Glossary
The vocabulary of sequential analysis, with links to the pages that explain each term.
- Alpha spending function
- The cumulative type I error \(\alpha(t)\) allowed to be spent by information fraction \(t\) (Alpha spending).
- Always-valid p-value
- A p-value that remains valid whatever the stopping time; the reciprocal of the running maximum of an e-process (Anytime-valid).
- B-value
- \(B(t) = Z(t)\sqrt t\); a Brownian motion with drift \(\eta\) under the canonical distribution (Information).
- Beta spending
- Spending of the type II error over the looks, used to build futility boundaries (Futility).
- Binding / non-binding futility
- Whether the efficacy boundaries assume the futility rule is always obeyed (binding) or ignore it (non-binding) (Futility).
- Boundary
- The critical value of the test statistic at a look. Crossing the efficacy boundary rejects \(H_0\); crossing the futility boundary stops for lack of effect.
- Canonical joint distribution
- \(Z_k \sim N(\theta\sqrt{I_k}, 1)\) with \(\operatorname{Cov}(Z_j, Z_k) = \sqrt{I_j/I_k}\); the common structure of almost all sequential statistics (Information).
- Christmas-tree correction
- Adjustment of continuous boundaries (such as the triangular test’s) for discrete looks (Triangular tests).
- Conditional power
- Probability of rejecting \(H_0\) at the end, given the current data and an assumed effect (Monitoring).
- Confidence sequence
- Intervals that contain the parameter at all sample sizes simultaneously with probability \(1-\alpha\) (Anytime-valid).
- Data monitoring committee (DMC)
- Independent committee that reviews unblinded interim results and recommends continuation or stopping.
- Drift
- \(\eta = \theta\sqrt{I_{\max}}\), the expected value of the B-value at the end of the study.
- E-value, e-process
- A non-negative statistic with null expectation at most 1; a sequence of them forming a supermartingale (Anytime-valid).
- Expected sample size (ASN)
- Average sample size of a sequential design under a given true effect; also called average sample number.
- Inflation factor
- Ratio of the maximum information of a sequential design to that of the fixed-sample design with the same \(\alpha\) and power.
- Information, information fraction
- \(I = 1/\operatorname{Var}(\hat\theta)\); \(t_k = I_k/I_{\max}\) (Information).
- Inner wedge
- Futility region \(|Z_k| < a_k\) of a two-sided design (Futility).
- Look (interim analysis)
- One of the \(K\) analyses of the accumulating data.
- MaxSPRT
- Maximised sequential probability ratio test for safety surveillance (MaxSPRT).
- Median-unbiased estimate
- Estimate whose sampling distribution has median \(\theta\), computed under the stagewise ordering (Inference).
- Predictive power (predictive probability)
- Conditional power averaged over the posterior distribution of the effect (Monitoring, Bayesian).
- Repeated confidence interval
- Sequence of intervals with simultaneous coverage across looks (Inference).
- SPRT
- Wald’s sequential probability ratio test (SPRT).
- Stagewise ordering
- Ordering of outcomes by stopping look, then by \(Z\), used for exact p-values and confidence intervals after a sequential test (Inference).
- Stochastic curtailment
- Stopping when conditional power makes the final decision nearly certain.
- Triangular test
- Whitehead’s closed sequential test with straight-line boundaries on the \((V, Z)\) plane (Triangular tests).