based on your research question. Because doing this loses the granularity of the data, this test may

be less efficient at detecting gradual trends across the whole age range.

The log-rank test doesn’t let you analyze the simultaneous effect of different predictors. If

you try to create subgroups of participants for each distinct combination of categories for more

than one predictor (such as three treatment groups and three diagnostic groups), you will quickly

see that you have too many groups and not enough participants in each group to support the test. In

this example — with three different treatment groups and three diagnostic groups — you would

have 3 × 3 groups, which is nine, and is already too many for a log-rank test to be useful. Even if

you have 100 participants in your study, dividing them into nine categories greatly reduces the

number of participants in each category, making the subgroup estimate unstable.

Use survival regression when the outcome (the Y variable) is a time-to-event variable, like

survival time. Survival regression lets you do all of the following, either in separate models or

simultaneously:

Determine whether there is a statistically significant association between survival and one or more

other predictor variables

Quantify the extent to which a predictor variable influences survival, including testing whether

survival is statistically significantly different between groups

Adjust for the effects of confounding variables that also influence survival

Generate a predicted survival curve called a prognosis curve that is customized for any particular

set of values of the predictor variables

Grasping the Concepts behind Survival

Regression

Note: Our explanation of survival regression has a little math in it, but nothing beyond high school

algebra. In laying out these concepts, we focus on multiple survival regression, which is survival

regression with more than one predictor. But everything we say is also true when you have only one

predictor variable.

Most kinds of regression require you to write a formula to fit to your data. The formula is easiest to

understand and work with when the predictors appear in the function as a linear combination in which

each predictor variable is multiplied by a coefficient, and these terms are all added together (perhaps

with another coefficient, called an intercept, thrown in). Here is an example of a typical regression

formula:

. Linear combinations (such as c2x2 from the example

formula) can also have terms with higher powers — like squares or cubes — attached to the predictor

variables. Linear combinations can also have interaction terms, which are products of two or more

predictors, or the same predictor with itself.