Chapter 22: case study on
a binary outcome (GUSTO-I)

Calculating predictions

Predictions can be calculated with a spreadsheet. The programmed formula can roughly be checked by filling in the average values of the patients in GUSTO-I and calculating the predicted probability of 30-day mortality. This should be close to the average observed mortality. Because of the non-linearity in a logistic transformation, the predicted mortality at the mean of the predictor values is not equal to the mean observed mortality: prob(mean covariates) != mean(mortality).
This also holds for other non-linear models such as the Cox proportional hazard regression model.

In the case of the GUSTO-I model, we attempted to fill in an average risk profile. The medians were used for continuous predictors. A problem arises for the truncated variable indicating the effect of systolic blood pressure (SBP: min(SBP, 120)), where the average systolic blood pressure was 130 mm Hg. We filled in 110 mm to reflect the contribution of some patients with lower pressures. This average profile had a predicted probability of 3.4%. This is further from the 7.0% observed mortality than we might anticipate. Estimates for some specific patients are however more reasonable. For example, we may fill in the data for a hypothetical 65-year-old male

• age 65 years

• systolic blood pressure of 100 mm Hg

• Killip class II

• heart rate 75

• anterior infarct location

• no previous MI nor other history other than hypertension

• height 180 cm, weight 90 kg

• treated with tPA after 3 hours

The formula leads to a predicted probability of 12.8%, consistent with the more unfavorable risk profile than the average (Table below).