Bayesian Approaches in Oncology Using R and OpenBUGS

Atanu Bhattacharjee

• Publisher: Chapman and Hall/CRC
• Year: 2020
• ISBN:
  9781000330069
• Edition: 1
• Topic: Mathematik
• Subtopic: Wahrscheinlichkeitsrechnung & Statistiken

Bayesian Approaches in Oncology Using R and OpenBUGS serves two audiences: those who are familiar with the theory and applications of bayesian approach and wish to learn or enhance their skills in R and OpenBUGS, and those who are enrolled in R and OpenBUGS-based course for bayesian approach implementation. For those who have never used R/OpenBUGS, the book begins with a self-contained introduction to R that lays the foundation for later chapters.

Many books on the bayesian approach and the statistical analysis are advanced, and many are theoretical. While most of them do cover the objective, the fact remains that data analysis can not be performed without actually doing it, and this means using dedicated statistical software. There are several software packages, all with their specific objective. Finally, all packages are free to use, are versatile with problem-solving, and are interactive with R and OpenBUGS.

This book continues to cover a range of techniques related to oncology that grow in statistical analysis. It intended to make a single source of information on Bayesian statistical methodology for oncology research to cover several dimensions of statistical analysis. The book explains data analysis using real examples and includes all the R and OpenBUGS codes necessary to reproduce the analyses. The idea is to overall extending the Bayesian approach in oncology practice. It presents four sections to the statistical application framework:

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• Bayesian in Clinical Research and Sample Size Calcuation
• Bayesian in Time-to-Event Data Analysis
• Bayesian in Longitudinal Data Analysis
• Bayesian in Diagnostics Test Statistics

This book is intended as a first course in bayesian biostatistics for oncology students. An oncologist can find useful guidance for implementing bayesian in research work. It serves as a practical guide and an excellent resource for learning the theory and practice of bayesian methods for the applied statistician, biostatistician, and data scientist.

Part II

Bayesian in Time-to-Event Data Analysis

Chapter 6

Survival Analysis

Abstract

The survival analysis is widely adopted statistical analysis in oncology. Commonly, the Kaplan-Meier estimate and Cox proportional hazard models are performed in survival analysis. The Kaplan-Meier showed by assuming the censoring mechanism is non-informative. However, it gets violated some times. The informative censoring procedure using a Bayesian framework is suitable to overcome this violation. This chapter is dedicated to Bayesian survival analysis. Real-life data analysis is illustrated with OpenBUGS software. Similarly, survival analysis with R by Kaplan-Meier method, Cox PH model, Schoenfeld Residuals and other tools are theoretically explained.

6.1 Introduction

The objective of the survival analysis is to estimate and interpret hazard functions from survival data. Secondly, compare the hazard functions. Thirdly, explore the relationship of explanatory variables to survival time. Hazard function created from several groups.

Survival analysis comes with an analytical problem as censoring. Censoring comes while we have some information about individual survival time, but we do not have actual survival time.

The censoring data occurred if the event may not occur before the study end, the person is lost to follow-up during the study ends, and a person withdraws from the study due to other causes of death.

If the real survival time is equal to or greater than the observed survival time then it is defined as Right censoring.

Similarly, if the real survival time is less than or equal to the observed survival time, then it is defined as Left censoring.

Conventionally, the survival...