pseudostate computes Aalen–Johansen pseudo-observations at a fixed time horizon. These pseudo-observations can be used as individual-level outcomes in regression models for cumulative incidence or state occupation probabilities.
Installation
With uv:
Alternatively, with pip:
A reproducible example
import polars as pl
from pseudostate import calculate_pseudostates
times_and_reals = pl.DataFrame(
{
"times": [1, 2, 2, 3, 4, 5, 6],
"reals": [1, 0, 2, 1, 0, 2, 1],
}
)
calculate_pseudostates(times_and_reals, fixed_time_horizon=5)
shape: (7, 6)| estimate_origin | times | state_occupancy_probability_0 | state_occupancy_probability_1 | state_occupancy_probability_2 | row_id |
|---|
| enum | f64 | f64 | f64 | f64 | i32 |
| "fixed_time_horizons" | 5.0 | 0.0 | 1.0 | 4.4409e-16 | 0 |
| "fixed_time_horizons" | 5.0 | 0.375 | 0.25 | 0.375 | 1 |
| "fixed_time_horizons" | 5.0 | 0.0 | 0.0 | 1.0 | 2 |
| "fixed_time_horizons" | 5.0 | -0.125 | 1.25 | -0.125 | 3 |
| "fixed_time_horizons" | 5.0 | 0.541667 | -0.083333 | 0.541667 | 4 |
| "fixed_time_horizons" | 5.0 | -0.791667 | -0.083333 | 1.875 | 5 |
| "fixed_time_horizons" | 5.0 | 1.875 | -0.083333 | -0.791667 | 6 |
Background
The theoretical foundation for pseudo-observations in multi-state models was laid out by Andersen, Klein, and Rosthøj (2003), Generalised linear models for correlated pseudo-observations, with applications to multi-state models, Biometrika, 90(1), 15–27.
The pseudo R package provides a widely used implementation of this approach.