## How do you test proportional hazards assumptions?

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 do you do when the 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 are Cox-Snell residuals calculated?

The Cox-Snell residual for this individual, evaluated at the censored survival time, is then given by roi = К;(t) = – log ŝi(ti), where Hi(t) and Si(tk) are the estimated cumulative hazard and survivor functions, respectively, for the ith individual at the censored survival time.

**What are martingale residuals?**

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)).

#### How are Cox Snell residuals calculated?

**What is Cox Zph?**

The cox. zph function will test proportionality of all the predictors in the model by creating interactions with time using the transformation of time specified in the transform option. In this example we are testing proportionality by looking at the interactions with log(time).

## What is the Schoenfeld residuals test?

In simple words hazard for any individual is a fixed proportion of hazard for any other individual. The Schoenfeld Residuals Test is analogous to testing whether the slope of scaled residuals on time is zero or not. If the slope is not zero then the proportional hazard assumption has been violated.

**What is the Schoenfeld test in statistics?**

Definition: Schoenfeld Residuals Test. If the slope is not zero then the proportional hazard assumption has been violated. In this test, there is separate residual for each individual for each covariate, and the covariate value for individuals that failed minus its expected value is defined as Schoenfeld residuals.

### What are some common residual plot types?

Common Residual Plots • Plot martingale residuals vs continuous covariates – to check functional form of covariates • Plot deviance residuals vs Observation # – to check for outliers • Plot Schoenfeld residuals for each covariate, vs Time or log(Time)