Below, some extra details are shown for the presentation of the testicular cancer model.
Below we discuss the construction of the score chart with continuous predictor values. We consider 2 predictors in the testicular cancer model: postsize and reduction in size.
In the nomogram, a size of 50 mm obtains a score of zero, such that smaller sizes have positive points. In the score chart we can choose a similar approach, but prefer a size of 10 mm corresponding to zero. The 10 mm size is clinically the most interesting, since many centers do not perform surgery for patients with masses smaller than 10 mm. Masses smaller than 10 mm are considered ‘normal size’ by radiologists. We cannot define Post.size with negative numbers however, since we want to study the square root of Post.size. Hence, we subtract – 10mm from Post.size only after the model was fitted. Based on Fig 18E.1 (below), we choose the following sizes to be shown with scores: <5mm, +0.5; 10mm, 0; 20mm, –0.5; 40mm, –1, and 70mm, –1.5 point.
A reduction of 0% is associated with 0 points, which is convenient. The relationship is simply linear (Fig 18E.2, see below). However, in the data we noted that none of the patients had necrosis when there was an increase in mass size during chemotherapy. We choose the following points: <0%: –1, 0%, 0; 50%, 1; 100%, 2 points.
Categorization of the three continuous predictors can also be considered. It should consider the distribution and the predictive effects of the predictors. Strong predictors, with a wide range of predictor values, should have more categories than weaker predictors. For LDHst, we could simply categorize the predictor as normal versus abnormal, as was done for AFP and HCG. (For the latter 2 tumor markers we found no clear benefit of a continuous coding with restricted cubic spline analysesStat Med 2001). For postchemotherapy size, we could use 3 categories: <20mm, 20-49mm, and >=50mm, with 2, 1, and 0 as scores respectively. For reduction in size, we create 3 categories, with increase, 0 – 49% reduction, and >=50% reduction in size having –1, 0 and +1 points respectively. These categorizations can also be checked in a regression analysis, where the coefficient for the categorized predictors should have values around 0.8. Indeed, this is the case when we fit the following model, where coefficients were 0.92, 0.86, 0.66, 0.91, 0.86, and 0.79:
lrm(NEC ~ Teratoma+Pre.AFP+Pre.HCG+PRELDH+POST2+REDUCr, data=n544)
The same procedure was followed for the categorized scores, which resulted in a similar estimate of shrunk.beta (0.79). Using categorized versions of the continuous predictors led to a substantial important drop in c statistic (from 0.839 to 0.808). Hence, categorizing may simplify presentation at the cost of performance. The score chart is shown in Tables 18.extra.