Statistical Notes

Notes on statistical theory, clinical-trial design, multiplicity, and statistical programming.

Working notes on statistics, clinical trials, and statistical programming. Use the category filters or site search to find a topic.

Reference-based Multiple Imputation (3) - Algorithm of J2R

mathematical statistics

A comprehensive and detailed review of the implementation of J2R using DIA Five-Macros has been conducted in this post.

Reference-based Multiple Imputation (2) - J2R and CR Methods

mathematical statistics

A comprehensive and detailed review of the J2R and CR methods has been conducted.

Reference-based Multiple Imputation (1) - RTB and Washout Methods

mathematical statistics

Introduce RTB and Washout methods, also provide two FDA review reports.

Treatment Policy Strategy and Retrieved Dropout

mathematical statistics

Under the treatment policy framework, missing data resulting from study withdrawal can be addressed using the Retrieved Dropout (RDO) imputation method.

Methodological Replication of Power Simulations for the NCT04435626 Primary Endpoint (Heart Failure)

mathematical statistics

survival analysis

Outline the process for replicating power simulation results by applying the prespecified primary analysis methodology established in the NCT04435626 clinical protocol for…

Analyzing Binary Outcomes in a Trial With Small Sample Sizes

mathematical statistics

A pilot Monte Carlo simulation study to evaluate and compare the performance of three statistical methods for analyzing binary outcomes in a randomized clinical trial with…

Missing Data and EM Algorithm

mathematical statistics

The expectation-maximization algorithm is an approach in which values of the statistics which would be computed if a complete dataset were available are estimated (imputed)…

Hessian Matrix and Its Role in Convex Optimization

mathematical statistics

The Hessian matrix is the multivariable generalization of the second derivative. It captures curvature information in all directions simultaneously.

Wishart Distribution and Bartlett’s Decomposition

mathematical statistics

The Wishart distribution is the multivariate generalization of chi-squared. It describes the distribution of sample covariance matrices. Bartlett’s decomposition provides an…

Why symmetric positive-(semi)definite matrices matter

mathematical statistics

Symmetric positive-(semi)definite matrices are fundamental objects in statistics, optimization, and machine learning. Their unique mathematical properties make them…

A Brief Introduction to Causal Inference

mathematical statistics

causal inference

This post outlines the fundamental principles of causal inference, contrasting correlation with causation and introducing key frameworks like the Rubin Causal Model and…

Competing Risks in Clinical Trials

mathematical statistics

survival analysis

A special type of survival analysis that aims to correctly estimate marginal probability of an event in the presence of competing events.

Further reflections on the Serial Gatekeeper

multiple testing

decision making

Finally, I had some time to review this MTP strategy thoroughly and realized there are many MTPs that can be used in conjunction with this serial gatekeeping strategy.

Generate dummy variables in SAS

mathematical statistics

Review the methods to generate design matrix in SAS.

Delta Method for Standard Error Estimates

mathematical statistics

Method to calculate SD of log-transformed data.

Measures of Missing Data Information from PROC MIANALYZE

mathematical statistics

Some measures to evaluate the multiple imputation.

Specification of Covariance Structure for Repeated Measures

mathematical statistics

A method proposed by Lu and Mehrotra to address the convergence issues in fitting a mixed model.

A Discussion of Multiple Testing in Group Sequential Trial D4191C00004

multiple testing

decision making

A review of the ideas of multiple testing strategies used in Study ID: D4191C00004.

Group Sequential Holm Procedure

multiple testing

decision making

An innovative Holm procedure used in group sequential design (usually in oncology trials).

Linear Model in SAS (2) - Hypothesis Testing and Estimable Functions

mathematical statistics

An estimable function is a linear combination of the parameters in a statistical model that can be uniquely and unbiasedly estimated from the data. This concept is most…

Linear Model in SAS (1) - Type I~IV SS and Contrast/Estimate Statement

mathematical statistics

In SAS, Type I through IV tests are used to analyze the significance of effects in a linear model, with each type addressing a different hypothesis about the contribution of…

A Family-based Graphical Approach for Testing Hierarchically Ordered Families of Hypotheses

multiple testing

decision making

Use graphical approaches to demonstrate gatekeeping ideas for hypothesis tests based on families.

