# New Interface

    library(TrialEmulation)

To improve usability, we have implemented a new user interface. This allows a more structured specification of the target trial emulation process.

It also gives flexibility to add new methods and tools for parts of the analysis. For example, we now allow different ways of storing the expanded data: as CSV files and in a DuckDB database. We also allow different weight fitting model procedures: using `stats::glm` or `parglm::parglm`. New components can quickly and easily be specified for use with this package.

## User Interface

A sequence of target trials analysis starts by specifying which estimand will be used:

    trial_pp <- trial_sequence(estimand = "PP") # Per-protocol
    trial_itt <- trial_sequence(estimand = "ITT") # Intention-to-treat

Additionally it is useful to create a directory to save files for later inspection.

    trial_pp_dir <- file.path(tempdir(), "trial_pp")
    dir.create(trial_pp_dir)
    trial_itt_dir <- file.path(tempdir(), "trial_itt")
    dir.create(trial_itt_dir)

### Observational Data

Next the user must specify the observational input data that will be used for the target trial emulation. Here we need to specify which columns contain which values and how they should be used.

    data("data_censored")
    trial_pp <- trial_pp |>
      set_data(
        data = data_censored,
        id = "id",
        period = "period",
        treatment = "treatment",
        outcome = "outcome",
        eligible = "eligible"
      )

    # Function style without pipes
    trial_itt <- set_data(
      trial_itt,
      data = data_censored,
      id = "id",
      period = "period",
      treatment = "treatment",
      outcome = "outcome",
      eligible = "eligible"
    )

We can inspect our object by printing:

    trial_itt
    #> Trial Sequence Object
    #> Estimand: Intention-to-treat
    #>
    #> Data:
    #>  - N: 725 observations from 89 patients
    #>         id period treatment    x1           x2    x3        x4   age      age_s
    #>      <int>  <int>     <num> <num>        <num> <int>     <num> <num>      <num>
    #>   1:     1      0         1     1  1.146148362     0 0.7342030    36 0.08333333
    #>   2:     1      1         1     1  0.002200337     0 0.7342030    37 0.16666667
    #>  ---
    #> 724:    99      6         1     1 -0.033762356     1 0.5752681    71 3.00000000
    #> 725:    99      7         0     0 -1.340496520     1 0.5752681    72 3.08333333
    #>      outcome censored eligible time_on_regime
    #>        <num>    <int>    <num>          <num>
    #>   1:       0        0        1              0
    #>   2:       0        0        0              1
    #>  ---
    #> 724:       0        0        0              1
    #> 725:       1        0        0              2
    #>
    #> IPW for informative censoring:
    #>  - No weight model specified
    #>
    #> Sequence of Trials Data:
    #> - Use set_expansion_options() and expand_trials() to construct the sequence of trials dataset.
    #>
    #> Outcome model:
    #>  - Outcome model not specified. Use set_outcome_model()

We see the newly attached data. Some pre-processing has occurred: the id, period, treatment, outcome and eligible columns are renamed to have those names, and some additional columns required for later processing have been created. We also see some hints that other components of the analysis are not yet defined.

### Weight Models

To adjust for the effects of informative censoring, inverse probability of censoring weights (IPCW) can be applied. To estimate these weights, we construct time-to-(censoring-)event models. Two sets of models are fit for the two censoring mechanisms which may apply: censoring due to deviation from assigned treatment and other informative censoring.

The data which will be used for fitting those weight models is accessible with the `ipw_data` method.

