## Scores to probabilities of outcome

Most of the current scoring systems are developed either to yield a score and then an estimate of the probability of a given outcome (TISS, APACHE II, APACHE III, SAPS II) or to yield directly an estimate of the probability of a given outcome (MPM II). The outcome measure which has been the main focus in adult intensive care is hospital mortality, defined as death before discharge from hospital following intensive care.

The weights or coefficients associated with the factors in scoring systems are derived from analysis of large databases of intensive care patients (usually thousands of patients) containing information on both the patient factors required for the scoring system and the outcome, survival, or death before discharge from hospital following intensive care.

For each scoring system, the association between the independent variables (treatments, patient characteristics, physiological measurements) and the dependent variable (death before discharge from hospital following intensive care) is described in the form of a mathematical equation, known as a multiple logistic regression model. APACHE II, APACHE III, and SAPS II sum weights for some or all of the independent variables into a score before incorporation into the model. The model describes the strength of the association of each of the different independent variables with the dependent variable, while allowing for the effect of all the other independent variables in the same model.

Once estimated, the model can be applied to a group of intensive care patients for whom data are available on the independent variables to estimate the expected hospital death rate. By applying the model, the probability of death before discharge from hospital following intensive care can be estimated for each patient and summed for all patients to yield the expected hospital death rate for the whole group of patients.

The expected hospital death rate can then be compared with the actual hospital death rate. This is often displayed in the form of a ratio of actual to expected hospital death rates, referred to as the standardized mortality ratio (SMR). When the actual hospital death rate is greater than the expected the resultant SMR is greater than 1.0, and when the actual hospital death rate is less than expected the resultant SMR is less than 1.0. Confidence intervals can be calculated to determine whether the difference from 1.0 is statistically significant ( Raopogort.e,L§L 1994).

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