Cause Specific Hazard Calculator

Enter Interval Data

Use one row per interval: start, end, at risk, cause events, competing events, censored.

Study label

Time unit

Rate multiplier

Confidence level (%)

Decimal places

Interval dataset

Header row is optional. Values can be separated by commas, tabs, or semicolons.

Example Data Table

This sample matches the prefilled dataset and illustrates interval follow-up with one target cause, one competing cause, and censoring.

Start	End	At Risk	Cause Events	Competing Events	Censored
0	1	150	3	2	1
1	2	144	4	1	2
2	3	137	2	3	1
3	4	131	3	2	2

Formula Used

Effective risk set
\( Y_i^* = Y_i - \frac{d_{1i} + d_{2i} + c_i}{2} \)
This midpoint assumption approximates person-time when events and censoring occur uniformly across the interval.

Cause-specific hazard rate
\( h_{1i} = \frac{d_{1i}}{Y_i^* \Delta t_i} \)
Here, \( d_{1i} \) is target-cause events, \( Y_i^* \Delta t_i \) is interval person-time, and \( \Delta t_i \) is interval width.

Poisson standard error and interval estimate
\( SE(h_{1i}) = \frac{\sqrt{d_{1i}}}{Y_i^* \Delta t_i} \), \( CI = h_{1i} \times e^{\pm z/\sqrt{d_{1i}}} \)
When the event count is zero, the upper limit uses \( -\ln(\alpha) / person\text{-}time \).

Cumulative cause hazard and approximate cumulative incidence
\( H_1(t) \approx \sum \frac{d_{1i}}{Y_i^*} \)
\( CIF_1(t) \approx \sum S(t_{i-1}) \times (1 - e^{-h_i \Delta t_i}) \times \frac{h_{1i}}{h_i} \)
These give the accumulated event intensity and the approximate event probability for the target cause under competing risks.

How to Use This Calculator

Enter a study label, time unit, rate multiplier, confidence level, and decimal precision.
Paste one interval per line using six values: start, end, at risk, cause events, competing events, censored.
Submit the form. The results panel appears above the form and includes summary cards and an interval table.
Review consistency notes if the next interval risk set does not match the previous interval after removals.
Export the computed summary and interval table as CSV or PDF for reporting, auditing, or documentation.

Frequently Asked Questions

1) What does cause-specific hazard measure?

It measures the instantaneous event rate for one selected cause among individuals still at risk, while other causes remain possible competing events.

2) Is hazard the same as probability?

No. Hazard is a rate over person-time. Probability is a bounded chance over a period. The calculator reports both hazard-related measures and an approximate cumulative incidence.

3) Why are competing events entered separately?

Competing events remove individuals from the risk set for the selected cause. Ignoring them can distort survival and incidence interpretation in competing-risk settings.

4) Why is person-time estimated with a midpoint adjustment?

When exact event times are unavailable, midpoint withdrawal assumes events and censoring occur evenly within the interval. This provides a practical person-time approximation.

5) What confidence interval method is used?

The tool uses a Poisson log-rate approximation for positive event counts and a one-sided upper bound when the target cause has zero events.

6) Can I use years or weeks instead of months?

Yes. Enter any time label you prefer. Keep the start and end columns in that same unit so person-time and hazard rates stay consistent.

7) What does the cause fraction show?

It shows the share of interval failures attributed to the target cause among all recorded failures in that interval, excluding censoring.

8) When should I avoid this calculator?

Avoid it when you need exact time-to-event modeling with covariates, left truncation, time-varying effects, or formal regression such as Fine-Gray or Cox models.