    ipw_data(trial_itt)
    #> Key: <id>
    #> Indices: <first>, <am_1>
    #>         id period treatment    x1           x2    x3        x4   age      age_s
    #>      <int>  <int>     <num> <num>        <num> <int>     <num> <num>      <num>
    #>   1:     1      0         1     1  1.146148362     0 0.7342030    36 0.08333333
    #>   2:     1      1         1     1  0.002200337     0 0.7342030    37 0.16666667
    #>   3:     1      2         1     0 -0.481762418     0 0.7342030    38 0.25000000
    #>   4:     1      3         1     0  0.007872396     0 0.7342030    39 0.33333333
    #>   5:     1      4         1     1  0.216053715     0 0.7342030    40 0.41666667
    #>  ---
    #> 721:    99      3         0     0 -0.747905701     1 0.5752681    68 2.75000000
    #> 722:    99      4         0     0 -0.790056043     1 0.5752681    69 2.83333333
    #> 723:    99      5         1     1  0.387429397     1 0.5752681    70 2.91666667
    #> 724:    99      6         1     1 -0.033762356     1 0.5752681    71 3.00000000
    #> 725:    99      7         0     0 -1.340496520     1 0.5752681    72 3.08333333
    #>      outcome censored eligible time_of_event  first  am_1  cumA switch
    #>        <num>    <int>    <num>         <num> <lgcl> <num> <num>  <num>
    #>   1:       0        0        1          9999   TRUE     0     1      0
    #>   2:       0        0        0          9999  FALSE     1     2      0
    #>   3:       0        0        0          9999  FALSE     1     3      0
    #>   4:       0        0        0          9999  FALSE     1     4      0
    #>   5:       0        0        0          9999  FALSE     1     5      0
    #>  ---
    #> 721:       0        0        0             7  FALSE     0     2      0
    #> 722:       0        0        0             7  FALSE     0     2      0
    #> 723:       0        0        0             7  FALSE     0     3      1
    #> 724:       0        0        0             7  FALSE     1     4      0
    #> 725:       1        0        0             7  FALSE     1     4      1
    #>      regime_start time_on_regime eligible0 eligible1
    #>             <int>          <num>     <num>     <num>
    #>   1:            0              0         1         0
    #>   2:            0              1         0         1
    #>   3:            0              2         0         1
    #>   4:            0              3         0         1
    #>   5:            0              4         0         1
    #>  ---
    #> 721:            2              1         1         0
    #> 722:            2              2         1         0
    #> 723:            5              3         1         0
    #> 724:            5              1         0         1
    #> 725:            7              2         0         1

#### Censoring due to treatment switching

We specify model formulas to be used for calculating the probability of receiving treatment in the current period. Separate models are fitted for patients who had `treatment = 1` and those who had `treatment = 0` in the previous period. Stabilized weights are used by fitting numerator and denominator models.

There are optional arguments to specify columns which can include/exclude observations from the treatment models. These are used in case it is not possible for a patient to deviate from a certain treatment assignment in that period.

    trial_pp <- trial_pp |>
      set_switch_weight_model(
        numerator = ~age,
        denominator = ~ age + x1 + x3,
        model_fitter = stats_glm_logit(save_path = file.path(trial_pp_dir, "switch_models"))
      )
    trial_pp@switch_weights
    #>  - Numerator formula: treatment ~ age
    #>  - Denominator formula: treatment ~ age + x1 + x3
    #>  - Model fitter type: te_stats_glm_logit
    #>  - Weight models not fitted. Use calculate_weights()

This type of censoring is not used with an ITT estimand, so we cannot use `set_switch_weight_model()` with `trial_ITT` objects. Note that we calculated stabilised weights, so a numerator and denominator model is required. The numerator should contain terms that are not time varying. These terms are later included in the final time-to-event model for the outcome.

#### Other informative censoring

In case there is other informative censoring occurring in the data, we can create similar models to estimate the IPCW. These can be used with all types of estimand. Compared to `set_switch_weight_model` there are additional required arguments:

- `censor_event` which specifies the column containing the censoring indicator
- `pool_models` which species that models may be fit separately (as in `set_switch_weight_model`) or pooled across the treatments in the previous period. The choices are `"none"`, `"both"`, or `"numerator"` only. The default and allowed choices depends on the estimand.

    trial_pp <- trial_pp |>
      set_censor_weight_model(
        censor_event = "censored",
        numerator = ~x2,
        denominator = ~ x2 + x1,
        pool_models = "none",
        model_fitter = stats_glm_logit(save_path = file.path(trial_pp_dir, "switch_models"))
      )
    trial_pp@censor_weights
    #>  - Numerator formula: 1 - censored ~ x2
    #>  - Denominator formula: 1 - censored ~ x2 + x1
    #>  - Model fitter type: te_stats_glm_logit
    #>  - Weight models not fitted. Use calculate_weights()

    trial_itt <- set_censor_weight_model(
      trial_itt,
      censor_event = "censored",
      numerator = ~x2,
      denominator = ~ x2 + x1,
      pool_models = "numerator",
      model_fitter = stats_glm_logit(save_path = file.path(trial_itt_dir, "switch_models"))
    )
    trial_itt@censor_weights
    #>  - Numerator formula: 1 - censored ~ x2
    #>  - Denominator formula: 1 - censored ~ x2 + x1
    #>  - Numerator model is pooled across treatment arms. Denominator model is not pooled.
    #>  - Model fitter type: te_stats_glm_logit
    #>  - Weight models not fitted. Use calculate_weights()

