Copyright © Leland Stanford Junior University. All rights reserved. Warning: This presentation is protected by copyright law and international treaties. Unauthorized reproduction of this presentation, or any portion of it, may result in severe civil and criminal penalties and will be prosecuted to maximum extent possible under the law. HRP Topic 10 - Categorical Outcomes

Pearson Modeling Effect Size +/- 1 for 2x2 tables with Less Adverse Events Odds ratio = 22/44 ÷ 28/24 Relative Risk 1 = 22/66 ÷ 28/52 (χ 2 /N) ^.5

HRP Chi-Square Working  χ 2 = (Observed # - Expected #) 2 / Expected #  χ 2 determines if an association exits  χ 2 does not measure the strength of the association  χ 2 depends on and reflects sample size

 Right click on the flowchart or File > New…

HRP Tables Bigger than 2 x 2

Type “ Yes” with a leading blank

HRP

(16 * * * 3) / 71 = mean for ACT (24 * * * 3) / 71 = mean for Placebo

OR: 29/23 ÷ 40/60 = 1.891

If you model the wrong outcome, tweak this. You can control parameterization here.

Impact of drug relative to an on placebo baseline The model found an answer. If you have prefect prediction (0 frequencies in the contingency tables), expect problems. Use the response variable sort order if you are predicting the wrong outcome. Watch for missing data.

Akaike’s Information Criterion, Schwartz Criterion, -2 log likelihood are here. All are used to compare nested models. AIC and SC penalize you for the number of parameters. Overall, is the model any good?

Domer’s D (nc-nd) / t Gamma (nc –nd) / (nc + nd) Tau-a (nc – nd) / (.5 * N * N-1) c = (nc +.5 * (t-nc –nd)) / t nc = # concordant pairs Nd = # discordant pairs t = pairs with different response values c = area under the ROC curve Somer’s D = 2(c-.5) Concordant = Given a pair of observations with different values in the response variable, the model correctly assigns the higher probability of the outcome to the person with the outcome.

Sensitivity: Correctly identify the presence of a condition in those with the disease. Specificity: Correctly identify the lack of a condition in those without the disease.

HRP Odds of a Month in Remission

HRP Profile likelihood are more accurate (especially for small samples) but they need extra horsepower to calculate.

HRP Confidence Intervals

Don’t interpret these as the % of variance accounted for in your model.

Image from: Categorical Data Analysis Using Logistic Regression Course Notes (2005) SAS.

Like leverage Standardized change in parameters if this observation is dropped How good does the model do at predicting each person Overall change in parameters if this observation is dropped. Like cooks distance.

Events (healthy) Not events (sick) Poorly fit are in the upper corners. Rough rule of thumb is > 4. See Hosmer and Lemeshow (2000).

Modify the code to get a better plot showing the impact on the CLs.

HRP Look for big bubbles and you can hover the mouse over the dots to see the subject- observation number.

HRP Are you missing interactions?  Compare you model vs. a saturated model.  It does not make sense if you have continuous variables in the model.

HRP Use H and L if you have continuous predictors in the model.

Logistic “issues”

Conditional Logistic They forgot the strata task role! Use “Group analysis by” then tweak the code. You want to predict BBD, so change response variable sort order to descending.

HRP Change “by” into strata.