Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Accelerated Failure Time Model
The Accelerated Failure Time model is a parametric regression approach to survival analysis — formally reviewed and advocated by L. J. Wei in 1992 — in which covariates act as multiplicative factors that directly stretch or compress the tim...
Bioequivalence Analysis
Bioequivalence Analysis is a regulatory-grade statistical framework used to determine whether a test drug formulation (generic or reformulated) delivers the active ingredient to the systemic circulation at a rate and extent comparable to a...
Competing Risks Analysis
Competing risks analysis, formalized by Fine and Gray in 1999, is a survival analysis framework for settings where a subject can experience one of several mutually exclusive event types. The key quantity is the cumulative incidence function...
Cox Regression
Cox proportional hazards regression, introduced by D. R. Cox in 1972, is a semi-parametric model that estimates how one or more covariates affect the hazard — the instantaneous rate of experiencing an event — while leaving the baseline haza...
DeepHit
DeepHit is a deep neural network framework for survival analysis with competing risks. Introduced by Lee et al. in 2018, it extends DeepSurv to handle settings where multiple, mutually exclusive events can occur, such as disease-specific mo...
DeepSurv
DeepSurv is a deep neural network approach to survival analysis that learns personalized survival distributions directly from data. Introduced by Katzman et al. in 2018, it extends the Cox proportional hazards model using deep learning to c...
Emax Model
The Emax model is a nonlinear pharmacodynamic model that describes the relationship between drug concentration and biological effect. Introduced by Holford and Sheiner in 1981, it characterizes dose-response curves using three fundamental p...
Endemic Compartmental Models
Endemic compartmental models extend the classical SIR framework to capture diseases that persist indefinitely in a population rather than burning out after a single epidemic wave. The SIS model allows recovered individuals to return to susc...
Frailty Model
The shared frailty model, introduced by Vaupel, Manton, and Stallard in 1979, extends standard survival regression by incorporating a random effect — the 'frailty' — that captures unobserved heterogeneity among subjects or clusters. When su...
Joint Model for Longitudinal and Survival Data
The joint model for longitudinal and time-to-event data, formalised by Tsiatis and Davidian in 2004 and extended comprehensively by Rizopoulos in 2012, simultaneously estimates a mixed-effects model for repeatedly measured biomarkers and a...
Kaplan-Meier
The Kaplan-Meier estimator, introduced by Kaplan and Meier in 1958, is a non-parametric method that estimates the survival curve — the probability of remaining event-free over time — from right-censored time-to-event data. The log-rank test...
Landmark Analysis
Landmark analysis, introduced by Anderson, Cain, and Gelber in 1983, estimates conditional survival probabilities for subjects who are still at risk at a pre-specified point in time — the landmark — rather than at study entry. It was develo...
Log-Rank Test
The log-rank test, developed by Nathan Mantel in 1966, is a non-parametric hypothesis test that compares the overall survival experience of two or more groups throughout the entire follow-up period. It is the standard companion to Kaplan-Me...
Mixture Cure Model
The mixture cure model, first proposed by Boag in 1949 for cancer survival data, is a parametric survival model that explicitly accounts for a fraction of subjects who will never experience the event of interest — the so-called cured or imm...
Multi-State Model
The multi-state model is a generalised survival framework, formalised in the work of Andersen and Keiding and brought to wide biostatistical practice by Putter, Fiocco and Geskus (2007), that models individuals moving through multiple disti...
Nelson-Aalen Estimator
The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function from right-censored time-to-event data. Developed by Wayne Nelson for reliability hazard plotting in 1972 and placed on a rigorous counting-process f...
Pharmacokinetic Compartment Model
The pharmacokinetic compartment model represents the body as one or more hypothetical compartments interconnected by first-order rate processes, describing how a drug is absorbed, distributed, and eliminated over time. Systematized by Gibal...
Population Pharmacokinetics
Population Pharmacokinetics (PopPK) is a nonlinear mixed-effects modeling framework that characterizes how drugs are absorbed, distributed, metabolized, and eliminated across a patient population, estimating both typical population paramete...
Random Survival Forest
Random Survival Forest (RSF), introduced by Ishwaran, Kogalur, Blackstone, and Lauer in 2008, is an ensemble machine learning method that adapts the Random Forest algorithm to time-to-event (survival) data. Trees are grown using log-rank sp...
Recurrent Event Model
A recurrent event model is a survival analysis extension, formalised through the landmark contributions of Prentice, Williams and Peterson (1981), Andersen and Gill (1982), and Wei, Lin and Weissfeld (1989), that models time-to-event data w...
Reproduction Number
The basic reproduction number R0 is the expected number of secondary infections produced by a single infectious individual introduced into a fully susceptible population. Formally defined and computationally grounded by Diekmann, Heesterbee...
Royston-Parmar Model
The Royston-Parmar model, introduced by Royston and Parmar in 2002, is a modern parametric approach to survival analysis that replaces the rigid distributional assumptions of classical models with a restricted cubic spline fitted to the log...
SEIR Model
The SEIR model is a deterministic compartmental model that partitions a closed population into four epidemiological states: Susceptible (S), Exposed (E), Infectious (I), and Recovered (R). It extends the classic SIR framework by explicitly...
SIR Model
The SIR model is a foundational mathematical framework for describing the spread of infectious diseases through a population. Introduced by William Ogilvy Kermack and Anderson Gray McKendrick in 1927, it partitions a closed population of si...