I'm reading a paper that uses survival regression to examine hospital length of stay, and then assigns variable importance based on the contribution of the deviance for each variable to model fit. They did not give any references for this, and I am having difficulty understanding their conclusion, based on their table.
Their method section states:
Table 2 reports the results of a Weibull parametric survival regression. The exploratory variables were entered in five sequential blocks, based on unadjusted deviance for that block. Diagnostic category was entered first, hospital setting second, age third, race fourth, gender fifth. The Log Likelihood (LL) statistics in Table 2 are reported for each block entry. The deviance statistics, calculated as -2LL, are interpreted as the block’s relative contribution to the model fit. By this criterion, hospital setting made the largest unadjusted contribution to model fit (631.8), followed by age at admission (397.1), diagnosis (371.7), race (97.7) and gender (24).
In their Table 2, they list the deviance statistics as:
- Diagnosis - 1480.7
- Hospital - 1263.6
- Age at Admission - 794.3
- Race - 195.5
- Sex - 48.1
I'm asking for a reference, because a) my understanding is that "variable importance" is a complicated topic, and b) I can see how they calculated their deviances from their log-likelihoods, but I cannot see how they proceeded from their deviance value for Diagnosis (1480.7) in their table to what they stated in their results (the paragraph above, where they refer to the value of Diagnosis as 371.1). Every other deviance value matches what I obtain when I look at the log likelihoods statistics in their table.