Unit 4: Contingency Tables & Simple Logistic Regression: Inference in Case CC and QC

Learning Objectives

Contingency Table Methods for Binary Outcomes

  • Apply contingency tables for binary outcomes with binary or multi-level predictors
  • Identify the appropriate conditional percentages to compare to answer specific research questions.
  • Conduct the appropriate chi-square test for association or when appropriate use Fisher’s exact test.
  • Calculate and interpret measures of association for binary outcomes
    • Excess Risk (or Risk Difference)
    • Relative Risk
    • Odds Ratio
  • Discuss issues related to the three measures of association for binary outcomes.

Logistic Regression using One Predictor

  • Use LOG rules for powers and division appropriately as needed to work with logistic models.
  • Discuss the reasons the logistic model is preferred for modeling probabilities.
  • Discuss the benefit of the logistic model that it can be rewritten in terms of a linear model using an appropriate LOGIT transformation.
  • Use the logistic model to predict probabilities or LOG-ODDS.
  • State the assumptions of the logistic regression model.
  • Derive and appropriately interpret the log-odds-ratio and odds-ratio for comparing levels of a categorical predictor to the reference group.
  • Derive and appropriately interpret the log-odds-ratio and odds-ratio for a one-unit increase or a c-unit increase for a continuous predictor.
  • Appropriately use SAS output to conduct logistic regression analysis for one predictor and multiple predictors, possibly including interactions.
  • Construct confidence intervals for parameter estimates and odd-ratios by hand for comparisons to a reference group for categorical predictors.
  • Construct confidence intervals for parameter estimates and odd-ratios by hand for a one-unit or c-unit increase in a continuous predictor.
  • Be able to find odd-ratio and confidence intervals in the reverse direction of comparisons given in software output by taking the reciprocal of the values in the output.
  • Use contrast and oddsratio statements to test and estimate complex comparisons.
  • Appropriately use percent increase or percent decrease interpretations for odd-ratios.

The following lessons from Penn State STAT 501 are linked in the materials as support materials for Unit 4. Our videos will be the primary instruction for Unit 4 and Unit 5.