# Articles

### NPH background

An introduction to non-proportional hazards.

- Non-proportional effect size in group sequential design
- Power for delayed effect scenarios
- Computing bounds under non-constant treatment effect
- Numerical integration non-proportional effect size in group sequential design
- Futility bounds at design and analysis under non-proportional hazards
- Approximating an arbitrary survival distribution

### Spending bound

An introduction to spending bounds.

### Design by AHR

Develop designs for time-to-event endpoints by average hazard ratio.

- Design using average hazard ratio
- Average hazard ratio and sample size under non-proportional hazards
- Computing expected events by interval at risk
- Summarize group sequential designs in gt tables
- Canonical joint distribution of Z-score and B-values under null and alternative hypothesis
- Statistical information under null and alternative hypothesis

### Design for binary endpoints

Develop designs for binary endpoints.

### Key functions in gsDesign2

- ahr: computes AHR under NPH assumptions and (stratified) populations
- expected_accrual: computes the expected cumulative enrollment (accrual) given a set of piecewise constant enrollment rates and times
- expected_event: compute expected number of events at 1 time point
- expected_time: compute time when a targeted number of events is made
- fixed_design_*: compute sample size/power of a fixed design
- gs_b: specify fixed boundaries in group sequential designs
- gs_info_ahr: compute statistical information by the AHR method
- gs_power_npe: derives bounds and crossing probabilities for group sequential designs under NPH assumptions
- Computing spending boundaries in group sequential design
- summary & as_gt: summarize group sequential design