Inputs
Dataset, covariates, and model options
Tip: start with the example dataset below.
Example data table
Illustrative dataset with two covariates (X1, X2).
| Time | Event | X1 | X2 |
|---|---|---|---|
| 5 | 1 | 0.7 | 12 |
| 6 | 0 | 1.1 | 9 |
| 7 | 1 | 0.2 | 15 |
| 9 | 1 | 1.5 | 7 |
| 10 | 0 | 0.9 | 11 |
| 11 | 1 | 1.8 | 6 |
| 13 | 1 | 0.4 | 14 |
| 15 | 0 | 1.2 | 8 |
Use “Load example” to auto-fill the editable table.
Formula used
The Cox model specifies the hazard at time t for covariates x as h(t|x)=h0(t)·exp(βᵀx), where h0(t) is an unspecified baseline hazard.
Estimates are obtained by maximizing the partial log-likelihood ℓ(β)=∑_{i:δi=1}[βᵀxi − log(∑_{j∈R(ti)} exp(βᵀxj))]. Tied event times can be handled using the Breslow or Efron approximations.
Standard errors come from the inverse observed information matrix. Hazard ratios are HR=exp(β). Baseline survival is estimated from the cumulative baseline hazard S0(t)=exp(−H0(t)).
How to use this calculator
- Choose the number of covariates, ties method, and confidence level.
- Enter covariate names, then select manual entry or CSV upload.
- Provide rows with positive time, event indicator, and covariate values.
- Optionally enable standardization and fill prediction profiles.
- Press Calculate to view results above the form.
- Use the CSV and PDF buttons to export the latest output.
FAQs
1) What does a hazard ratio mean here?
A hazard ratio compares instantaneous event rates between covariate values. HR>1 suggests higher risk, HR<1 suggests lower risk, holding other covariates constant in the model.
2) How should I code the event column?
Use event=1 for observed events and event=0 for right-censored observations. Times must be positive and should use a consistent unit across the dataset.
3) Which ties method should I choose?
Efron generally performs well when many events share the same time. Breslow is simpler and often adequate when ties are rare or sample size is small.
4) Why might the model fail to converge?
Convergence can fail with strong collinearity, too many covariates for the number of events, extreme values, or separation. Try standardization, fewer covariates, more iterations, or cleaner data.
5) What does baseline survival represent?
Baseline survival is the estimated survival for a covariate vector of zeros. If you standardize covariates, this corresponds to average covariate levels after scaling.
6) How is predicted survival computed?
The calculator estimates a cumulative baseline hazard H0(t). For a profile x, it uses S(t|x)=exp(−H0(t)·exp(βᵀx)). Prediction time uses the nearest prior event time.
7) Can I include categorical variables?
Yes. Use numeric coding such as 0/1 indicators or one-hot columns for multi-level categories. Keep the coding consistent and consider standardization only for continuous variables.
8) How accurate are the p-values and intervals?
They are Wald-based using the estimated variance from the information matrix. For small samples or heavy censoring, interpret cautiously and consider validation with a statistical package.