Cox Proportional Hazard P Value Calculator

Check Cox regression evidence with structured inputs. Compare coefficients, errors, and hazard ratios. Download clear outputs for survival analysis reports.

Calculator Form

Example Data Table

Variable Coefficient Standard Error Z Statistic Hazard Ratio P Value
Treatment -0.430 0.180 -2.389 0.650 0.0169
Age 0.025 0.010 2.500 1.025 0.0124
Risk Score 0.780 0.310 2.516 2.181 0.0119

Formula Used

The calculator uses the Wald test from a fitted Cox proportional hazard model.

Z = (β - β0) / SE

Two-tailed p value = 2 × [1 - Φ(|Z|)]

Hazard Ratio = eβ

Confidence limits for HR = e(β ± Zc × SE)

Here, β is the model coefficient. β0 is the null value. SE is the standard error. Φ is the standard normal cumulative distribution function.

How to Use This Calculator

  1. Enter the variable name from your Cox model output.
  2. Enter the estimated coefficient for that variable.
  3. Enter its standard error from the regression table.
  4. Keep the null coefficient as zero for most tests.
  5. Select the tail type needed for your hypothesis.
  6. Select the confidence level for hazard ratio limits.
  7. Press the calculate button and review the result.
  8. Use CSV or PDF buttons to save the output.

Article

Purpose of the Calculator

A Cox proportional hazard model studies time to an event. It is often used in survival analysis. The event may be death, relapse, churn, failure, or recovery. The model estimates how each variable changes the hazard rate. This calculator focuses on one key output. It estimates the p value for one Cox coefficient.

Why the P Value Matters

The p value helps test whether a model coefficient differs from a null value. The usual null value is zero. A zero coefficient means no log hazard effect. When the p value is small, the data gives stronger evidence against that null. This does not prove causation. It only supports statistical evidence within the fitted model.

Advanced Inputs

The calculator accepts the coefficient, standard error, null coefficient, test tail, and confidence level. These options allow flexible testing. A two-tailed test is common. It checks for any difference from the null. A right-tailed test checks whether the coefficient is greater. A left-tailed test checks whether it is lower.

Hazard Ratio Output

The hazard ratio is easier to read than the coefficient. It is found by exponentiating the coefficient. A hazard ratio above one suggests higher hazard. A value below one suggests lower hazard. The calculator also reports confidence limits. These limits show a likely range for the hazard ratio.

Interpreting Results

A p value below 0.05 is often called statistically significant. That cutoff is only a convention. Good analysis should also consider study design, sample size, censoring, clinical value, and model assumptions. The proportional hazards assumption is especially important. If that assumption fails, the p value may mislead.

Use in Reports

This tool is useful when a Cox regression table is already available. It does not fit the full Cox model from raw survival data. Instead, it calculates the Wald p value from published or exported model values. The CSV and PDF options help save results for reports, checks, and documentation.

FAQs

What is a Cox proportional hazard p value?

It is a probability from a statistical test. It checks whether a Cox model coefficient differs from the null value, usually zero.

Which test does this calculator use?

It uses the Wald test. The coefficient is divided by its standard error. The result is compared with a standard normal distribution.

What is the usual null coefficient?

The usual null coefficient is zero. This means the variable has no estimated effect on the log hazard.

What does the hazard ratio mean?

The hazard ratio is the exponentiated coefficient. Values above one suggest higher hazard. Values below one suggest lower hazard.

Can this fit a Cox model?

No. It calculates a p value from an existing Cox model coefficient and standard error. Raw survival data needs separate modeling software.

Should I use one-tailed or two-tailed testing?

Use two-tailed testing for most reports. Use one-tailed testing only when your hypothesis was defined before analysis.

What does a small p value show?

It shows stronger evidence against the null coefficient. It does not prove importance, causation, or model validity.

Why are confidence limits included?

They show uncertainty around the hazard ratio. They help readers judge effect size, precision, and possible practical meaning.