#### Calculate Weights

Next we need to fit the individual models and combine them into weights. This is done with `calculate_weights()`.

    trial_pp <- trial_pp |> calculate_weights()
    trial_itt <- calculate_weights(trial_itt)

The full model objects are saved to disk in the directories we created above. The summaries are stored in the trial sequence object and can be printed:

    show_weight_models(trial_itt)
    #> Weight Models for Informative Censoring
    #> ---------------------------------------
    #>
    #> [[n]]
    #> Model: P(censor_event = 0 | X) for numerator
    #>
    #>  term        estimate   std.error statistic p.value
    #>  (Intercept)  2.4480907 0.1405726 17.415128 6.334656e-68
    #>  x2          -0.4486482 0.1368765 -3.277759 1.046346e-03
    #>
    #>  null.deviance df.null logLik    AIC      BIC      deviance df.residual nobs
    #>  404.2156      724     -196.7002 397.4004 406.5727 393.4004 723         725
    #>
    #>  path
    #>  /tmp/RtmpVNgvQ1/trial_itt/switch_models/model_ecf459c2c.rds
    #>
    #> [[d0]]
    #> Model: P(censor_event = 0 | X, previous treatment = 0) for denominator
    #>
    #>  term        estimate   std.error statistic p.value
    #>  (Intercept)  1.8941961 0.2071122  9.145746 5.921948e-20
    #>  x2          -0.5898292 0.1693402 -3.483101 4.956409e-04
    #>  x1           0.8552603 0.3452930  2.476912 1.325247e-02
    #>
    #>  null.deviance df.null logLik    AIC      BIC      deviance df.residual nobs
    #>  283.0723      425     -132.1655 270.3309 282.4943 264.3309 423         426
    #>
    #>  path
    #>  /tmp/RtmpVNgvQ1/trial_itt/switch_models/model_ecf4c45e29.rds
    #>
    #> [[d1]]
    #> Model: P(censor_event = 0 | X, previous treatment = 1) for denominator
    #>
    #>  term        estimate    std.error statistic  p.value
    #>  (Intercept)  2.81443372 0.3122688  9.0128570 2.007570e-19
    #>  x2          -0.03713196 0.2699579 -0.1375472 8.905983e-01
    #>  x1           0.89351418 0.7771954  1.1496648 2.502819e-01
    #>
    #>  null.deviance df.null logLik    AIC      BIC      deviance df.residual nobs
    #>  113.0528      298     -55.72938 117.4588 128.5601 111.4588 296         299
    #>
    #>  path
    #>  /tmp/RtmpVNgvQ1/trial_itt/switch_models/model_ecf1c4450e8.rds
    #>

### Specify Outcome Model

Now we can specify the outcome model. Here we can include adjustment terms for any variables in the dataset. We can also specify how `followup_time` and `trial_period` terms should be included in the model. As for the weight models, we can specify a `model_fitter`. The numerator terms from the stabilised weight models are automatically included in the outcome model formula.

    trial_pp <- set_outcome_model(trial_pp)
    trial_itt <- set_outcome_model(trial_itt, adjustment_terms = ~x2)

It is necessary to specify the outcome model at this stage because we need to know which columns should be retained and expanded in the construction of the sequence of trials data set. After expansion it is possible to set the outcome model again to modify how covariates are modelled, e.g. to add an interaction or squared term. To add a term for a variable not in the expanded data, the expansion procedure will need to be repeated.

### Expand Trials

Now we are ready to create the data set with all of the sequence of target trials. First we specify some options for the expansion and then expand.

#### Set Expansion Options

There are two options to set

- output: specifies how and where the expanded data will be saved. As it can be very large, we may need to save it to disk with CSV files or DuckDB, using a `save_to_*` function.
- chunk_size: if the expanded data is too large to fit in memory, we need to process it in chunks by specifying how many patients are processed at one time.

    trial_pp <- set_expansion_options(
      trial_pp,
      output = save_to_datatable(),
      chunk_size = 500
    )
    trial_itt <- set_expansion_options(
      trial_itt,
      output = save_to_datatable(),
      chunk_size = 500
    )

Other options for big data are to save to csv or DuckDB:

    trial_pp <- trial_pp |>
      set_expansion_options(
        output = save_to_csv(file.path(trial_pp_dir, "trial_csvs")),
        chunk_size = 500
      )

    trial_itt <- set_expansion_options(
      trial_itt,
      output = save_to_csv(file.path(trial_itt_dir, "trial_csvs")),
      chunk_size = 500
    )

    trial_itt <- set_expansion_options(
      trial_itt,
      output = save_to_duckdb(file.path(trial_itt_dir, "trial_duckdb")),
      chunk_size = 500
    )

    # For the purposes of this vignette the previous `save_to_datatable()` output
    # option is used in the following code.

