STAT 513 -- POST-EXAM 3 REVIEW SHEET 

** NOTE:  The final exam will contain questions from throughout the semester.
** Also study the material on the first 3 review sheets!!!

I. Extra Bayesian Topics
   A. Bayesian Hypothesis Testing
    1. Finding posterior probabilities that H0 is true
      a. Useful R functions like pbeta, pgamma, pexp, pnorm, etc.
    2. Using two-sided credible intervals to make decisions with two-tail ("point null") tests
   B. Additional Comments about Bayesian Inference
    1. Situation with non-conjugate priors
    2. Usefulness of the predictive distribution
    3. Judging quality of a Bayesian estimator using MSE
    4. Bayes risk and the posterior mean
    5. Large-sample properties of Bayes estimators
II. Survival Analysis
   A. Definition of Lifetime Data (a.k.a. survival data or time-to-event data)
   B. Censoring in Lifetime Data
    1. Reasons why Censoring might occur
    2. Types of Censoring
   C. Parametric Models for Survival Data
    1. Survival function S(t)
      a. How does it relate to the cdf F(t) and the pdf f(t)?
    2. Exponential model
      a. Finding the survival function, the cdf, and the pdf of the exponential distribution
      b. Finding survival probabilities using S(t)
    3. Definition of "stochastically larger"
    4. Mortality rate m(t)
    5. Hazard function lambda(t)
      a. How does the shape of a hazard function characterize a survival r.v.?
      b. Cumulative hazard function
    6. Weibull model
      a. Finding the survival function, the cdf, and the hazard function of the Weibull distribution
      b. Advantage of Weibull model compared to the exponential
   D. Life Table Estimates
    1. Form of Life Tables (grouped data)
    2. Estimating S(t) via cumulative product of (1 - mortality rate) pieces
    3. Best way to estimate mortality rate m(t) for each row of life table
    4. Greenwood's formula
    5. Forming a CI for S(t) at a fixed time t
   E. Kaplan-Meier Estimator
    1. Ungrouped data
    2. K-M estimator as a limit of the Life Table Estimator
    3. Key terms:  number of deaths, number censored, number at risk
    4. Reading R output to get: estimates of S(t), CI for S(t), plot of survival function, median survival time
   F. Two-Sample tests
    1. Survival studies with two treatment groups
    2. Null and alternative hypotheses about survival functions
    3. Log-rank test based on sequence of 2-by-2 tables
    4. Log-rank Test statistic T_{LR} and rejection region for each alternative
    5. Correct conclusions of Log-rank test based on R output