Discrete-time proportional hazards¶

A grouped-duration model whose conditional event probability in each interval is linked to covariates so their effects correspond to proportional underlying hazards or a specified discrete analogue.

Version: v1 · 2026-09-08 · History
Domain-specific #: 4211
Origin domain: survival analysis
Subdomain: discrete duration models

Core Idea¶

Discrete-time proportional hazards models represent interval-specific failure risk as a baseline time effect modified multiplicatively on an underlying hazard scale by covariates. Person-period records encode whether failure occurs in each at-risk interval; a link function separates baseline duration dependence from a constant covariate effect and yields a binary-response likelihood. 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.

Scope of Application¶

Discrete-time proportional hazards belongs to survival analysis and is useful where the analyst can specify subjects at risk, discrete time intervals, event indicator and censoring, baseline interval hazard, covariates, complementary-log-log or other link, proportional effect coefficients and likelihood, then evaluate risk sets, interval grouping, censoring and link are fixed and covariate effects retain their declared time-constant scale. The scope is broad within that domain but bounded by the need for risk sets, interval grouping, censoring and link are fixed and covariate effects retain their declared time-constant scale. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making risk sets, interval grouping, censoring and link are fixed and covariate effects retain their declared time-constant scale 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 Discrete-time proportional hazards 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 Discrete-time proportional hazards. Discrete-time proportional hazards 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: subjects at risk, discrete time intervals, event indicator and censoring, baseline interval hazard, covariates, complementary-log-log or other link, proportional effect coefficients and likelihood. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express risk sets, interval grouping, censoring and link are fixed and covariate effects retain their declared time-constant scale independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of survival analysis because they reuse subjects at risk, discrete time intervals, event indicator and censoring, baseline interval hazard, covariates, complementary-log-log or other link, proportional effect coefficients and likelihood, Person-period records encode whether failure occurs in each at-risk interval; a link function separates baseline duration dependence from a constant covariate effect and yields a binary-response likelihood., and type the carrier, state every parameter and convention in the definition, test that risk sets, interval grouping, censoring and link are fixed and covariate effects retain their declared time-constant scale, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Discrete-time proportional hazards Domain-specific

Parents (1) — more general patterns this builds on

Discrete-time proportional hazards is a kind of Statistical Inference Prime

The proposed strict upward parent is prime:statistical_inference.

Hierarchy paths (4) — routes to 4 parentless roots

Discrete-time proportional hazards → Statistical Inference → Inductive Reasoning

Show alternative paths (3)

Neighborhood in Abstraction Space¶

Discrete-time proportional hazards sits in a moderately populated region (50^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Risk, Scheduling & Operational Control (32 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08