Probability of Survival Calculator

Analyze time based survival with adjustable hazards. Test censoring, treatment effects, exposure shifts, and intervals. Generate charts, exports, and clear summaries for faster reviews.

Calculator Inputs

Starting group size for the analysis.
Constant event rate per time unit.
Total time for the survival estimate.
Risk multiplier relative to baseline.
Additional scaling for exposure intensity.
Percent reduction applied to hazard.
Used for approximate confidence bounds.
Number of rows used in chart and export.
Used for approximate interval coverage.
Reset Form

Plotly Survival Curve

The chart displays the estimated survival curve over the selected time horizon using the adjusted constant hazard assumption.

Example Data Table

Example scenario: cohort 500, baseline hazard 0.04, hazard ratio 1.10, exposure 1.00, protection 15%, censoring 8%, horizon 12, intervals 6.

Time Adjusted Hazard Survival Probability Failure Probability Expected Survivors
2.00 0.037400 0.927927 0.072073 463.96
4.00 0.037400 0.861046 0.138954 430.52
6.00 0.037400 0.799000 0.201000 399.50
8.00 0.037400 0.741425 0.258575 370.71
10.00 0.037400 0.687998 0.312002 344.00
12.00 0.037400 0.638420 0.361580 319.21

Formula Used

This calculator uses a simplified constant hazard survival model. It is useful for instructional statistics, reliability studies, retention analysis, and introductory survival analysis practice.

Adjusted Hazard = Baseline Hazard × Hazard Ratio × Exposure Factor × (1 - Protection Percent / 100)
Survival Probability at time t = exp(-Adjusted Hazard × t)
Failure Probability at time t = 1 - Survival Probability
Expected Survivors = Initial Cohort × Survival Probability
Cumulative Hazard = Adjusted Hazard × Time Horizon
Median Survival Time = ln(2) / Adjusted Hazard
Approximate Confidence Interval = exp(ln(S) ± z × SE(ln(S)))

Censoring is used here to reduce the effective cohort for a simple confidence approximation. This model assumes a constant hazard over time, so it is best treated as an educational estimator.

How to Use This Calculator

  1. Enter the starting cohort size.
  2. Provide the baseline hazard rate per time unit.
  3. Set the total time horizon for prediction.
  4. Adjust the hazard ratio for comparative risk.
  5. Use exposure factor to scale risk intensity.
  6. Enter protection percent to reduce the hazard.
  7. Enter censoring rate for interval estimation.
  8. Choose interval count for table and chart detail.
  9. Select a confidence level.
  10. Click the calculate button to view results.
  11. Download the table as CSV or PDF if needed.

FAQs

1. What does survival probability mean here?

It is the estimated chance that a unit, person, or observation remains event free through the selected time horizon under the model assumptions.

2. Is this a Kaplan Meier calculator?

No. This page uses a simplified constant hazard approach. It is helpful for education, rough planning, and quick scenario testing when full interval event data is unavailable.

3. What does hazard ratio change?

Hazard ratio scales the baseline hazard. Values above one increase risk. Values below one reduce risk relative to the baseline scenario.

4. Why include a protection percent?

Protection percent reduces the hazard after other risk adjustments. It can represent mitigation, shielding, treatment benefit, or any factor that lowers event intensity.

5. What is censoring rate used for?

This version uses censoring to reduce the effective cohort for approximate confidence bounds. It does not rebuild a full nonparametric survival table.

6. Can I use this for reliability studies?

Yes. The model can represent machine, component, subscription, or cohort survival when a constant hazard assumption is acceptable for the study.

7. What if the hazard is zero?

Survival remains one across time, failure stays zero, and median survival becomes infinite because the model predicts no events during the horizon.

8. Are the confidence intervals exact?

No. They are approximate instructional bounds. Use a full survival analysis workflow for research grade inference, censoring structure, and hypothesis testing.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.