This is the notebook for the two-part coursera course “mathematical Biostatistics Boot Camp”.
Part 1
Lecture 1, introduction
Biostatistics
Experiments
Set notation
Probability
Lecture 2, probability
Probability
Random variables
PMFs (probability mass function) and PDFs (probability density function)
CDFs (cumulative distribution function), survival functions and quantiles
Summary
Lecutre 3, Expectations
Expected values: discrete/continuous random variables
Rules about expected values
Variances
Chebyshev’s inequality
Lecture 4, Random Vectors
Random vectors
Independence: independent events, independent random variables, IID random variables
Correlation
Variance and Correlation properties
Variances properties of sample mean (standard error)
The sample variance
Some discussion
Lecture 5, Conditional Probability
Conditional probability
Conditional densities
Bayes’ Rule
Diagnostic tests
DLR (diagnostic likelihood ratios)
Lecture 6, Likelihood
Defining likelihood
Interpreting likelihood
Plotting likelihoods
Maximum likelihood
Interpreting likelihood ratios
Leture 7, Some common distributions
The Bernoulli distribution
Binomial trials
The normal distribution: properties and ML estimate of $\mu$
Lecture 8, Asymptotics
limits (极限)
LLN (The Law of Large Numbers)
CLT (The Central Limit Theorem)
CI (Confidence Intervals)
Lecture 9, Confidence Intervals
Confidence intervals
CI for a normal variance
Student’s t distibution
Confidence intervals for normal means
Profile likelihoods
Lecture 10, T Confidence Intervals
Independent group t intervals
Likelihood method
Unequal variances
Lecture 11, Plotting
Histograms
Stem and Leaf
Dotcharts
Boxplots
KDEs (Kernel density estimates)
QQ-plots
Mosaic plots
Lecture 12, Bootstrapping
The jackknife
The bootstrap principle
The bootstrap
Lecture 13, Binomial Proportions
Intervals for binomial proportions
Agresti-Coull interval
Bayesian analysis: Prior specification, posterior, credible intervals
Lecutre 14, Logs
Logs
The geometri mean
GM and the CLT
Comparisons
The log-normal distribution
Part 2
Lecture 1, Hypothesis Testing
Hypothesis testing
General rules
Notes
Two sided tests
Confidence intervals
P-value
Lecture 2, Power
Power
Calculating power
T-tests
Monte Carlo
Lecture 3, Two sample tests
Matched data
Aside, regression to the mean
Two independent groups
Lecture 4, Two sample binomial tests
The score statistic
Exact tests
Comparing two binomial proportions
Bayesian and likelihood analysis of two proportions
Lecture 5, Relative risks and odds ratios
Relative measures
The relative risk
The odds ratio
Lecture 6, Delta method
Recap
The delta method
Derivation of the delta method
Fisher’s Exact test
Fisher’s exact test
The hypergeometric distribution
Fisher’s exact test in practice
Monte Carlo
Lecture 8, Chi-Squared tests
Chi-squared testing
Testing independence
Testing equality of several proportions
Generalization
Independence
Monte Carlo
Goodness of fit testing
Lecture 9, Simpson’s Paradox and Confouding
Simpson’s paradox
More examples
Confouding
Weighting
Mantel/Haenszel estimator
Lecture 10, Case Control Data
Case-control methods
Rare disease assumption
Exact inference for the odss ratio
Lecture 11, Matched Two by Two tables
Matched pairs data
Dependence
Marginal homogeneity
McNemar’s test
Estimation
Relationship with CMH
Marginal odds ratios
Conditional versus marginal
Conditional ML
Lecture 12
Nonparametric tests
Sign test
Signed rank test
Monte Carlo
Independent groups
Mann/Whitney test
Monte Carlo
Permutation tests
Lecture 13
The Poisson distribution
Poisson approximation to the binomial
Person-time analysis
Exact tests
Time-to-event modeling
Lecutre 14
Multiplicity
Bonferoni
FDR