Receipt r851

{
  "forbids": null,
  "inputs": {
    "measure_id": "PSI_11"
  },
  "payload": {
    "basis": "measured",
    "basis_detail": {
      "inputs": [
        {
          "basis": "measured",
          "name": "score",
          "source": "cms-hospital-compare at gavel vintage 2026-08-03"
        },
        {
          "basis": "measured",
          "name": "published_interval",
          "source": "cms-hospital-compare at gavel vintage 2026-08-03"
        },
        {
          "basis": "measured",
          "name": "denominator",
          "source": "cms-hospital-compare at gavel vintage 2026-08-03"
        }
      ],
      "rule": "A figure computed from inputs of more than one basis carries the weakest basis among them, strongest to weakest being measured, then cited, then assumption, so a figure is never stronger than the weakest input that produced it."
    },
    "between_provider_variance": 22.00402793530006,
    "caveat": "This world's own cannot_answer states that 30 to 60 percent of small-cell variation is sampling error before anything else is said, and that a per-provider ranking is refused. That applies to a file CMS publishes exactly as it applies to a private one. What is served here is the spread across providers and nothing about which provider sits where in it: the cut this reads carries no facility identifier at all, and the ordering of a named roster is refused by name rather than dropped.",
    "corpus_vintage": "2026-08-03",
    "denominator_quartiles": {
      "max": 9218.0,
      "median": 235.0,
      "min": 28.0,
      "p25": 79.0,
      "p75": 726.0
    },
    "derivation": "between_provider_variance = var(score) + mean(v), where var(score) is the sample variance of the published scores across the providers that reported one and v is each provider's own posterior variance, taken from the published interval's half-width divided by the normal quantile and squared. The step is the law of total variance: the variance of a provider's true rate is the mean of its posterior variances plus the variance of its posterior means. It is an ADDITION because these are risk-standardised rates from a hierarchical model, already shrunk toward the national rate, so the spread of the published scores understates the spread of the true rates. Subtracting a binomial sampling term here, which is the formula for raw proportions, would subtract the shrinkage a second time.",
    "extract_generated_at": "2026-08-29",
    "is_not": "NOT a ranking, NOT a roster, and NOT a verdict about any provider or about the measure. NOT a readmission measure under another name: this corpus carries no readmission measure at any horizon, and the mortality and complication measures it does carry count deaths and complications rather than returns. NOT a statement about what any measure counts: this world holds no measure specification, no HEDIS specification, no Star Rating methodology and no HRRP methodology, and reading a published result licenses none of them.",
    "mean_sampling_variance": 15.413492359357145,
    "measure_id": "PSI_11",
    "measure_name": "Postoperative respiratory failure rate",
    "observed_mean": 9.32412844036697,
    "observed_variance": 6.590535575942916,
    "on_the_proportion_scale_if_score_is_a_percentage": 0.0022004027935300058,
    "on_the_proportion_scale_if_score_is_a_rate_per_thousand": 0.000022004027935300057,
    "providers_in_the_table": 162,
    "providers_in_the_variance": 109,
    "providers_suppressed": 53,
    "providers_with_a_denominator": 109,
    "providers_with_a_score": 109,
    "published_interval": {
      "asymmetry_median": 0.010000000000001563,
      "coverage_assumed": "95 percent, read as a normal posterior interval on this provider's own rate; a different coverage rescales the sampling component by the square of the quantile ratio and changes nothing else in the derivation",
      "normal_quantile_used": 1.96,
      "published_width_median": 16.39
    },
    "rows_in_the_corpus": 3240,
    "scale_note": "This variance is in the square of the units of `PSI_11`'s own `score` column, whose values here run 2.63 to 21.31 with a mean of 9.3241. Those units are not written in the table: they are CMS's measure specification, which this world does not hold, so this answer states the scale rather than choosing a conversion. measure_reliability computes p(1-p)/n on a PROPORTION, so a variance handed to it must be on the proportion scale: divide by 10,000 if this measure's score is a percentage, or by 1,000,000 if it is a rate per 1,000, both of which are served above. Handing over the unconverted figure is a factor-of-ten-thousand error, and a variance in one measure is not a variance in any other.",
    "score_max": 21.31,
    "score_median": 8.77,
    "score_min": 2.63,
    "shrinkage_share_of_the_true_spread": 0.700485038679213,
    "source": "cms-hospital-compare, gavel vintage 2026-08-03, the published measure table CMS releases for hospitals, cut to one state",
    "source_name": "cms-hospital-compare",
    "state": "NY",
    "window_end": "06/30/2024",
    "window_start": "07/01/2022",
    "world_version": "hammer-coverage-intelligence:2026-10-01+2"
  },
  "redeemed": false,
  "refused": false,
  "tool": "hospital_variance"
}