• Mastering Statistics with R
  • Welcome
    • Prerequisites
    • Who am I ?
    • Acknowledgement
    • Progress of this book
  • Part I: Basic Probability
  • 1 Introduction to Probability
    • 1.1 What is probability ?
    • 1.2 Basic Mathematic
      • 1.2.1 Combinatorics
      • 1.2.2 Set Theory
    • 1.3 History of probability
      • 1.3.1 Experiment, Sample space and Events
      • 1.3.2 Definitions of Probability
    • 1.4 Conditional Probability and Independence
      • 1.4.1 Conditional Probability
      • 1.4.2 Independence
    • 1.5 Bayes’ Theorem
  • 2 Random variables
    • 2.1 Random variables and probability functions
      • 2.1.1 Random variables
      • 2.1.2 Discrete Probability Function
      • 2.1.3 Continuous Probability Function
      • 2.1.4 * Mixed Type Probability Function
    • 2.2 Expected values and Variance
      • 2.2.1 *Approximation of a random variable
    • 2.3 Transformation of random variables
      • 2.3.1 Discrete r.v. transformation
      • 2.3.2 Continuous r.v. transformation
    • 2.4 Families of distributions
      • 2.4.1 Discrete probability distributions
      • 2.4.2 Continuous probability distributions
  • 3 Multivariate random variables
    • 3.1 Joint distributions
      • 3.1.1 Marginal Distribution
      • 3.1.2 Sum of two independent random variables
    • 3.2 Change of variables
    • 3.3 Families of multivariate distributions
      • 3.3.1 Trinomial distribution
      • 3.3.2 Bivariate hypergeometric distribution
      • 3.3.3 Multivariate normal distribution
      • 3.3.4 Wishart distribution
      • 3.3.5 Wilks’ lambda distribution
      • 3.3.6 Hotelling’s \(T^2\)-distribution
  • 4 System of Moments
  • 5 Limit Theorem
    • 5.1 Some inequality
      • 5.1.1 Markov inequality
      • 5.1.2 Chebshev inequality
      • 5.1.3 Jensen inequality
    • 5.2 Law of large numbers
  • Part II: Basic Statistic
  • 6 Descriptive Statistics
    • 6.1 Frequency distribution
    • 6.2 Measures of statistical characteristics
    • 6.3 Exploratory data analysis (EDA)
      • 6.3.1 Steam-and-leaf plot
      • 6.3.2 Histogram and Bar chart
      • 6.3.3 Pareto chart
      • 6.3.4 Density plot
      • 6.3.5 Box-plot and Violin plot
  • 7 Sampling
    • 7.1 Random sampling methods (probability sampling techniques)
      • 7.1.1 Simple random sampling
      • 7.1.2 Systematic sampling
      • 7.1.3 Stratified sampling
      • 7.1.4 Cluster sampling
    • 7.2 Nonrandom sampling methods (non-probability sampling techniques)
      • 7.2.1 Convenience sampling
      • 7.2.2 Snowball sampling
      • 7.2.3 Judgmental sampling
      • 7.2.4 Quota sampling
      • 7.2.5 Consecutive sampling
    • 7.3 Other sampling methods
      • 7.3.1 Latin hypercube sampling
  • 8 Estimation
    • 8.1 Point Estimation
      • 8.1.1 Method of Moments (MoM)
      • 8.1.2 Maximum Likelihood Estimation (MLE)
      • 8.1.3 Uniformly Minimum Variance Unbiased Estimator (UMVUE)
    • 8.2 Interval Estimation
  • 9 Testing Hypotheses
    • 9.1 Null hypothesis vs. alternative hypothesis
    • 9.2 The Neyman-Pearson Lemma
  • 10 Some statistical test
    • 10.1 Parametric statistical test
      • 10.1.1 \(t\)-test
      • 10.1.2 \(F\)-test
      • 10.1.3 \(\chi^2\)-test
    • 10.2 Non-parametric statistical test
      • 10.2.1 Mann–Whitney \(U\)-test (Wilcoxon rank-sum test)
      • 10.2.2 Wilcoxon signed-rank test
      • 10.2.3 Kolmogorov–Smirnov test
  • 11 Analysis of Variance (ANOVA)
    • 11.1 Levene’s test
    • 11.2 Bartlett’s test
    • 11.3 One-way ANOVA
    • 11.4 Two-way ANOVA
    • 11.5 Welch’s ANOVA
    • 11.6 Kruskal–Wallis test
    • 11.7 Friedman test