Rejection Algorithm for A Recycling MTP in Terms of The Default Graph (Burman et al. 2009)

multiple testing

decision making

My understandings for Section 3.2 in the paper A recycling framework for the construction of Bonferroni-based multiple tests.

An Intuitive Explanation For The Interaction Of Factors In A Multiple Regression

mathematical statistics

Here is an excellent answer I have read when I was in university for the interpretation of interactions in linear model.

Parallel Gatekeeping - Alpha Propagation & General Multistage Gatekeeping Procedure

multiple testing

decision making

A review of the ideas behind parallel gatekeeping strategy for multiple-stage.

Immune-Related Response Criteria Derived From RECIST v1.1 (irRECIST)

iRECIST is a modified version of RECIST criteria designed specifically for immunotherapy, accommodating unique tumor response patterns like ‘pseudoprogression,’ where a…

A Review of Mixed Effect Model - REML & BLUE & BLUP

mathematical statistics

The 1st post to review the Mixed Effect Model.

Further Considerations on Simon Two-Stage Design

mathematical statistics

Although there are many articles introducing the Simon’s two-stage design, based on my communication with medical teams at work, there are still points that can be explored…

A Review of Best Unbiased Estimators

mathematical statistics

In statistics, an unbiased estimator is one that, on average, correctly estimates the true value of a parameter. This means its expected value is equal to the parameter it’s…

Standard Conventions for Time-to-event (TTE) Analyses

mathematical statistics

survival analysis

General methods for TTE endpoints.

Estimate Odds Ratio by Logistic Model with Baseline Adjustment

mathematical statistics

Some thoughts based on FDA’s comments on non-collapsibility issues.

A Review of ANCOVA Model

mathematical statistics

A simple review of ANCOVA model based on the workshop by Naitee Ting.

Posterior Probability v.s. Predictive Probability

mathematical statistics

A comprehensive comparison between Posterior Probability and Predictive Probability

BOP2 v.s. Predictive Probability

A comprehensive comparison between BOP2 and Predictive Probability

Sequential Enrichment Designs for Early Phase Clinical Trials (Reproducing Results)

Reproduced the results from the slide Sequential Enrichment Designs for Early Phase Clinical Trials published by Pfizer

A Bayesian Single-Arm Design Using PP Monitoring (Replication of Paper from AZ)

mathematical statistics

This document aims to replicate the results from an AZ trial.

Basket Trial Design - A Simulated Study

mathematical statistics

A basket trial is a type of clinical trial design used in oncology that tests the effectiveness of a single drug in treating multiple types of cancer that share a specific…

A Simulated Phase II Single Arm Design (ORR as Primary Endpoint)

mathematical statistics

It is a dummy Phase II single-arm study using ORR (binary endpoint) as primary endpoint. The purpose of this post is to illustrate the theory of Predictive Probability (Lee, J. J., & Liu, D. D. (2008)).

PoC sample for ORR (simulation)

mathematical statistics

GO/NO-Go: use bayesian predictive probability to monitor ORR.

Missing Data and MI in SAS

mathematical statistics

A general introduction of Multiple Imputation implemented by SAS.

Pseudo SAS Code For Cox Model

mathematical statistics

survival analysis

Analysis methods for Time-to-event endpoints.

Dose Limiting Toxicity (DLT)

Some concepts about DLT in early phase dose finding studies.

Pseudo SAS Code For Exact CI / (Un)stratified Analysis

mathematical statistics

Analysis methods for binary variables.

Multiplicity Principle

mathematical statistics

multiple testing

decision making

My notes on the ‘very basic’ ideas of multiplicity issues.

Exact Method

mathematical statistics

A notes of exact methods

Missing Data and EM Algorithm (My Notes)

mathematical statistics

My note on missing data and EM algorithm in MSc course.

Extended Linear Models Coursework with R

mathematical statistics

The dataframe YouthSurvey in the YouthSurvey.RData workspace contains data on the tolerance of 16 youths to deviant behaviour. Each year, when participants were ages 11, 12, 13, 14, and 15, they filled out a nine-item instrument designed to assess their tolerance of deviant behavior.

Cross v.s. Nested and lmer()

mathematical statistics

A more general definition of crossed random effects is simply: not nested.

A General Testing Problem in Linear Model

mathematical statistics

The linear model notation we are using in this post is