionTHR = 0
    ## SuccessfulRevision = 0
    ## Death = 0
    ##
    ## Counting method: 'beginning'.
    ##
    ## Values:
    ##
    ##               cost     qaly
    ## standard 304266.73 14641.51
    ## new       80960.18 14685.77
    ##
    ## Efficiency frontier:
    ##
    ## new
    ##
    ## Differences:
    ##
    ##     Cost Diff. Effect Diff.      ICER     Ref.
    ## new  -223.3065   0.04426563 -5044.693 standard

    plot(result$psa,
         type = "ce")

    plot(result$dsa,
         result = "cost",
         strategy = "new")

    result$demographics

    ## An analysis re-run on 8 parameter sets.
    ##
    ## * Weights distribution:
    ##
    ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    ## 0.00219 0.01194 0.01482 0.01489 0.01994 0.02264
    ##
    ## Total weight: 0.1191407
    ##
    ## * Values distribution:
    ##
    ##                                  Min.       1st Qu.        Median          Mean
    ## standard - Cost          3.892620e+01  4.392518e+01   993.2017848   708.5801137
    ## standard - Effect        4.098947e+00  4.403150e+00    13.1467098    10.0487221
    ## standard - Cost Diff.               -             -             -             -
    ## standard - Effect Diff.             -             -             -             -
    ## standard - Icer                     -             -             -             -
    ## new - Cost               1.022389e+01  1.154223e+01   279.3495600   200.4971884
    ## new - Effect             4.103704e+00  4.408382e+00    13.2912790    10.1504406
    ## new - Cost Diff.        -9.174158e+02 -8.167007e+02  -713.8522248  -508.0829253
    ## new - Effect Diff.       4.587073e-03  5.172165e-03     0.1418194     0.1017185
    ## new - Icer              -6.263848e+03 -6.256979e+03 -5032.9834879 -5471.8546606
    ##                               3rd Qu.          Max.
    ## standard - Cost          1139.7822107  1284.1587856
    ## standard - Effect          13.8274561    14.4422790
    ## standard - Cost Diff.               -             -
    ## standard - Effect Diff.             -             -
    ## standard - Icer                     -             -
    ## new - Cost                323.0815351   366.7429773
    ## new - Effect               13.9929427    14.6290526
    ## new - Cost Diff.          -32.3829481   -28.7023186
    ## new - Effect Diff.          0.1643751     0.1867736
    ## new - Icer              -4968.9381888 -4911.9130861
    ##
    ## * Combined result:
    ##
    ## 2 strategies run for 50 cycles.
    ##
    ## Initial state counts:
    ##
    ## PrimaryTHR = 1000
    ## SuccessfulPrimary = 0
    ## RevisionTHR = 0
    ## SuccessfulRevision = 0
    ## Death = 0
    ##
    ## Counting method: 'beginning'.
    ##
    ## Values:
    ##
    ##              cost     qaly
    ## standard 708580.1 10048.72
    ## new      200497.2 10150.44
    ##
    ## Efficiency frontier:
    ##
    ## new
    ##
    ## Differences:
    ##
    ##     Cost Diff. Effect Diff.      ICER     Ref.
    ## new  -508.0829    0.1017185 -4994.989 standard

1. French `csv` (with `;` separator) are not supported.↩︎

2. A single discount rate can be duplicated across states, or specified in one state and left blank elsewhere. Specifying two different discount rates for a single variable in different states will cause an error.↩︎

3. Having multiple files with the same base name but different extensions in the directory will cause an error.↩︎