Table of Contents

## What do you do when proportional hazards assumption is violated?

Sometimes the proportional hazard assumption is violated for some covariate. In such cases, it is possible to stratify taking this variable into account and use the proportional hazards model in each stratum for the other covariates.

## How do you test the proportional hazards assumption?

The proportional hazards (PH) assumption can be checked using statistical tests and graphical diagnostics based on the scaled Schoenfeld residuals. In principle, the Schoenfeld residuals are independent of time. A plot that shows a non-random pattern against time is evidence of violation of the PH assumption.

## What is Cox proportional hazards model assumptions?

The Cox proportional hazards model makes two assumptions: (1) survival curves for different strata must have hazard functions that are proportional over the time t and (2) the relationship between the log hazard and each covariate is linear, which can be verified with residual plots.

## What are Schoenfeld residuals?

Schoenfeld residuals. The Schoenfeld residual is defined as the covariate value for the individual that failed minus its expected value. (Yields residuals for each individual who failed, for each covariate).

## Do I need to care about the proportional hazard assumption?

An important question to first ask is: *do I need to care about the proportional hazard assumption?* – often the answer is no. The proportional hazard assumption is that all individuals have the same hazard function, but a unique scaling factor infront.

## How do you interpret Cox regression?

The coefficients in a Cox regression relate to hazard; a positive coefficient indicates a worse prognosis and a negative coefficient indicates a protective effect of the variable with which it is associated.

## How do you interpret hazard ratios?

It is the result of comparing the hazard function among exposed to the hazard function among non-exposed. As for the other measures of association, a hazard ratio of 1 means lack of association, a hazard ratio greater than 1 suggests an increased risk, and a hazard ratio below 1 suggests a smaller risk.

## How does Cox regression work?

In the context of an outcome such as death this is known as Cox regression for survival analysis. The coefficients in a Cox regression relate to hazard; a positive coefficient indicates a worse prognosis and a negative coefficient indicates a protective effect of the variable with which it is associated.

## What is a martingale residual?

Martingale residuals take a value between [1,−∞] for uncensored observations and [0,−∞] for censored observations. Martingale residuals can be used to assess the true functional form of a particular covariate (Thernau et al. (1990)).

## What do hazard ratios mean?

The hazard ratio is an estimate of the ratio of the hazard rate in the treated versus the control group. The hazard rate is the probability that if the event in question has not already occurred, it will occur in the next time interval, divided by the length of that interval.

## What does violation of proportional hazards mean?

The fundamental assumption in the Cox model is that the hazards are proportional (PH), which means that the relative hazard remains constant over time with different predictor or covariate levels. Violation of the PH assumption may lead to biased effect estimates in Cox regression analysis.