# How to interpret hazard ratios for time-segmented variables?

I'm constructing a Cox regression model where patients were randomised to treatment or placebo, and then had certain continuous covariates measured at multiple time points through the course of the study. Risk of developing arthritis is being modelled.

Dependent:
Arthritis status

Independents:
Treatment (ordinal)
CII (continuous, measured at 3 separate timepoints)
GlyCII (continuous, measured at 3 separate timepoints)
HOClCII (continuous, measured at 3 separate timepoints)

As these covariates change over time, I've created time-segmented variables as shown here (SPSS syntax):

COMPUTE T_COV_CII = (T_ < 3) * CII.0 + (T_ >= 3 & T_ < 9) * CII.6 + (T_ >= 9) * CII.12.


Where T_COV_CII is my new variable which uses the measurement at 0 months (CII.0) when time is less than 3 months, the measurement at 6 months (CII.6) when time is between 3 and 9 months, and the measurement at 12 months (CII.12) when time is later than 9 months. As suggested here:http://www-01.ibm.com/support/knowledgecenter/SSLVMB_20.0.0/com.ibm.spss.statistics.help/idh_coxt.htm

Here are my hazard ratios:
Treatment                3.32
T_COV_CII             344.0
T_COV_GlyCII        0.000
T_COV_HOClCII     0.9

I know how to interpret hazard ratios for time-independent variables like my treatment, but how to I interpret hazard ratios of my time-segmented variables? Thanks for your help.

The interpretation is essentially the same as with non-timevarying covariates. The model is $h(t|Z(t)) = h_0(t) \exp(\beta Z(t))$, so $\exp(\beta)$ measures the hazard ratio of having a "current" value of $Z$ that is one unit larger. This effect is modeled as being time-invariant. Given the extreme hazard ratios in your model, your predictors likely have a small dynamic range (so in reality you never see a one unit increase).