What are the advantages and disadvantages of using stratified Cox models?

1 What is the proportional hazards assumption?

One of the key assumptions of the standard Cox model is that the hazard ratio between two subjects with different values of a covariate is constant over time. This is called the proportional hazards assumption, and it implies that the covariate has a multiplicative effect on the hazard rate. However, this assumption may not hold in some situations, such as when the covariate has a time-varying effect, or when there are interactions between the covariate and other factors. If the proportional hazards assumption is violated, the Cox model may produce biased or misleading results.

2 How can stratification help?

Stratification is a technique that can address the violation of the proportional hazards assumption by allowing each group of subjects to have its own baseline hazard function. This means that the hazard rate of a subject depends not only on the covariate, but also on the stratum to which the subject belongs. For example, you can stratify by gender, age group, or treatment arm, and estimate the effect of a covariate within each stratum. By doing so, you can account for the heterogeneity among the strata, and relax the assumption of proportional hazards across the whole population.

3 What are the advantages of stratified Cox models?

Stratified Cox models have several advantages over the standard Cox model. For instance, they can handle situations where the proportional hazards assumption is violated within strata, but not across strata, such as when the effect of a covariate differs by gender. Additionally, they can improve the efficiency and precision of the estimates by reducing the variability of the baseline hazard function and increasing the sample size within each stratum. Furthermore, stratified Cox models can test for interactions between the covariate and the strata, as well as provide more clinically relevant information by showing how the covariate affects different subgroups of subjects.

4 What are the disadvantages of stratified Cox models?

Stratified Cox models have certain limitations and drawbacks that must be taken into consideration. For instance, they require a sufficient number of events and subjects within each stratum to ensure the stability and reliability of the estimates. If the strata are too small or too few, the stratified model may not be as powerful or accurate. Additionally, stratified models do not provide a global measure of the effect of the covariate, only within-stratum estimates. This may make it challenging to compare or summarize the results across different strata, or to generalize them to a broader population. Furthermore, stratified models do not account for possible confounding or modifying effects of other covariates that are not included in the stratification. Therefore, if you stratify by gender but ignore other factors that may affect the hazard rate, such as smoking or comorbidities, you may still obtain biased or inconsistent estimates.

5 How to choose between stratified and standard Cox models?

When deciding between stratified and standard Cox models, several factors must be taken into account. These include the research question and hypothesis, data availability and quality, and model assumptions and diagnostics. If the goal is to estimate the effect of a covariate within specific subgroups of subjects or to test for interactions between the covariate and the strata, then stratification may be more appropriate. Likewise, if there is enough data to create meaningful and balanced strata, or if there is evidence or suspicion that the proportional hazards assumption is violated within or across strata, then stratification may be more feasible and reliable. On the other hand, if the goal is to estimate the effect of a covariate across the whole population or to test for the significance of the covariate, or if there is limited or sparse data, then the standard model may be more suitable. Additionally, if there is no reason or indication that the proportional hazards assumption is violated, then stratification may be more redundant and wasteful.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?