Example Dataset for a Survival Outcome

A simulated dataset with time-varying and baseline variables for 3000 subjects with a discrete-time survival outcome, suitable for use with the g-formula and mediation functions under survival settings.

Usage

survivaldata

Format

A data frame with 10,223 rows and 11 variables, in long at-risk format (one row per subject per time point while still at risk; 3000 subjects, 1822 events, 283 censored, no missing values):

id: Unique subject identifier (1-3000).
time: Time variable (integer, 0 to 4).
V: Time-fixed baseline covariate.
L: Time-varying confounder (continuous).
A: Time-varying binary exposure.
M: Time-varying binary mediator.
Y: Event indicator at this time point (1 = event, 0 = still at risk).
C: Loss-to-follow-up indicator at this time point (1 = censored). Censoring is drawn only among subjects who did not have the event at that time, so Y and C are never both 1.
lag1_A: Exposure at the previous time point; 0 at time == 0.
lag1_M: Previous value of M; 0 at time == 0.
lag1_L: Previous value of L; 0 at time == 0.

Source

Simulated from the parametric process given under Details.

Details

The data-generating structure can be summarized as: $$ A_t \leftarrow V, L_{t-1}, A_{t-1}, t;\quad L_t \leftarrow V, A_t, L_{t-1}, t;\quad M_t \leftarrow V, A_t, L_t, M_{t-1}, t;\quad Y_t \leftarrow V, A_t, M_t, L_t, A_t*M_t, t. $$

The generating parameters are, with $V \sim N(0, 1)$ and all lagged terms set to zero at $t = 0$:


  logit P(A_t = 1) = -0.40 + 0.60 V + 0.40 L_{t-1} + 0.58 A_{t-1} + 0.05 t
  E(L_t)           =  0.50 + 0.60 V + 0.30 A_t + 0.20 L_{t-1} + 0.05 t
                      (Gaussian, SD 0.10)
  logit P(M_t = 1) = -0.95 + 0.50 V + 1.50 A_t + 0.40 L_t
                           + 0.20 M_{t-1} + 0.05 t
  logit P(Y_t = 1) = -3.40 - 0.50 V + 0.25 A_t + 1.70 M_t + 0.30 L_t
                           + 0.50 A_t M_t
  logit P(C_t = 1) = -3.80 + 0.30 V + 0.30 L_t + 0.10 t

The hazard carries no time trend. The confounder $L$ depends on current exposure, so exposure-affected confounding of the mediator-outcome relationship is present.

Large-sample true values (cumulative risk by the fifth period, computed under the same permuted-pool construction the package uses for mediation_type = "I", at 200,000 subjects):

Risk under no exposure	0.39
Risk under exposure	0.79
Interventional direct effect (IDE)	0.194
Interventional indirect effect (IIE)	0.191
Total effect (TE)	0.400
Mediated-interaction residual (TE $-$ overall)	0.015

Follow-up stops at the event or at loss to follow-up, whichever comes first, so no rows are retained for a subject after either. Of the 3000 subjects, 1822 have the event, 283 are censored and the remaining 895 reach the end of the fifth period.

Censoring depends on $V$ and on the current confounder $L$, so it is informative given the observed history and a censoring model is required for valid estimation: pass one as a mod_type = "censor" entry in models. Because censoring is independent of the counterfactual event process given that history, the target estimand – risk with censoring eliminated – is unchanged by its presence, so the true values below are the same as they would be without it.

Usage

Format

Source

Details

See also