Master CDA and GLM applications

Distinguish between categorical, ordinal, and nominal data and identify appropriate summary measures for each.

Construct and interpret a contingency table from raw categorical data.

Explain different sampling schemes (e.g., product-multinomial, multinomial) and their implications for analysis.

Compute and interpret joint, marginal, and conditional distributions from a contingency table.

Define, compute, and interpret the difference in proportions for a 2×2 table.

Define, compute, and interpret the relative risk for a 2×2 table.

Define, compute, and interpret the odds ratio for a 2×2 table, including its key properties.

Explain when the odds ratio vs. relative risk is the appropriate measure of association based on the study design.

State the null and alternative hypotheses for a test of independence in a contingency table.

Explain how the Pearson chi-square statistic is constructed and determine its degrees of freedom.

Identify when the chi-square test assumptions are violated (e.g., small expected counts).

Explain the logic behind Fisher's exact test and when to prefer it over the chi-square test.

Explain the concept of a permutation test as a general approach for hypothesis testing.

Apply chi-square, Fisher's exact, and permutation-based tests to real data and report findings correctly.

Explain when a trend test is more powerful and appropriate than a general chi-square test of independence.

Describe the Cochran-Armitage trend test: its hypotheses, assumptions, and application for ordinal-by-nominal tables.

Explain the linear-by-linear association test and its application for ordinal-by-ordinal tables.

Apply and interpret the results of both the Cochran-Armitage and linear-by-linear association tests to data.

Explain why standard chi-square tests are inappropriate for paired or matched categorical data.

Describe the McNemar test for analyzing pre-post changes in paired 2×2 tables.

Apply the McNemar test and interpret its results in a practical context.

Describe the Stuart-Maxwell test as a generalization of the McNemar test for k×k tables.

Describe and apply the Cochran Q test for comparing proportions across more than two related groups.

Contrast test-based approaches (e.g., McNemar) with model-based approaches (e.g., Conditional Logistic Regression) for analyzing paired data.

Define confounding and explain how it can distort the measure of association between two variables.

Use stratification to identify the presence of confounding in contingency table analysis.

Describe the purpose of the Cochran-Mantel-Haenszel (CMH) test for testing conditional independence.

Explain the concept of a 'common odds ratio' across strata and how it is estimated.

Apply the CMH test to stratified 2×2 tables and interpret the results, including the test for homogeneity of odds ratios.

Explain why ordinary linear regression is insufficient for non-normal response variables like binary outcomes or counts.

Identify the three core components of a GLM: random component, systematic component, and link function.

Explain the concept of the exponential family of distributions and its role in unifying the GLM framework.

Define a canonical link function and identify the canonical links for the Normal, Binomial, and Poisson distributions.

Distinguish between canonical and non-canonical link functions (e.g., logit vs. probit) and explain the trade-offs in their selection.

Explain the concept of deviance in a GLM and its role in measuring goodness of fit.

Describe the Wald, Deviance (Likelihood Ratio), and Score tests for hypothesis testing on GLM coefficients.

Compare the practical and theoretical differences between the Wald, Deviance, and Score tests.

Interpret the standard output of a fitted GLM, including coefficient estimates, standard errors, and test statistics.

Assess overall model fit using the deviance and the goodness-of-fit chi-squared test.

Use residual diagnostics (e.g., Pearson, deviance residuals) to check for model misspecification and influential points.

Formulate a binary logistic regression model and explain the interpretation of the logit link function.

Interpret logistic regression coefficients as log-odds and convert them to odds ratios with confidence intervals.

Assess the goodness of fit of a logistic regression model using deviance-based statistics and the Hosmer-Lemeshow test.

Define a confusion matrix and calculate performance metrics like sensitivity and specificity.

Construct a ROC curve and use the Area Under the Curve (AUC) to evaluate a model's discriminative power.

Fit, interpret, and evaluate a binary logistic regression model using a real dataset.

Explain when multinomial logistic regression is appropriate and describe its structure, including the role of a reference category.

Fit and interpret the coefficients from a multinomial logistic regression model.

Explain when ordinal logistic regression is appropriate and describe the proportional odds (cumulative logit) model.

Interpret the coefficients of an ordinal logistic regression model in terms of cumulative odds.

State and test the proportional odds assumption (e.g., using a Brant test).

Describe alternative modeling strategies for when the proportional odds assumption is violated.

Explain why standard (unconditional) logistic regression can produce biased estimates in matched study designs.

Relate the McNemar test to a simple conditional logistic regression model.

Describe how conditional logistic regression uses a conditional likelihood to eliminate nuisance parameters.

Fit a conditional logistic regression model to a matched case-control dataset and interpret the resulting coefficients.

Formulate a Poisson regression model for count data and explain the interpretation of the log link function.

Interpret Poisson regression coefficients as log rate ratios and convert them to rate ratios.

Explain the issue of overdispersion, its consequences for inference, and how to detect it.

Describe how log-linear models represent association structures in contingency tables.

Explain the relationship between the chi-square test of independence and the saturated log-linear model.

Connect the concepts of Poisson regression and log-linear models.

Apply a log-linear model to a multi-way contingency table to interpret its association structure.