    • 11.8 Normality Test
  • 12 Correlation Analysis and Linear Regression
  • 13 Limiting Distributions
    • 13.1 Converge in probability
    • 13.2 Converge in distribution
  • Part III: Statistical Inference
  • 14 (Generalized) Linear Models
    • 14.1 Ordinary Least Squares (OLS)
    • 14.2 Fixed Effect and Random Effect
    • 14.3 Analysis of Covariance (ANCOVA)
    • 14.4 Logistic Regression
    • 14.5 Fractional Model
    • 14.6 Weighted Least Square (WLS) and Generalized Least Square (GLS)
    • 14.7 Hierarchical Linear Model
    • 14.8 Multilevel Model
    • 14.9 Quantile Regression
  • 15 Applied Probability Models
    • 15.1 Stochastic Process
      • 15.1.1 Random Walk
      • 15.1.2 Poisson Process
      • 15.1.3 Markov Process
      • 15.1.4 Wiener Process
      • 15.1.5 Lévy Process
    • 15.2 Markov Chain
    • 15.3 Ergodic Theory
    • 15.4 Stochastic Calculus
      • 15.4.1 Ito’s Lemma
  • 16 Probability Theory
    • 16.1 Basics from Measure Theory
    • 16.2 Limit of the sets
    • 16.3 Stochastic ordering
    • 16.4 Malliavin Calculus
  • 17 Bayesian Analysis
    • 17.1 Laplace Approximation and BIC
  • Part IV: Sequential Data
  • 18 Quality Control
    • 18.1 History
    • 18.2 7 tools
    • 18.3 ARL
    • 18.4 \(R\) chart
    • 18.5 \(s\) chart
    • 18.6 \(\bar{X}\) chart
    • 18.7 \(p\) chart
    • 18.8 CUSUM
    • 18.9 EWMA
    • 18.10 Sequential probability ratio test
  • 19 Time Series Analysis
    • 19.1 Time Series Decomposition
    • 19.2 ACF and PACF
    • 19.3 White Noise
    • 19.4 Autoregressive (AR)
    • 19.5 Moving Average (MA)
    • 19.6 Kalman Filter and Savitzky–Golay filter
    • 19.7 ARMA, ARIMA, SARIMA, SARFIMA
    • 19.8 Granger causality
    • 19.9 VAR
    • 19.10 GARCH
    • 19.11 Factor Model
    • 19.12 Some advanced topics
      • 19.12.1 Lag regression
      • 19.12.2 Mixed-frequency data in time series
  • Part V: Computational Statistic
  • 20 Statistical Learning
    • 20.1 Root finding
      • 20.1.1 Newton’s method (Newton–Raphson algorithm)
      • 20.1.2 Gauss–Newton algorithm
      • 20.1.3 Gradient Descent
      • 20.1.4 Conjugate gradient method
      • 20.1.5 Nelder–Mead method
      • 20.1.6 Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm
    • 20.2 Information Criteria
      • 20.2.1 AIC
      • 20.2.2 BIC
    • 20.3 Desicion Tree and Random Forest
    • 20.4 Bagging
    • 20.5 Boosting
      • 20.5.1 Gradient Boost Desicion Tree (GBDT)
      • 20.5.2 XGBoost
      • 20.5.3 LightGBM
      • 20.5.4 CATBoost
      • 20.5.5 RUSBoost
  • 21 Statistical Computing
    • 21.1 Generate random variables
      • 21.1.1 Inverse transform method
      • 21.1.2 Accept-Rejection method
    • 21.2 Variance reduction
    • 21.3 Monte-Carlo and Markov chain (MCMC)
    • 21.4 EM algorithm
    • 21.5 Particle Swarm Optimization (PSO)
  • Part VI: Biostatistic
  • 22 Survial Analysis
    • 22.1 Survival Function and Hazard Function
    • 22.2 Kaplan–Meier Estimator
    • 22.3 Log-rank Test
    • 22.4 Proportional Hazards Model
    • 22.5 Accelerated Failure Time (AFT) Model
    • 22.6 Nelson–Aalen Estimator
    • 22.7 Restricted Median Survival Time (RMST)
    • 22.8 Firth’s penalized logistic regression
    • 22.9 Competing Risks
  • 23 Biostatistical Data Analysis
    • 23.1 Trend Tests
      • 23.1.1 Cochran-Armitage test
      • 23.1.2 Jonckheere’s trend test
    • 23.2 Propensity score
    • 23.3 PLINK
    • 23.4 Polygenic Risk Score
    • 23.5 RNA-seq Analysis
    • 23.6 Metabolomics Analysis
      • 23.6.1 SMART
      • 23.6.2 pareto normalization
    • 23.7 Permutational multivariate analysis of variance (PERMANOVA)
