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Statistical Models for Prognostication
Author Bio
Introduction
Predictions: Statistical Models
Insight: Statistical Models
Ingredients: Statistical Models
Theoretical Aspects
Central Concepts
Regression Models
Currently selected section: Problems: Regression
Practical Advice
Example 1
Example 2
Chapter 8: Statistical Models for Prognostication: Problems with Regression Models
        

You Answered:

Selection A1

INCORRECT

More than 1 model is considered in the model specification. The correct answer is either (c) 210 or (d) 1024.

  • When it is pre-specified that 4 predictors have to be chosen, the number of combinations is given by the formula k!/((k-n)!n! with k=10 covariables and n=4 predictors selected:10!/(10-4)!4!= 10x9x8x7 / (4x3x2) = 210.
  • When it is NOT pre-specified that 4 predictors have to be chosen, models with 0, 1, 2, … , 10 predictors are in fact considered. Every covariable can or cannot be selected, leading to 2^10 = 1024 combinations of predictors in the model. This large number indicates that a kind of fishing expedition was set up to catch the one model with 4 predictors. This model may well be determined too much by chance findings in the particular data set under study (i.e. be "overfitted"). It may not validate well in new patients unless a very large data set was used to construct the model.

 

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