STREAM-SMR: Sequential Bayesian state-space monitoring of standardized mortality ratios — a simulation comparison with risk-adjusted CUSUM and EWMA
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Background
Sequential monitoring of risk-adjusted mortality in intensive care typically relies on alarm-generating control charts — the risk-adjusted CUSUM, EWMA, or VLAD. These charts signal deterioration but do not return what clinicians and registry stewards ultimately need to interpret: a calibrated, continuously updated estimate of the standardized mortality ratio (SMR) itself.
Methods
STREAM-SMR is a conjugate gamma–Poisson dynamic generalized linear model in which the latent log-SMR evolves through a discount factor δ and the alarm statistic is the posterior exceedance probability P(SMR > 1). The construction is closed-form, exact for zero-death months, and computationally trivial at registry scale. Under a protocol frozen before any evaluation runs and calibrated to published national ICU registry aggregates, we compared STREAM-SMR (δ in {0.90, 0.95, 0.97}) with the risk-adjusted CUSUM and risk-adjusted EWMA across three facility-volume strata (50, 200, and 800 annual admissions) and five change scenarios (sustained steps, gradual drift, transient deterioration, and improvement). All methods were Monte-Carlo-calibrated to a common 5% false-alarm probability over a 60-month horizon, with 1,000 replications per cell.
Results
At δ = 0.90, STREAM-SMR matched the detection frontier of the risk-adjusted CUSUM to within one to two months across sustained-shift scenarios — median delay for an SMR step to 1.5 of 6 versus 5 months in large facilities, 14 versus 14 in medium, and 20 versus 22 in small — while returning filtered SMR estimates whose 95% credible intervals held ≥ 91% empirical coverage in every scenario–stratum cell. Empirical false-alarm probabilities were close to the 5% nominal target for all methods (range 0.035–0.066). For a three-month transient deterioration, detection was faster with STREAM-SMR conditional on occurring, but overall detection probability favored the CUSUM in large facilities.
Conclusions
STREAM-SMR unifies monitoring and estimation in a single Bayesian object: for a detection-delay premium of at most one to two months against the theoretically optimal CUSUM, it returns an interpretable, uncertainty-quantified SMR trajectory at every time point. The discount factor is an explicit dial between estimate smoothness and detection speed. Simulation code and the frozen protocol are publicly archived.
