Calculator Inputs
Large screens show three columns, smaller screens show two, and mobile shows one.
Example Data Table
| Interval | Dose Level | Biomarker Score | Activity Index | Hazard Ratio | Conditional Survival |
|---|---|---|---|---|---|
| 0 to 3 | 2.00 to 2.45 | 1.20 to 1.44 | 0.70 to 0.61 | 2.8941 | 0.8782 |
| 3 to 6 | 2.45 to 2.90 | 1.44 to 1.68 | 0.61 to 0.52 | 3.3108 | 0.8611 |
| 6 to 9 | 2.90 to 3.35 | 1.68 to 1.92 | 0.52 to 0.43 | 3.7485 | 0.8420 |
| 9 to 12 | 3.35 to 3.80 | 1.92 to 2.16 | 0.43 to 0.34 | 4.2033 | 0.8201 |
Use the example values to test how rising exposures and changing coefficients alter interval risk in a survival analysis setting.
Formula Used
This calculator approximates cumulative hazard over the chosen interval with midpoint numerical integration. It is useful for scenario analysis, teaching, and quick planning with time-varying predictors.
How to Use This Calculator
- Enter the interval start and end times for the follow-up period you want to examine.
- Provide a base hazard rate and, if needed, a starting survival probability and model offset.
- Name each covariate, then enter its starting value, time trend, base coefficient, and time interaction value.
- Choose an integration step count. More steps improve precision but increase calculation time slightly.
- Click the calculate button to display results above the form, including survival, hazards, and covariate contributions.
- Use the CSV and PDF buttons to download a structured copy of your output and interval snapshots.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates interval hazard, survival, event probability, hazard ratios, and expected events for a subject or cohort when predictor values change over time.
2. What are time dependent covariates?
They are predictors whose values can change during follow-up, such as dose, biomarker level, exposure intensity, or adherence over repeated observation periods.
3. Why include the gamma time interaction?
Gamma lets the effect size change with time. That helps model situations where a predictor becomes more important or less important later.
4. Is this a full survival model fitting tool?
No. It does not estimate coefficients from raw patient records. It applies coefficients you provide and calculates projected risk measures over one interval.
5. How should I choose the base hazard?
Use a value from your baseline model, published analysis, or internal estimate. Keep the time unit consistent with your interval and covariate rates.
6. What do more integration steps do?
More steps reduce approximation error because hazard is sampled more often. Use larger values when covariates or coefficients change quickly.
7. Can I use negative coefficients or declining covariates?
Yes. Negative coefficients lower hazard as the covariate rises, and negative change rates model decreasing covariate values over time.
8. Is the projected end survival unconditional?
It multiplies the starting survival by the interval survival estimate. That gives a practical projection, assuming your starting survival is already known.