Bios 6311 Syllabus 2018

Mini Calendar

  1. Aug 23 (First day of class: 23)
  2. Aug 28 & 30
  3. Sep 4 & 6
  4. Sep 11 & 13
  5. Sep 18 & 20 -- 1st Exam
  6. Sep 25 & 27
  7. Oct 2 & 4
  8. Oct 9 & 11
  9. Oct 16 (Fall Break: 18-19)
  10. Oct 23 & 25 -- 2nd Exam
  11. Oct 30 & Nov 1
  12. Nov 6 & 8
  13. Nov 13 & 15
  14. Nov (T-Giving Break: 17-25)
  15. Nov 27 & 29
  16. Dec 4 & 6 (Last day of class: 6) -- Final Exam
  17. Dec (Reading days and exams 7-15)

Topics Covered

Week 1 (Aug 23)

Review of Probability.
  • Random Variables: Z
  • Sample Space: S = {a, b, c, d}
  • Events: a, b, c, d
  • Probability of Events: P[Z=a]
Craps
  • Basic rules for the pass the line bet
Big Picture
  • Statistics is about estimation
  • ... and checking your methods

Week 2 (Aug 28 & 30)

Intro to coding in R. Detecting a weighted die.
  • Using R to perform theoretical experiments.
  • The Exact (1-α) level confidence interval for a proportion
    • The probability statements that define the method
    • Calculating the bounds "by hand", i.e. solving using trial and error in R

Week 3 (Sept 4 & 6)

How good is the exact interval?
  • Developing theoretical experiments to test operating characteristics of methods
At least three (1-α) level confidence intervals for a proportion
  • Exact interval
  • Asymptotic Normal interval (Wald interval)
  • Wilson interval
  • Add 2 successes and 2 failures interval
P[LB < θ < UB] < 1-α Central Limit Theorem. Normal approximation for the Binomial.

Week 4 (Sept 11 & 13)

What makes x/n a "good" estimator for θ? Unbiasedness - definition, proof for x/n. Likelihood function L[θ]. Maximum likelihood estimator (MLE). Values that are well supported by the data. Likelihood Support interval for a proportion. Big Picture - when examining a statistical method:
  1. Understand the philosophical justification
  2. Understand the mathematical justification
  3. Understand the performance in various simulated settings

Week 5 (Sept 18 & 20)

Sensitivity, Specificity, Positive Predictive Value, Negative Predictive Value. Bayes theorem Prior probability distribution and posterior probability distribution. Bayesian Credible interval for a proportion.

Week 6 (Sept 25 & 27)

Interval methods for the population mean. Wald interval (Z interval) with variance known. Z interval with variance unknown. t interval with variance unknown. Likelihood support interval using Normal distribution.

Week 7 (Oct 2 & 4)

Bayesian credible interval using Normal distribution. Estimating Power by hand. Interval methods for the difference of two population means.
  • Wald interval (Z interval) with variance known.
  • Z interval with variance unknown.
  • t interval with variance unknown.
  • Likelihood support interval using Normal distribution.
Estimating sample size needed to achieve a given level of precision, e.g. SE < 0.001. Interval methods for the difference of two population means.
  • When X and Y are dependent,
  • When X and Y are independent, i.e. Cov(X,Y) = 0.

Week 8 (Oct 9 & 11)

Interval methods for the difference of two population proportions (RD).
Intervals for other measures comparing population proportions (RR, OR).
Graphical assessments of Normality: Quantile-Quantile (QQ) Plots

Week 9 (Oct 16)

Intervals for other measures comparing population proportions (RR, OR).
  • Delta method
  • Numerical approximation of a posterior distribution (ratio of two independent Beta distributions)

Week 10 (Oct 23 & 25)

2nd Exam

Week 11 (Oct 30 & Nov 1)

Inference.
  • Hypothesis testing vs a point null
Power curves
  • Type I and Type II errors
  • Pre-specifying a Type I error rate (α)

Week 12 (Nov 6 & 8)

Randomization Inference
  • Permuting treatment assignment to generate a null distribution
Nonparametric tests
  • Wilcoxon-Mann-Whitney test (wilcox.test)
When the null shapes the variance
  • one-sample proportions test
  • equality of two proportions test (as Z and as Chi-squared)

Week 13 (Nov 13 & 15)

Omnibus Tests
  • Chi-squared test
  • ANOVA
Multiple comparisons
  • Familywise Error Rate
  • Bonferroni procedure
  • False Discovery Rate
  • Benjamini Hochberg procedure
  • Controlling pre-experimental probabilities like Type I error, FWER, and FDR

Week 14 (T-Giving Break: 17-25)

Week 15 (Nov 27 & 29)

Statistical vs Clinical Significance
  • Second generation p-values
  • Indirect control of Type I error
Estimating post-experimental probabilities
  • P[Ho true | rejected Ho] as opposed to P[reject Ho | Ho true]

Week 16 (Dec 4 & 6)

Final Exam
Topic revision: r17 - 15 Nov 2018, RobertGreevy
 

This site is powered by FoswikiCopyright © 2013-2017 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding Vanderbilt Biostatistics Wiki? Send feedback