#### Create Sequence of Trials Data

Now we are ready to construct the sequence of trials dataset using the `expand_trials()` method. This can take some time for large input data.

    trial_pp <- expand_trials(trial_pp)
    trial_itt <- expand_trials(trial_itt)

The resulting object shows the settings used for the expansion and where the expanded data has been saved.

    trial_pp@expansion
    #> Sequence of Trials Data:
    #> - Chunk size: 500
    #> - Censor at switch: TRUE
    #> - First period: 0 | Last period: Inf
    #>
    #> A TE Datastore Datatable object
    #> N: 500 observations
    #>         id trial_period followup_time outcome    weight treatment         x2
    #>      <int>        <int>         <int>   <num>     <num>     <num>      <num>
    #>   1:     1            0             0       0 1.0000000         1  1.1461484
    #>   2:     1            0             1       0 0.8951447         1  1.1461484
    #>  ---
    #> 499:    99            0             0       0 1.0000000         1 -0.3463778
    #> 500:    99            0             1       0 1.0122336         1 -0.3463778
    #>        age assigned_treatment
    #>      <num>              <num>
    #>   1:    36                  1
    #>   2:    36                  1
    #>  ---
    #> 499:    65                  1
    #> 500:    65                  1

### Sample or Load from Expanded Data

Now that the expanded data has been created, we can prepare the data to fit the outcome model. For data that can fit comfortably in memory, this is a trivial step using `load_expanded_data`. For large datasets, it may be necessary to sample from the expanded by setting the `p_control` argument. This sets the probability that an observation with`outcome == 0` will be included in the loaded data. A seed can be set for reproducibility. Additionally, a vector of periods to include can be specified, eg `period = 1:60`, and/or a subsetting condition, `subset_condition = "age > 65"`.

    trial_itt <- load_expanded_data(trial_itt, seed = 1234, p_control = 0.5)

The loaded data can be accessed and/or modified with `outcome_data()`.

    x2_sq <- outcome_data(trial_itt)$x2^2
    outcome_data(trial_itt)$x2_sq <- x2_sq
    head(outcome_data(trial_itt))
    #>       id trial_period followup_time outcome weight treatment          x2
    #>    <int>        <int>         <int>   <num>  <num>     <num>       <num>
    #> 1:    15            0             0       1      1         1 -0.73652563
    #> 2:    32            0             0       1      1         1  1.98613804
    #> 3:    26            0             0       0      1         0  1.64332982
    #> 4:    10            0             0       0      1         1  0.05091841
    #> 5:     5            0             0       0      1         1  0.74909203
    #> 6:    46            0             0       0      1         1 -0.88598258
    #>    assigned_treatment sample_weight       x2_sq
    #>                 <num>         <num>       <num>
    #> 1:                  1             1 0.542470010
    #> 2:                  1             1 3.944744297
    #> 3:                  0             2 2.700532894
    #> 4:                  1             2 0.002592685
    #> 5:                  1             2 0.561138869
    #> 6:                  1             2 0.784965131

### Fit Marginal Structural Model

To fit the outcome model we use `fit_msm()`. There are two options to specify how weights are used in the model. First we can select which weights columns are used, by default the product of columns `weight` and `sample_weight` is used. We can also apply a modifier function, for example, to trim large weights to some fixed value or a percentile.

    trial_itt <- fit_msm(
      trial_itt,
      weight_cols = c("weight", "sample_weight"),
      modify_weights = function(w) {
        q99 <- quantile(w, probs = 0.99)
        pmin(w, q99)
      }
    )
    #> Warning in eval(family$initialize): non-integer #successes in a binomial glm!
    #> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

