Recurrent event analysis¶
Statistical analysis of repeated event times experienced by the same observational unit.
Core Idea¶
Events may reset or continue a common clock, within-unit dependence and terminal events must be modeled, and intensity, rate and gap-time estimands differ. Repeated event histories are represented as counting processes or ordered gap times, while risk sets and dependence structures relate covariates to recurrence frequency or hazard. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of survival analysis. It is the domain-specific identity fixed by the units and follow-up, event definition and ordering, time scale, at-risk intervals, censoring and terminal events, dependence model, covariates, estimand, variance method and diagnostics are explicit.
Scope of Application¶
Recurrent event analysis belongs to survival analysis and is useful where the analyst can specify the typed survival analysis carrier, including objects, relations, parameters, conventions, evidence, and comparison cases, then evaluate the units and follow-up, event definition and ordering, time scale, at-risk intervals, censoring and terminal events, dependence model, covariates, estimand, variance method and diagnostics are explicit. The scope is broad within that domain but bounded by the need for the units and follow-up, event definition and ordering, time scale, at-risk intervals, censoring and terminal events, dependence model, covariates, estimand, variance method and diagnostics are explicit. Conceptual statistical-method identity only; clinical conclusions require qualified analysis.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the units and follow-up, event definition and ordering, time scale, at-risk intervals, censoring and terminal events, dependence model, covariates, estimand, variance method and diagnostics are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Recurrent event analysis can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Recurrent event analysis. Recurrent event analysis compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed survival analysis carrier, including objects, relations, parameters, conventions, evidence, and comparison cases. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the units and follow-up, event definition and ordering, time scale, at-risk intervals, censoring and terminal events, dependence model, covariates, estimand, variance method and diagnostics are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of survival analysis because they reuse the typed survival analysis carrier, including objects, relations, parameters, conventions, evidence, and comparison cases, Repeated event histories are represented as counting processes or ordered gap times, while risk sets and dependence structures relate covariates to recurrence frequency or hazard., and type the carrier, state every parameter and convention in the definition, test that the units and follow-up, event definition and ordering, time scale, at-risk intervals, censoring and terminal events, dependence model, covariates, estimand, variance method and diagnostics are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Recurrent event analysis Domain-specific
Parents (1) — more general patterns this builds on
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Recurrent event analysis is a kind of Statistical Inference Prime
The proposed strict upward parent is
prime:statistical_inference.
Hierarchy paths (4) — routes to 4 parentless roots
- Recurrent event analysis → Statistical Inference → Inductive Reasoning
- Recurrent event analysis → Statistical Inference → Uncertainty
- Recurrent event analysis → Statistical Inference → Probability → Measure → Set and Membership
- Recurrent event analysis → Statistical Inference → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Recurrent event analysis sits in a moderately populated region (49th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Risk, Scheduling & Operational Control (32 abstractions)
Nearest neighbors
- Discrete-time proportional hazards — 0.91
- Logrank test — 0.89
- Recurrence plot — 0.88
- Regression diagnostic — 0.88
- Failure rate — 0.88
Computed from structural-signature embeddings · 2026-09-08