Survival Analysis with Python

Survival analysis uses statistics to calculate time to failure . Survival Analysis with Python takes a fresh look at this complex subject by explaining how to use the Python programming language to perform this type of analysis As the subject itself is very mathematical and full of expressions and formulations, the book provides detailed explanations and examines practical implications. The book begins with an overview of the concepts underpinning statistical survival analysis. It then delves into: Parametric models with coverage of: Concept of maximum likelihood estimate (MLE) of a probability distribution parameter MLE of the survival function Common probability distributions and their analysis Analysis of exponential distribution as a survival function Analysis of Weibull distribution as a survival function Derivation of Gumbel distribution as a survival function from Weibull Nonparametric models including: Kaplan-Meier (KM) estimator, a derivation of expression using MLE Fitting KM estimator with an example dataset, Python code, and plotting curves Greenwood’s formulae and its derivation Models with covariates explaining: The concept of time shift and the Accelerated Life Time model (AFT) Weibull AFT model and derivation of parameters by MLE Proportional Hazard (PH) model Cox-PH model Significance of covariates Selection of covariates The Python lifelines library is used for coding examples. Mapping theory to practical examples featuring datasets, the book is a hands-on tutorial as well as a handy reference. Cover Half Title Title Page Copyright Page Contents Preface About the Author 1. Introduction Concept of Failure Time Concept of Survival Censoring Right Censoring Left Censoring Interval Censoring Sample Dataset Structure Control and Treatment Group Risk Set Comparison with Regression 2. General Theory of Survival Analysis Survival Function Hazard Function Analysis of Relationships Estimating Survival Distribution Predicting Survival Probability Computing Accuracy Mean and Median Survival Time 3. Parametric Models Maximum Likelihood Estimation (MLE) of Parameters MLE for Survival Function Weibull Distribution MLE for ρ and κ Newton–Raphson Method for Solving MLE Equation Confidence Intervals of Survival Function Gumbel Distribution Transformation of Variables for Integrals – Jacobian Inception of Gumbel Distribution Survival and Hazard Function of Gumbel Distribution Exponential Distribution MLE for ρ Comparison of Models Akaike Information Criterion (AIC) 4. Non-Parametric Models Kaplan–Meier Estimator Derivation of SKM(t) Computation of Survival Function for Unknown Time Instance Confidence Intervals of the Survival Function – Greenwood’s Estimator Log-Rank Test Analysis of Log-Rank Test 5. Models with Covariates Accelerated Life Model Weibull-AFT Model Determining Parameters β, κ, ρ for Weibull-AFT Plotting Baseline vs Original Survival Function Stepwise Computation of Relation S1(t, β) = S0(teβ.x) Proportional Hazard Model Hazard Ratio Cox-PH Model Breslow’s Method Plotting Baseline vs Original Hazard Function Computing Hazard Ratio Weibull–Cox Model Determining Parameters β, κ, ρ for Weibull–Cox Significance of Covariates Wald Test Likelihood Ratio Test Selection of Covariates Forward Selection Algorithm Explainability of Models Index Survival analysis uses statistics to calculate time to failure. Survival Analysis with Python takes a fresh look at this complex subject by explaining how to use the Python programming language to perform this type of analysis. As the subject itself is very mathematical and full of expressions and formulations, the book provides detailed explanations and examines practical implications. The book begins with an overview of the concepts underpinning statistical survival analysis. It then delves into Parametric models with coverage of Concept of maximum likelihood estimate (MLE) of a probability distribution parameter MLE of the survival function Common probability distributions and their analysis Analysis of exponential distribution as a survival function Analysis of Weibull distribution as a survival function Derivation of Gumbel distribution as a survival function from Weibull Non-parametric models including Kaplan–Meier (KM) estimator, a derivation of expression using MLE Fitting KM estimator with an example dataset, Python code and plotting curves Greenwood's formula and its derivation Models with covariates explaining The concept of time shift and the accelerated failure time (AFT) model Weibull-AFT model and derivation of parameters by MLE Proportional Hazard (PH) model Cox-PH model and Breslow's method Significance of covariates Selection of covariates The Python lifelines library is used for coding examples. By mapping theory to practical examples featuring datasets, this book is a hands-on tutorial as well as a handy reference. Survival analysis uses statistics to calculate time to failure**. Survival Analysis with Python** takes a fresh look at this complex subject by explaining how to use the Python programming language to perform this type of analysis As the subject itself is very mathematical and full of expressions and formulations, the book provides detailed explanations and examines practical implications. The book begins with an overview of the concepts underpinning statistical survival analysis. It then delves into: * Concept of maximum likelihood estimate (MLE) of a probability distribution parameter * MLE of the survival function * Common probability distributions and their analysis * Analysis of exponential distribution as a survival function * Analysis of Weibull distribution as a survival function * Derivation of Gumbel distribution as a survival function from Weibull Kaplan-Meier (KM) estimator, a derivation of expression using MLE - Greenwood’s formulae and its derivation * The concept of time shift and the Accelerated Life Time model (AFT) * Weibull AFT model and derivation of parameters by MLE * Proportional Hazard (PH) model * Cox-PH model * Significance of covariates * Selection of covariates The Python __lifelines__ library is used for coding examples. Mapping theory to practical examples featuring datasets, the book is a hands-on tutorial as well as a handy reference. Survival analysis uses statistics to calculate time to failure. The book takes a fresh look at this complex subject by explaining how to use the Python programming language to perform this type of analysis.