The summary of the model fit is shown:

    trial_itt@outcome_model
    #> - Formula: outcome ~ assigned_treatment + x2 + followup_time + I(followup_time^2) + trial_period + I(trial_period^2)
    #> - Treatment variable: assigned_treatment
    #> - Adjustment variables: x2
    #> - Model fitter type: te_stats_glm_logit
    #>
    #> Model Summary:
    #>
    #>  term               estimate std.error statistic p.value conf.low conf.high
    #>  (Intercept)        -6.02    0.780      -7.72    1.2e-14 -7.550   -4.4916
    #>  assigned_treatment  1.63    0.496       3.28    1.0e-03  0.654    2.5977
    #>  x2                  0.31    0.418       0.74    4.6e-01 -0.511    1.1282
    #>  followup_time       0.34    0.244       1.38    1.7e-01 -0.141    0.8148
    #>  I(followup_time^2) -0.02    0.014      -1.42    1.5e-01 -0.049    0.0077
    #>  trial_period        7.29    0.978       7.45    9.2e-14  5.371    9.2042
    #>  I(trial_period^2)  -7.68    0.537     -14.31    2.0e-46 -8.738   -6.6320
    #>
    #>  null.deviance df.null logLik AIC BIC deviance df.residual nobs
    #>  158           800     -69.1  152 185 135      794         801

Depending on the model fitter used, we can also access the model object. For the default `stats::glm` logistic model, we have the `glm` object as well as the `sandwich` variance-covariance matrix.

    trial_itt@outcome_model@fitted@model$model
    #>
    #> Call:  glm(formula = formula, family = binomial("logit"), data = data,
    #>     weights = weights, x = FALSE, y = FALSE)
    #>
    #> Coefficients:
    #>        (Intercept)  assigned_treatment                  x2       followup_time
    #>           -6.02067             1.62585             0.30837             0.33673
    #> I(followup_time^2)        trial_period   I(trial_period^2)
    #>           -0.02049             7.28762            -7.68478
    #>
    #> Degrees of Freedom: 800 Total (i.e. Null);  794 Residual
    #> Null Deviance:       157.8
    #> Residual Deviance: 134.7     AIC: 152.2
    trial_itt@outcome_model@fitted@model$vcov
    #>                     (Intercept) assigned_treatment           x2 followup_time
    #> (Intercept)         0.608651263       -0.007606479  0.042942422  -0.143451214
    #> assigned_treatment -0.007606479        0.245882729  0.087953406  -0.052364376
    #> x2                  0.042942422        0.087953406  0.174977954  -0.045052691
    #> followup_time      -0.143451214       -0.052364376 -0.045052691   0.059487800
    #> I(followup_time^2)  0.007130666        0.002815736  0.002843807  -0.003362158
    #> trial_period       -0.105885453       -0.341609248 -0.097440741   0.104454026
    #> I(trial_period^2)   0.049055894        0.165009684  0.046219048  -0.054969078
    #>                    I(followup_time^2) trial_period I(trial_period^2)
    #> (Intercept)              0.0071306658 -0.105885452        0.04905589
    #> assigned_treatment       0.0028157357 -0.341609248        0.16500968
    #> x2                       0.0028438066 -0.097440741        0.04621905
    #> followup_time           -0.0033621580  0.104454026       -0.05496908
    #> I(followup_time^2)       0.0002067028 -0.005143791        0.00265172
    #> trial_period            -0.0051437905  0.956232062       -0.51353487
    #> I(trial_period^2)        0.0026517200 -0.513573594        0.28851494

The complete object shows all the specifications:

