Solved – Interaction in Survival analysis

cox-modelinteractionsurvival

I am a physician and clearly not a statistician (I try to understand why and how to perform the right analysis, but I don't understand the formulas). I am using SPSS v.19 in analyzing my data.
I try to analyze if a biomarker is associated with an increased mortality risk in a subpopulation from my study and I don't know if my analysis is correctly performed.

This the result (part of it) for the entire population:
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This is for the one of the subgroups:
enter image description here

This is for the other subgroup:
enter image description here

In this situation, I wanted to see if the association with the mortality risk in the second group was truly significant and I performed a Cox survival analysis with an interaction term: Biomarker value*LOT_1:
enter image description here

Is this analysis correct? And if it is, from this output I should understand that there is no statistically significant association with mortality for the studied biomarker in the second subgroup (no difference for this association in between the two subgroups)?
Thank you.

LE: This is the output including also the main effect of LOT_1.
enter image description here

Best Answer

You should almost never include an interaction without both main effects.

In your final table, the interaction and the LOT variable are highly significant and Biomarker is not sig and is also small.

In summary, this means that Biomarker has little effect when LOT1 = 0 (which would be that it is the other lot) but has more of an effect when LOT1 = 1.

(The above assumes that LOT1 is coded 0-1)

Related Solutions

Solved – Sample size and cross-validation methods for Cox regression predictive models

You have nicely described the problem and have set it up well in a number of ways. I wasn't clear on the definition of "prognostic score", but it is very unlikely that a 2-level score is clinically helpful. It is important to adjust for all pertinent available clinical variables, based on expert opinion when choosing them. Here are some opportunities for improvement:

10-fold cross-validation is unstable and needs to be repeated 100 times to obtain adequate precision (or use the Efron-Gong optimism bootstrap with 400 resamples; both of these are available in the R rms package)
Dividing the signal into "good" and "bad" driven by ROC curves is a popular technique but was not based on any good statistical principles. Any biomarker worth its salt should have a dose-response relationship, and division into two very arbitrary groups is unnecessary, misleading, and information- and power-losing.
ROC curves have absolutely nothing to offer in this context
Choosing cutpoints on the biomarkers is a statistical disaster. Among other things it fails to recognize that mathematically if any cutpoints are useful they can only be on the back end, not on the covariate end, because the cutpoint for each marker depends on the absolute value of all the other marker values for a patient.
Stepwise regression without penalization is not reliable. In your setup there is no reason not to put all the markers into one model and to do a likelihood ratio $\chi^2$ test to test the value they add to clinical variables.
A good alternative to 5. is to do a redundancy analysis or variable clustering of the biomarkers to reduce their number before relating them to the outcome.
If your sample size were larger you could allow all the variables to enter into the model nonlinearly using regression splines. Occasionally allowing one biomarker to be smooth and nonlinear doubles its value over forcing linearity.
Let the log likelihood, which is an optimal scoring rule (penalized likelihood would be even better) do its job. Don't spend time on improper accuracy scoring rules.
Consider using the "adequacy index", based on log likelihood, for describing the utility of the biomarkers, as described in my book Regression Modeling Strategies.

Solved – How to deal with differences in subgroup analysis but no significant interaction

One problem is that you are using "significance" as your criterion. Look at the effect size.

This can easily happen if the effect for men and women is in the same direction, but stronger for men. The effect size of the interaction relates to the difference in effect size between women and men.

Indeed, it could be (because of the nature of significance) that the effect for men and women is almost identical.

Here's an example: Interaction not sig., effect for males sig., effect for females not sig.

#set up model
set.seed(19749)
sex <- c(rep('M', 500), rep('F', 500))
x1 <- rnorm(1000)
y <- 1.2*x1 + 1*(sex == 'M') + 1.5*x1*(sex == 'M') + rnorm(1000, 0, 10)
m1 <- lm(y~x1 + sex + sex*x1)

#significant interaction
summary(m1)

#subgroup of men
m2 <- lm(y[1:500]~x1[1:500])
summary(m2)

#subgroup of women
m3 <- lm(y[501:1000]~x1[501:1000])
summary(m3)

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