Chap 11: Extra graphs on selection

Testimation is the underlying problem for biased regression coefficients after stepwise (or other types) of selection. Fig 11.1 illustrated the problem for small subsamples within GUSTO-I.

First row: p<0.05 selection; second row: AIC selection; third row: p<0.5 selection; fourth row: full model with all 8 predictors included. a65: age>65; dia: diabetes; hyp: hypotension; hrt; heart rate > 80; hig: high risk (anterior infarction or previous MI); sho: shock; ttr: time to relief>1 hour. Note that the coefficients in the stepwise selected models should be interpreted with caution: they are based on different sets of selected predictors. The general pattern is however that the coefficients in the stepwise selected models are zero or a value clearly above zero, since predictors with accidentally small effects are not selected. The coefficients follow an approximately normal distribution in the full models.

The problem is smaller in larger samples, as illustrated below (Fig 11 E1 and Fig 11 E2).

First row: p<0.05 selection; second row: AIC selection; third row: p<0.5 selection; fourth row: full model with all 8 predictors included. In the large subsamples, distributions look more normal than in the small subsamples.

First row: p<0.05 selection; second row: AIC selection; third row: p<0.5 selection; fourth row: full model with all 8 predictors included. The testimation bias is much smaller in these samples with substantial sample sizes (>2000 patients, 178 events on average)