    trial_itt
    #> Trial Sequence Object
    #> Estimand: Intention-to-treat
    #>
    #> Data:
    #>  - N: 725 observations from 89 patients
    #>         id period treatment    x1           x2    x3        x4   age      age_s
    #>      <int>  <int>     <num> <num>        <num> <int>     <num> <num>      <num>
    #>   1:     1      0         1     1  1.146148362     0 0.7342030    36 0.08333333
    #>   2:     1      1         1     1  0.002200337     0 0.7342030    37 0.16666667
    #>  ---
    #> 724:    99      6         1     1 -0.033762356     1 0.5752681    71 3.00000000
    #> 725:    99      7         0     0 -1.340496520     1 0.5752681    72 3.08333333
    #>      outcome censored eligible time_on_regime        wt       wtC
    #>        <num>    <int>    <num>          <num>     <num>     <num>
    #>   1:       0        0        1              0 0.9835463 0.9835463
    #>   2:       0        0        0              1 0.9429254 0.9429254
    #>  ---
    #> 724:       0        0        0              1 0.9440988 0.9440988
    #> 725:       1        0        0              2 1.0092093 1.0092093
    #>
    #> IPW for informative censoring:
    #>  - Numerator formula: 1 - censored ~ x2
    #>  - Denominator formula: 1 - censored ~ x2 + x1
    #>  - Numerator model is pooled across treatment arms. Denominator model is not pooled.
    #>  - Model fitter type: te_stats_glm_logit
    #>  - View weight model summaries with show_weight_models()
    #>
    #> Sequence of Trials Data:
    #> - Chunk size: 500
    #> - Censor at switch: FALSE
    #> - First period: 0 | Last period: Inf
    #>
    #> A TE Datastore Datatable object
    #> N: 1558 observations
    #>          id trial_period followup_time outcome    weight treatment         x2
    #>       <int>        <int>         <int>   <num>     <num>     <num>      <num>
    #>    1:     1            0             0       0 1.0000000         1  1.1461484
    #>    2:     1            0             1       0 0.9429254         1  1.1461484
    #>   ---
    #> 1557:    99            0             6       0 0.8917236         1 -0.3463778
    #> 1558:    99            0             7       1 0.8999358         0 -0.3463778
    #>       assigned_treatment
    #>                    <num>
    #>    1:                  1
    #>    2:                  1
    #>   ---
    #> 1557:                  1
    #> 1558:                  1
    #>
    #> Outcome model:
    #> - Formula: outcome ~ assigned_treatment + x2 + followup_time + I(followup_time^2) + trial_period + I(trial_period^2)
    #> - Treatment variable: assigned_treatment
    #> - Adjustment variables: x2
    #> - Model fitter type: te_stats_glm_logit
    #>
    #> Model Summary:
    #>
    #>  term               estimate std.error statistic p.value conf.low conf.high
    #>  (Intercept)        -6.02    0.780      -7.72    1.2e-14 -7.550   -4.4916
    #>  assigned_treatment  1.63    0.496       3.28    1.0e-03  0.654    2.5977
    #>  x2                  0.31    0.418       0.74    4.6e-01 -0.511    1.1282
    #>  followup_time       0.34    0.244       1.38    1.7e-01 -0.141    0.8148
    #>  I(followup_time^2) -0.02    0.014      -1.42    1.5e-01 -0.049    0.0077
    #>  trial_period        7.29    0.978       7.45    9.2e-14  5.371    9.2042
    #>  I(trial_period^2)  -7.68    0.537     -14.31    2.0e-46 -8.738   -6.6320
    #>
    #>  null.deviance df.null logLik AIC BIC deviance df.residual nobs
    #>  158           800     -69.1  152 185 135      794         801
    #>
    #> Outcome data
    #> N: 801 observations from 76 patients in 18 trial periods
    #> Periods: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
    #>         id trial_period followup_time outcome   weight treatment         x2
    #>      <int>        <int>         <int>   <num>    <num>     <num>      <num>
    #>   1:    15            0             0       1 1.000000         1 -0.7365256
    #>   2:    32            0             0       1 1.000000         1  1.9861380
    #>  ---
    #> 800:    39            0            19       0 1.351756         1  0.2189413
    #> 801:    54            0            19       0 1.359294         0  1.2924128
    #>      assigned_treatment sample_weight     x2_sq        w
    #>                   <num>         <num>     <num>    <num>
    #>   1:                  1             1 0.5424700 1.000000
    #>   2:                  1             1 3.9447443 1.000000
    #>  ---
    #> 800:                  1             2 0.0479353 2.703512
    #> 801:                  0             2 1.6703309 2.718587

### Inference

We use the `predict()` method to estimate survival probabilities or cumulative incidences for different values of `assigned_treatment`. The `predict` method takes the baseline of the provided `newdata`, i.e. observations with `followup_time == 0` and constructs data with `followup_time` for the given `predict_times`. It is important to specify `newdata` correctly for a meaningful interpretation of the differences in survival.

    preds <- predict(
      trial_itt,
      newdata = outcome_data(trial_itt)[trial_period == 1, ],
      predict_times = 0:10,
      type = "survival",
    )
    plot(preds$difference$followup_time, preds$difference$survival_diff,
      type = "l", xlab = "Follow up", ylab = "Survival difference"
    )
    lines(preds$difference$followup_time, preds$difference$`2.5%`, type = "l", col = "red", lty = 2)
    lines(preds$difference$followup_time, preds$difference$`97.5%`, type = "l", col = "red", lty = 2)

### Flowchart

This flow chart helps visualise the complete workflow.

Flowchart