In CAM-Roche/RandomisedTrialsEmulation: Causal Analysis of Observational Time-to-Event Data

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

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

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)

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

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

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

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)

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

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 withoutcome == 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))

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)
  }
)

The summary of the model fit is shown:

trial_itt@outcome_model

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$model
trial_itt@outcome_model@fitted@model$vcov

The complete object shows all the specifications:

trial_itt

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.

{ width=80% }

CAM-Roche/RandomisedTrialsEmulation documentation built on April 14, 2025, 7:44 a.m.