Editverse Free Calculator
Cox Proportional Hazards Calculator
Estimate hazard ratios for one or more covariates on time-to-event data, without having to specify the shape of the baseline hazard — with the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
Cox proportional hazards regression models the instantaneous risk of an event (the hazard) as a baseline hazard multiplied by exp(Σβx) for your covariates. It is semi-parametric: it estimates the effect of each covariate as a hazard ratio without assuming a particular shape for how risk changes over time.
A hazard ratio (HR) above 1 means higher risk relative to the reference group; below 1 means lower (protective) risk. It extends a Kaplan-Meier curve, which shows survival for one or two groups, by letting you adjust for multiple covariates at once.
When to Use Cox Regression
Use it for time-to-event (survival) data when you want to compare groups or estimate covariate effects while adjusting for other variables and properly handling censoring — subjects who leave the study or reach its end before the event occurs.
If you only need an unadjusted, descriptive survival curve for one or two groups, a Kaplan-Meier analysis is simpler and sufficient. If your outcome is binary with no meaningful time-to-event component, use logistic regression instead. Not sure which fits? Our interactive Test Selector can help.
Expected: one row per record, time, event(1/0), x1, x2, …
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: one row per record, time, event(1/0), x1, x2, …
library(survival)
df <- read.csv(text = "time,event,x1
{cox_csv}")
summary(coxph(Surv(time, event) ~ ., data = df))User guide
When to use. Estimate hazard ratios for covariates on time-to-event outcomes without specifying the baseline hazard.
Assumptions. Proportional hazards (covariate effects constant over time); non-informative censoring.
Common mistakes. Test the proportional-hazards assumption (e.g. Schoenfeld residuals) before trusting the HRs.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Cox DR. Regression models and life-tables. J R Stat Soc B. 1972;34:187-220.
Worked Examples
Example 1 — Single binary covariate
Ten subjects each have a follow-up time, an event indicator (1 = event observed, 0 = censored), and a binary covariate x1 (for example, treatment vs control). Fitting the model gives a hazard ratio for x1 with its confidence interval and p-value — how much higher or lower the instantaneous risk is in one group relative to the other, averaged across the whole follow-up period.
Example 2 — Adding covariates
If age is added alongside treatment group, the treatment hazard ratio becomes an adjusted HR — the treatment effect after accounting for age. Comparing the unadjusted and adjusted HRs shows how much of the crude association was attributable to age rather than treatment itself.
Assumptions to Check
Proportional hazards. The model assumes each covariate’s hazard ratio is constant over the whole follow-up period. Check this with Schoenfeld residuals before trusting the HRs; a covariate whose effect changes over time needs a time-varying extension.
Non-informative censoring. Subjects who are censored should not have systematically different risk than those who are not — censoring should be unrelated to the event process.
Independent observations. Standard Cox regression assumes one event time per independent subject; correlated or clustered event times need a frailty or robust-variance extension.
Common Mistakes
Not checking the proportional-hazards assumption
A hazard ratio is only a fair summary if the true effect is roughly constant over time. Schoenfeld residual tests or plots should be checked before reporting the HR as final.
Reading an HR as an absolute risk
A hazard ratio of 2 means twice the instantaneous risk in the comparison group, not that twice as many people will experience the event — absolute risk depends on the baseline hazard too.
Ignoring censoring in the data setup
Subjects who leave the study early or reach its end without the event must be coded as censored (event = 0) at their last known time, not dropped or treated as event-free forever.
Over-interpreting a single p-value
With several covariates in the model, report each hazard ratio with its own confidence interval rather than reducing the whole model to significant/non-significant.
Frequently Asked Questions
How is Cox regression different from Kaplan-Meier?
Kaplan-Meier describes survival for one or a few groups with no covariate adjustment. Cox regression estimates the effect of one or more covariates on the hazard, adjusting for each other.
What does a hazard ratio of 1 mean?
No difference in instantaneous risk between the compared groups or per unit of a continuous covariate — the reference value for “no effect” in a Cox model.
How do I handle censored subjects?
Code them as event = 0 with their last observed follow-up time. The model uses this partial information correctly as long as censoring is non-informative.
Does the result match R?
Yes. The calculator fits the model the same way as R’s coxph() from the survival package and shows the exact command so you can reproduce it.
Related Calculators
References
- Cox DR. Regression models and life-tables. J R Stat Soc B. 1972;34(2):187–220.
- Schoenfeld D. Partial residuals for the proportional hazards regression model. Biometrika. 1982;69(1):239–241.
Need This Analysis Done for Your Manuscript?
Our PhD biostatisticians fit and report your survival model — proportional-hazards checks, adjusted hazard ratios, and publication-ready tables with reproducible R output.