Case study on binary outcome (GUSTO-I)
Calculations of 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 Extra).
Table Extra
Practical exercise
The small subsamples Sample2, sample4, and sample5 provide an excellent opportunity for an exercise on development of a valid prognostic model.
