This dataset demonstrates the construction of a Propensity Score-Integrated (PS) SAM prior. It simulates a two-arm randomized clinical trial (RCT) with a 2:1 randomization ratio between treatment and control arms, considering both binary and continuous endpoints.
PS_SAM_dataA data frame with 600 observations.
"A" is the treatment assignment (1 = treated, 0 = control).
"G" is the study indicator (1 = current, 0 = historical).
"\(X_1\)" is a binary covariate.
"\(X_2\)" is a continuous covariate.
"\(X_3\)" is a continuous covariate.
"\(Y_{binary}\)" is binary outcome.
"\(Y_{continuous}\)" is continuous outcome.
The dataset includes:
Sample size for treatment arm: \(n_t = 200\).
Sample size for control arm: \(n_c = 100\).
Sample size for historical control study: \(n_h = 300\).
Covariates for the control arm were generated from
$$X_1 \sim Ber(0.5), ~~ X_2 \sim N(0, 1), ~~ X_3 \sim N(0.5, 1),$$
where \(Ber(\cdot)\) stands for Bernoulli distribution. Covariates for the historical controls were generated from a mixture distribution, with half were generated the same as for the control arm, while the other half were drawn from
$$X_1 \sim Ber(0.8), ~~ X_2 \sim N(-0.4, 1), ~~ X_3 \sim N(-0.2, 1).$$
For the binary endpoint, \(y_i\) were generated from the logit model:
$$logit(\Pr(y_i = 1 | X_{1i}, X_{2i}, X_{3i}, A_i)) = -1.4 - 0.5 X_{1i} + X_{2i} + 2 X_{3i} + \lambda A_i,$$
where \(\lambda\) is the treatment effect size, and we let \(\lambda = 0.9\) to generate a moderate treatment effect size so that they study has a reasonable power.
For the continuous endpoint, \(y_i\) were generated from the following normal model:
$$y_i = 1.8 X_{1i} + 0.9 X_{2i} - 2 X_{3i} + \lambda A_i + \epsilon_i,$$
where we let \(\lambda = 1\), and \(\epsilon_i \sim N(0, 3.5^2)\).
This dataset enables evaluation of the PS-SAM prior's performance in addressing heterogeneity between the RCT control arm and historical controls.
# Load the dataset
data(PS_SAM_data)
# View the structure
str(PS_SAM_data)
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