Reproducing published PRS examples¶

The repository includes executable scripts for reproducing selected numerical results and simulation designs from the source PRS paper.

These scripts are deliberately separate from the unit-test suite. Unit tests protect correctness; the scripts provide inspectable, user-facing reproductions.

Table 2 calibration values¶

Run:

poetry run python examples/reproduce_table2.py

The script reproduces the four published combinations already covered by the regression tests:

Sample size	Categories	Published \(\delta\)	Published \(\tau_1\)	Published \(\tau_2\)
50	5	0.039598	0.07441	0.25722
500	10	0.009391	0.03063	0.04890
2,000	10	0.004696	0.00766	0.01222
10,000	20	0.001526	0.00394	0.00439

The script raises an error if the reproduced values exceed the documented numerical tolerances.

Selected Table 3 classifications¶

Run:

poetry run python examples/reproduce_table3.py

The script reproduces three selected small-sample examples spanning all three PRS decision regions:

\(R_1\), PRS approximately 0.068;
\(R_2\), PRS approximately 0.108;
\(R_3\), PRS approximately 0.300.

These are the same published examples used in the regression tests.

Source deviation-grid simulation¶

Run:

poetry run python examples/reproduce_deviation_grid.py

The paper states a grid of 30 equally spaced values from \(0\) to \((3M+2)\delta\). For the illustrated configuration \((n,B)=(50,5)\), \(c=0.7\), and \(M=2\), this means a stated upper endpoint of \(8\delta\).

There is an important feasibility constraint in that same simulation construction. The perturbed probabilities are formed as \(1/B-\delta_v\) and \(1/B+\delta_v\), so a valid multinomial distribution requires \(\delta_v\le 1/B\). In the illustrated case, \(\delta\approx0.039598\), hence \(8\delta\approx0.3168 > 0.2 = 1/B\). The final part of the stated grid would therefore imply negative category probabilities.

The script preserves the paper's stated 30-point grid for inspection, computes the feasibility boundary explicitly, and simulates only the feasible prefix rather than silently constructing invalid probability vectors.

By default, it uses:

reference distribution \((0.2,0.2,0.2,0.2,0.2)\);
sample size \(n=50\);
\(c=0.7\);
\(M=2\);
\(\alpha_1=0.05\);
\(\alpha_2=0.10\);
10,000 Monte Carlo samples per feasible grid point.

The repository seed is 2026. This seed is chosen for software reproducibility and is not claimed to be a seed reported by the paper.

For a faster smoke run:

poetry run python examples/reproduce_deviation_grid.py --simulations 200

For a larger numerical study, increase --simulations.

Interpretation¶

The deviation-grid outputs are operating-characteristic probabilities for the nested PRS decision framework. They should not be relabeled as conventional power estimates.

The scripts reproduce the published methodology and selected published numerical targets; they do not extend the statistical model.