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
KaplanMeier (KM) estimator, a derivation of expression using MLE
Fitting KM estimator with an example dataset, Python code and plotting curves
Greenwoods 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 Breslows 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.
| Preface |
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vii | |
| About the Author |
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ix | |
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2 | (1) |
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3 | (2) |
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3 | (1) |
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4 | (1) |
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5 | (1) |
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5 | (2) |
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Control and Treatment Group |
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6 | (1) |
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7 | (1) |
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Comparison with Regression |
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2 General Theory of Survival Analysis |
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9 | (3) |
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12 | (1) |
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Analysis of Relationships |
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13 | (1) |
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Estimating Survival Distribution |
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14 | (5) |
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Predicting Survival Probability |
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17 | (1) |
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18 | (1) |
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Mean and Median Survival Time |
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19 | (2) |
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21 | (16) |
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Maximum Likelihood Estimation (MLE) of Parameters |
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21 | (2) |
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MLE for Survival Function |
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22 | (1) |
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23 | (7) |
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24 | (1) |
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Newton-Raphson Method for Solving MLE Equation |
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25 | (3) |
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Confidence Intervals of Survival Function |
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28 | (2) |
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30 | (3) |
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Transformation of Variables for Integrals - Jacobian |
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30 | (1) |
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Inception of Gumbel Distribution |
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30 | (2) |
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Survival and Hazard Function of Gumbel Distribution |
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32 | (1) |
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33 | (2) |
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35 | (2) |
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Akaike Information Criterion (AIC) |
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37 | (18) |
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37 | (11) |
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40 | (2) |
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Computation of Survival Function for Unknown Time Instance |
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42 | (2) |
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Confidence Intervals of the Survival Function - Greenwoods Estimator |
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44 | (4) |
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48 | (7) |
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Analysis of Log-Rank Test |
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53 | (2) |
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55 | (26) |
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55 | (11) |
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58 | (1) |
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Determining Parameters (β, κ, ρ for Weibull-AFT |
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58 | (5) |
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Plotting Baseline vs Original Survival Function |
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63 | (1) |
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Stepwise Computation of Relation S1(t, β) = S0(teβ,x) |
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64 | (2) |
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Proportional Hazard Model |
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66 | (8) |
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67 | (1) |
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67 | (1) |
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68 | (3) |
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Plotting Baseline vs Original Hazard Function |
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71 | (2) |
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73 | (1) |
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73 | (1) |
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Determining Parameters β κ, ρ for Weibull-Cox |
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74 | (1) |
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Significance of Covariates |
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74 | (2) |
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75 | (1) |
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76 | (1) |
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76 | (5) |
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Forward Selection Algorithm |
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79 | (2) |
| Index |
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Avishek Nag has a Masters of Technology Degree in data analytics and machine learning from Birla Institute of Technology and Science, Pilani, India. He has more than 15 years of experience in Software Development and Architecting Systems. He also has professional experience in data science and machine learning, Java, Python, Big Data, including Spark and MongoDB. He has worked at VMWare, Cisco, Mobile Iron, and Computer Science Corporation (now called DXC). He is also the author of the book Pragmatic Machine Learning with Python, which is recommended in the ACM Education Digital Library.
