Example Dataset for a Non-Survival Outcome

A simulated dataset with time-varying and baseline variables for 3000 subjects over 5 time points, including exposure, mediator, confounders, and an end-of-follow-up outcome. Every subject contributes all 5 rows (there is no attrition), which makes this the simpler of the two simulated examples.

Usage

nonsurvivaldata

Format

A data frame with 15,000 rows (3000 subjects x 5 time points) and 13 variables:

id: Unique subject identifier (1-3000).
time: Time variable (0 to 4).
V: Time-fixed baseline covariate.
L1: Time-varying confounder 1 (continuous).
L2: Time-varying confounder 2 (binary).
A: Time-varying binary exposure.
M: Time-varying mediator (continuous).
Y_bin: Binary end-of-follow-up outcome. Recorded only at time == 4; NA at time 0-3.
Y_cont: Continuous end-of-follow-up outcome, on the same schedule as Y_bin: recorded only at time == 4, NA otherwise.
lag1_A: Exposure at the previous time point; NA at time == 0.
lag1_L1: Previous value of L1; NA at time == 0.
lag1_L2: Previous value of L2; NA at time == 0.
lag1_M: Previous value of M; NA at time == 0.

Source

Simulated from the parametric process given under Details.

Details

The simulated longitudinal data-generating structure can be summarized as: $$ A_t \leftarrow V, L1_{t-1}, L2_{t-1}, A_{t-1}, t;\quad L1_t \leftarrow V, A_t, L1_{t-1}, t;\quad L2_t \leftarrow V, A_t, L2_{t-1}, t;\quad M_t \leftarrow V, A_t, L1_t, L2_t, M_{t-1}, t;\quad Y \leftarrow V, A_4, M_4, L1_4, L2_4, A_4*M_4. $$ The exposure, mediator and confounders evolve at every time point, but the outcome is realised once, at the end of follow-up.

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) =  1.25 + 0.50 V + 0.25 L1_{t-1} + 0.25 L2_{t-1}
                           + 0.20 A_{t-1} + 0.01 t
  E(L1_t)          =  0.02 + 0.50 V + 0.18 A_t + 0.35 L1_{t-1} + 0.02 t
                     (Gaussian, SD 0.70)
  logit P(L2_t = 1)= -0.10 + 0.40 V + 0.18 A_t + 0.35 L2_{t-1} + 0.02 t
  E(M_t)           =  0.05 + 0.50 V + 0.45 A_t + 0.12 L1_t + 0.10 L2_t
                           + 0.30 M_{t-1} + 0.02 t   (Gaussian, SD 0.50)
  logit(pi)        = -2.60 + 0.50 V + 0.51 A_4 + 0.45 M_4
                           + 0.25 L1_4 - 0.25 L2_4 + 0.30 A_4 M_4

Both outcomes share that same $\pi$: Y_bin is $\mathrm{Bernoulli}(\pi)$ and Y_cont is $\mathrm{Beta}(50\pi,\, 50(1-\pi))$. Y_cont therefore lies strictly in $(0, 1)$; fitting it with var_type = "normal" is a working approximation, not the generating distribution.

The confounders $L1$ and $L2$ depend on current exposure, so exposure-affected confounding of the mediator-outcome relationship is present – the setting the interventional effects are designed for.

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

Interventional direct effect (IDE)	0.075
Interventional indirect effect (IIE)	0.071
Total effect (TE)	0.155
Mediated-interaction residual (TE $-$ overall)	0.009

The two pathways are deliberately of comparable size, and the residual is deliberately non-zero, so that the decomposition and its non-additivity are both visible in a worked example.

Two consequences for model specification:

Because the outcome exists at a single time point, time is constant among the rows used to fit the outcome model and must not appear in its formula: the term is not estimable and would be dropped (with a warning) from the simulation.
The lag1_* columns are NA at time == 0, so a baseline value must be supplied through init_recode, e.g. init_recode = recodes(lag1_A = 0, lag1_L1 = 0). (The lag columns of survivaldata are 0-filled at baseline instead, so no initialisation is strictly required there.)

Usage

Format

Source

Details

See also