Longitudinal Cox Regression analysis?

Question

So I have a dataset that is currently in wide format and I have multiple waves recording data such as age, death, diagnosis etc. I have done a simple Cox regression analysis:

summary(fit1 <- survfit(Surv(data$surv_time, data$status) ~ 1, data = data, conf.int=0.95))
plot(fit1, xlab = "Time to Dementia (years)", ylab = "Dementia Probability", main="Kaplan-Meier Estimate of S(t) for data")

cox1 <- coxph(Surv(dat$surv_time, dat$status) ~ sex + age_b, data = dat)
summary(cox1)

Where I have created my variable for survival/follow up time and also a status variable that records the desired outcome for each individual as equal to 1.

So my first question is, how would I go about doing a multivariate Cox regression if I wanted to i.e. adjust for a categorical variable that records educational attainment that is currently recorded in wide format (education_wave_1, education_wave_2, and so on) would I simply have to convert this variable into long format? Would adjusting for a variable in this way be correct and would I need to take into account the fact that this variable was recorded at different time points somehow? Or, would I just need to adjust for the variables at baseline?

so my other question is, how would I go about doing a longitudinal cox regression model? Is there such a thing?

Hope the post somewhat makes sense, thank you!

Answer 1

You certainly can do Cox regression with time-dependent covariates, as explained for R in this vignette. You need to specify, for each data line, a 3-part Surv() object that represents (start_time, stop_time, status at stop_time) along with all covariate values that hold during that time frame for a patient, and thus you must add an additional data line each time that a patient has a change in a covariate value. Tools for changing from wide format to this long format and how to proceed with such analyses are explained in the linked vignette.

Whether you should do this, however, is another question. Remember that the Cox model assumes that the hazard of a change in status at any time is a function of the covariate values at that particular time. As you seem to be modeling dementia, with a presumably long time course before diagnosis, it's not clear how well that assumption would hold for covariates whose values change comparatively rapidly during the course of your study. Next, models with time-dependent covariates can't always be used reliably for predictions. The fact that a patient has survived (in your case, survival without diagnosis) to a particular point in time and now has an updated value of a covariate is by itself related to longer such survival, a type of potential survivorship bias. Furthermore, if you are modeling dementia it seems that you should be including death from other causes as a competing risk. So before you continue with this analysis, and particularly if you choose to go down the path of time-dependent covariates, you should consult closely with a statistician who has expertise in such matters.

Also, one terminology note: what you are proposing with multiple predictors (whether constant in time or time-varying) is best called "Cox multiple regression." "Multivariate" is terminology best reserved for multiple outcomes rather than multiple predictors, although your usage does show up frequently in the literature (and I am to blame for at least one such instance myself).