Answered step by step
Verified Expert Solution
Question
1 Approved Answer
### Question for Chegg:A clinical trial was conducted to determine if hormone treatment benefits women who were previously treated for breast cancer. Each subject entered
### Question for Chegg:A clinical trial was conducted to determine if hormone treatment benefits women who were previously treated for breast cancer. Each subject entered the clinical trial when they had a recurrence. They were then treated with irradiation and assigned to a hormone treatment group or a control group. The observation of interest is the time until a second recurrence, which can be assumed to follow an exponential distribution with parameter hormone therapy group or control groupIn the table, a censoring time Q means that a woman was observed for Q months and did not have a recurrence during that time, so the recurrence time exceeds Q months. For example, women who received hormone treatment had recurrences, and the total recurrence time was months.Let yiH xiHdeltaiH be the data for the i th person in the hormone group, where xiH is the time yiH if it is a recurrence time and if it is a censoring time. The data for the control group can be written similarly.The likelihood is given by: pythetataupropto theta tausum deltaiH sum deltaiCexp lefttheta leftsum xiC tau sum xiH rightrightYou have been hired by the pharmaceutical company to analyze their data. They want to know if hormone treatment works. Your task is to find the marginal posterior distribution of tau using Gibbs sampling.The conjugate prior is given by: pthetataupropto thetaataubexp ctheta dtau theta Doctors who have worked extensively with this treatment have indicated that reasonable values for the hyperparameters are a b c d
Derive the necessary conditional distributions to implement Gibbs sampling.
Program and run your Gibbs sampler. Use a set of convergence diagnostics to evaluate the convergence and mixing of your algorithm. Interpret the diagnostics.
Calculate summary statistics of the estimated joint posterior distribution, including marginal means, standard deviations, and a credible interval for each parameter. Create a table with these results.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started