140.654.01 METHODS IN BIOSTATISTICS IV
Focuses on regression analysis for continuous and discrete data, and data analyses that integrate the methods learned in 140.651-652. Regression topics include simple linear regression; a matrix formulation of multiple linear regression; inference for coefficients, predicted values, and residuals; tests of hypotheses; graphical displays and regression diagnostics; specific models, including polynomial regression, splines, one- and two-way ANOVA; variable selection non-parametric regression; log-linear models for incidence rates and contingency tables; logistic regression; and generalized linear models.
Students who master the content of this course will be able to: 1) Formulate a scientific question about the relationship of a response variable Y and predictor variables X in terms of the appropriate logistic, log-linear or survival regression model; 2) Interpret the meaning of regression coefficients in scientific terms as if for a substantive journal (2.1 For binary responses collected in clusters, distinguish between marginal and cluster-specific regression coefficients estimated by ordinary and conditional logistic regression); 3) Develop graphical and/or tabular displays of the data to show the evidence relevant to describing the relationship of Y with X (3.1 For survival data, produce Kaplan-Meier and complimentary log, log plots of survival functions with standard errors); 4) Estimate the model using a modern statistical package such as STATA or R and interpret the results for substantive colleagues (4.1 Derive the estimating equations for the maximum likelihood estimates for the class of generalized linear models and state the asymptotic distributions of the regression coefficients and linear combinations thereof; 4.2 Give a heuristic derivation of the Cox proportional hazards estimating function in terms of Poisson regression for grouped survival data); 5) Check the major assumptions of the model including independence and model form (mean, variance and distribution of residuals, proportional hazards) and make changes to the model or method of estimation and inference to appropriately handle violations of standard assumptions (5.1 Use weighted least squares for situations with unequal variances; 5.2 Use robust variance estimates for violations of independence or variance or distributional assumptions; 5.3 Use stratification of follow-up time to deal with non-proportional hazards; 5.4 Use regression diagnostics to prevent a small fraction of observations from having undue influence on the results); 6) Write a methods and results section for a substantive journal, correctly describing the regression model in scientific terms and the method used to specify and estimate the model. Correctly interpret the regression results to answer the specific substantive questions posed in terms that can be understood by substantive experts; 7) Critique the methods and results from the perspective of the statistical methods chosen and alternative approaches that might have been.
- Tuesday 10:30 - 11:50
- Thursday 10:30 - 11:50