# Proportional hazards fit

A semi-parametric model that describes the relationship between a time to event response variable and one or more explanatory variables using a hazard function.

The Cox proportional hazard model is expressed as a hazard function h_{0}(t) +
exp(∑β_{i}X_{i}). The formula expresses the hazard at time t for an
individual with a given set of explanatory variables as the product of two quantities. The
first quantity is h_{0}(t), the baseline hazard function. The second quantity is
the exponent of the linear sum β_{i}X_{i} where the sum is over the p
explanatory variables. An important feature of the proportional hazards model is that the
baseline hazard function is a function of t but does not include the Xs. Therefore, it is
unnecessary to specify the form of the baseline function in estimating the parameters.
Also, the parameters in the second quantity are dependent only on the Xs and are
independent of time. The unknown model parameters are estimated using maximum-likelihood
estimation.

**Hazard ratio estimates**

Hazard ratios are the increase or decrease in the hazard associated with a change of the predictor, all other predictors been held constant.**Baseline survival function**

A baseline survivual function is an estimate of h_{0}(t) in a proportional hazards model.**Effect of model hypothesis test**

A likelihood ratio or Wald X² test formally tests the hypothesis of whether the model fits the data better than no model.**Effect of term hypothesis test**

A likelihood ratio or Wald X² test formally tests the hypothesis of whether a term contributes to the model.

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Kaplan-Meier survival function
- Plotting a Kaplan-Meier survival curve
- Equality of survival functions test
- Tests for the equality of survival functions
- Comparing two or more survival functions
- Proportional hazards fit
- Fitting a proportional hazard model
- Hazard ratio estimates
- Estimating hazard ratios
- Baseline survival function
- Effect of model hypothesis test
- Effect of term hypothesis test
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023