ScheduleHelp
Case-Based Introduction to Biostatistics
July 22 – August 25, 2013
Module 1 (Weeks 1 & 2) Question: What common background understanding do I need to get started in improving my ability to critically and quantitatively reason about health questions?
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Week 1: July 22-July 28
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Question
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Statistical ideas
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Statistical skills
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Videos
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Homework
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Quiz
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What is the scientific method?
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Experiments generate evidence that supports some competing hypotheses more than others.
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Specify hypotheses
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1.1. Scientific method
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1A
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1A
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How do we quantify evidence?
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Likelihood ratio updates the prior odds to obtain posterior odds
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Calculate odds from a probability;
Calculate a probability from an odds.
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1A
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1A
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What does it mean to say: “this drug prevents heart attacks” or “obesity increases the cost of medical care”
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The meaning of “cause” can usefully be made precise in terms of potential outcomes.
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Determine whether a statement is “causal” or not.
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1.2. On “cause”
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1A
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1A
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What is probability?
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Probability means long-run frequency or alternately is a quantification of the strength of belief; joint, marginal, conditional probabilities
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Calculate probabilities from data in a 2x2 table.
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1.3. On probability
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1A
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1A
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Week 2: July 29-August 4
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Question
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Statistical ideas
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Statistical skills
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Videos
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Homework
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Quiz
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What is a probability distribution for a random variable?
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Probability distribution is a function that takes a possible value (discrete) or set of values (continuous) as input and returns the probability the random variable assumes the input value(s).
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Calculate specified probabilities from a given probability distribution.
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1.4. Probability distributions.
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1B
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1B
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What is the binomial distribution? (What is meant by “independence” of two events?)
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A mathematical model for INDEPENDENT coin tossing-like systems in nature.
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Given the number of tosses (n) and probability of success on each INDEPENDENT toss (p), calculate the probability of observing x out of n successes for any x between 0 and n.
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1.5. Binomial distribution
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1B
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1B
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What is the Gaussian (“normal”) distribution and how is it derived?
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Mathematical model for the probability distribution of the average of independent random variables.
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Approximate the probability a Gaussian random variable with specified mean and variances falls in any given interval.
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1.6. Gaussian distribution
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1B
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1B
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Module 2 (Weeks 3 & 4) Question: How do the average medical care costs for people with a major smoking-caused disease (MSCD) differ from those for people without MSCDs who are otherwise similar?
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Week 3: August 5-August 11
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Question
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Statistical ideas
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Statistical skills
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Videos
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Homework
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Quiz
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What is the probability distribution of medical expenditures for persons with/without a MSCD?
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Distribution of medical expenditures; summaries of location, spread, and shape; transforming the variable to better understand the distribution.
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Calculate a mean, median, quartiles, standard deviation; Make and interpret a stem and leaf plot;
Make and interpret a boxplot.
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2.1. Distribution of medical expenditures
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2A
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2A
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What is the probability distribution of an independent sample of size n drawn from the observed distribution of medical expenditures
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Simple random sampling; Stratified sampling; Central limit theorem.
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2.2. Sampling and the Central Limit Theorem
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2A
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2A
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What is a confidence interval for the population mean?
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Confidence intervals as interval estimates for an unknown population mean (the truth we seek).
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Calculate a 95% or 99% confidence interval for an unknown population mean from a sample of n independent observations drawn from the population.
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2.3. Confidence intervals.
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2A
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2A
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Week 4: August 12-August 18
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How does the distribution of medical expenditures differ for persons with vs without a MSCD?
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Comparing distributions.
Differences of means;
Standardized mean differences;
Ratios.
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Make and interpret a Q-Q plot.
Calculate and interpret t-statistic.
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2.4. Comparing distributions
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2B
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2B
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How does the distribution of medical expenditures differ across age and poverty strata?
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Comparing distributions across several strata; table of pair-wise standardized mean differences
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Interpreting multiple boxplots after variable transformation
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2.4. Comparing distributions
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2B
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2B
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How does the distribution of medical expenditures differ for persons with vs without a MSCD of similar age and poverty level?
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Stratification by covariates;
Estimation within strata.
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Calculate a t-statistics for each stratum; interpret results across strata
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2.5. Pooling across strata
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2B
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2B
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When is it warranted to pool results across strata and how do we do it?
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“Effect modification” or “interaction”; Pooling multiple estimates, giving greater weight to the more precise estimates.
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Estimate the overall effect of MSCD on medical expenditures from the stratum specific values
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2.5. Pooling across strata
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2B
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2B
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How does the pooled result compare to the simple comparison in 2.4? Why are they different?
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Confounding when we fail to compare otherwise similar populations
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2.6. What we learned in module 2.
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2B
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2B
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Module 3 (Week 5) Question: What is the rate of infant survival during the first 26 weeks of life in southern Nepal and how does the rate of survival vary by infant’s gestational age, sex, or being a singleton versus twin birth?
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Week 5: August 19-August 25
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Question
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Statistical ideas
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Statistical skills
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Videos
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Homework
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Quiz
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What is an odds ratio; what is a log odds ratio; why is the log odds ratio so commonly used in health research?
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Defining parameters with unbounded support; odds approximate the risk; invariance of the odds ratio
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Estimate an odds ratio from a 2x2 table with 95% confidence interval
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3.1. Odds ratio estimation
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3A
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3A
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How does child survival depend upon sex and twin status?
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2x2 tables; log odds “model” or “logistic regression”
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Apply odds ratio estimation to answer a substantive question.
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3.2. Odd ratio estimation
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3A
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3A
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How does the log odds of child survival depend upon gestational age?
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Study outcome expressed as a function of a continuous predictor variable - regression
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Display the dependence of the log odds of survival on gestational age
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3.3. Introduction to logistic regression
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3A
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3A
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