How do you handle time dependent covariates in cox model?

1 What are time dependent covariates?

Time dependent covariates are variables that influence the hazard or risk of an event, such as death or failure, but also change over time. For example, blood pressure, weight, smoking status, and treatment exposure are all possible time dependent covariates in survival analysis. Time dependent covariates can be classified into two types: internal and external. Internal covariates are those that depend on the survival time of the individual, such as age or disease progression. External covariates are those that are independent of the survival time of the individual, such as environmental factors or policy changes.

2 Why are time dependent covariates problematic?

Time dependent covariates pose a challenge for cox regression because they violate the proportional hazards assumption, which states that the hazard ratio between two groups of individuals is constant over time. If the covariates change over time, the hazard ratio may also change over time, leading to biased and inconsistent estimates of the regression coefficients and the survival function. Moreover, time dependent covariates introduce additional complexity and uncertainty in the data structure, as they may be measured at different time points, with different frequencies, and with different levels of accuracy and completeness.

3 How do you handle time dependent covariates in cox model?

When handling time dependent covariates in a cox model, the type and nature of the covariates, the research question, and the available data must be taken into consideration. The most common methods include time splitting, extended cox model, and stratified cox model. Time splitting involves dividing the follow-up time into discrete intervals and creating a separate record for each interval. This is a simple and flexible method, but can lead to a loss of information and efficiency if the intervals are too short or long. An extended cox model uses a mathematical function to model the relationship between the covariate and survival time, such as a polynomial or a piecewise constant function. This method is more accurate but requires more assumptions and parameters. Stratified cox models create subgroups of individuals based on values or categories of the time dependent covariate, fitting a separate cox model for each subgroup. This is useful for dealing with discrete or categorical time dependent covariates, however it may reduce sample size and power of the analysis.

4 How do you choose the best method for your data?

Choosing the best method for handling time dependent covariates in cox model is complicated, as each method has its own advantages and limitations. The choice may depend on the research question, data quality, and statistical software. However, it is important to explore the data and understand the characteristics and patterns of the time dependent covariates. After applying any method, assumptions should be checked and results validated. If possible, it is advisable to compare different methods and evaluate their performance and robustness with criteria such as Akaike information criterion (AIC), Bayesian information criterion (BIC), or likelihood ratio test.