    • 23.8 PERMDISP
  • 24 Causal Inference
    • 24.1 DAG
  • 25 Statistical Designs and Analyses in Clinical Trials
  • Part VII: Applications
  • Part VIII: Other Topics
  • 26 Multivariate Analysis
    • 26.1 General Linear Model
    • 26.2 Multivariate Analysis of Variance (MANOVA)
    • 26.3 Multivariate Analysis of Covariance (MANCOVA)
    • 26.4 Structural Equation Modeling (SEM)
    • 26.5 Dimension Reduction Method
      • 26.5.1 t-SNE
      • 26.5.2 DBSCAN
      • 26.5.3 Locally Linear Embedding
      • 26.5.4 Laplacian Eigenmaps
      • 26.5.5 ISOMAP
      • 26.5.6 Uniform Manifold Approximation and Projection (UMAP)
    • 26.6 Clustering Method
      • 26.6.1 K-means, K-medoids
      • 26.6.2 KNN
      • 26.6.3 Principal Component Analysis (PCA)
      • 26.6.4 Principal Co-ordinates Analysis (PCoA)
      • 26.6.5 Multidimensional Scaling (MDS)
      • 26.6.6 Self-organizing map (SOM)
      • 26.6.7 Spectral clustering
      • 26.6.8 Quantum clustering
      • 26.6.9 Partial Least Squares Discriminant Analysis (PLS-DA)
      • 26.6.10 Unweighted Paired-Group Method Using Arithmetic Means (UPGMA)
    • 26.7 Factor Analysis
      • 26.7.1 Kaiser–Meyer–Olkin test
      • 26.7.2 Questionnaire
    • 26.8 Canonical-correlation Analysis (CCA)
    • 26.9 Analysis of Similarities (ANOSIM)
  • 27 Categorical Data Analysis
  • 28 Consulting in Statistics
  • 29 Spatial Statistics
    • 29.1 Point-referenced Data
      • 29.1.1 Gaussian Process
      • 29.1.2 Exploratory data analysis
      • 29.1.3 Models for spatial dependence
      • 29.1.4 Kriging (Spatial prediction)
    • 29.2 Areal/Lattice Data
      • 29.2.1 Spatial autocorrelation
      • 29.2.2 Conditionally auto-regressive (CAR) and Simultaneously auto-regressive (SAR) models
    • 29.3 Point Pattern Data
      • 29.3.1 Poisson processes
      • 29.3.2 Cox processes
      • 29.3.3 K-functions
    • 29.4 Other Topics
      • 29.4.1 Spatio-temporal models
      • 29.4.2 Frequency domain methods
      • 29.4.3 Deep Kriging
  • 30 Directional Statistics
    • 30.1 Circular Regression
  • 31 Functional Data Analysis
  • Part IV: Deal with Computer Science
  • 32 Information Theory
    • 32.1 Entropy
    • 32.2 Data compression
  • 33 Data Visualization and Visual Analytics
    • 33.1 Parallel coordinates
    • 33.2 Andrews plot
    • 33.3 Chord diagram (information visualization)
    • 33.4 Climate spiral and Warming stripes
  • 34 Big Data Analytics Techniques and Applications
    • 34.1 Visualization
    • 34.2 Hadoop
    • 34.3 Spark
  • 35 Data Mining
    • 35.1 Online machine learning
  • 36 Image Processing
  • 37 Deep Learning
    • 37.1 Basic concept
    • 37.2 DNN
    • 37.3 CNN
    • 37.4 RNN
      • 37.4.1 Long Short-Term Memory (LSTM)
      • 37.4.2 Gated Recurrent Unit (GRU)
    • 37.5 Generative adversarial networks (GAN)
    • 37.6 Transformer Networks
    • 37.7 Autoencoders & Variational Autoencoders (VAEs)
    • 37.8 Graph Neural Networks (GNNs)
    • 37.9 Deep Q-Networks (DQNs)
    • 37.10 Quantum neural network (QNN)
    • 37.11 Some famous models
      • 37.11.1 LeNet、AlexNet、VGG、NiN
      • 37.11.2 GoogLeNet
      • 37.11.3 ResNet
      • 37.11.4 DenseNet
      • 37.11.5 YOLO
    • 37.12 Modern NN models
      • 37.12.1 Liquid Neural Network (LNN)
      • 37.12.2 Kolmogorov-Arnold Networks (KAN)
  • Appendix
  • A Matrix calculus
  • B Functions in R
  • Published with bookdown

Mastering Statistics with R

22.7 Restricted Median Survival Time (RMST)

https://cran.r-project.org/web/packages/simtrial/vignettes/rmst.html https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9081686/