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Lecture 17: Review of earlier concepts Regression for Case-control Studies

Lecture 17: Review of earlier concepts Regression for Case-control Studies. BMTRY 701 Biostatistical Methods II. The likelihood function. What is it? What is the log-likelihood function? Why are they important?. Maximum Likelihood:. What does it mean? What are MLEs? binomial model

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Lecture 17: Review of earlier concepts Regression for Case-control Studies

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  1. Lecture 17:Review of earlier conceptsRegression for Case-control Studies BMTRY 701 Biostatistical Methods II

  2. The likelihood function • What is it? • What is the log-likelihood function? • Why are they important?

  3. Maximum Likelihood: • What does it mean? • What are MLEs? • binomial model • logistic regression

  4. Likelihood Ratio Test • What is it? • How do we do it?

  5. Logistic Regression Model • Logistic regression • Logit transformation

  6. Wald Test • What is it? • How do we find it in R?

  7. Additional Reading in Logistic REgression • Hosmer and Lemeshow, Applied Logistic Regression • http://en.wikipedia.org/wiki/Logistic_regression • http://luna.cas.usf.edu/~mbrannic/files/regression/Logistic.html • http://www.statgun.com/tutorials/logistic-regression.html • http://www.bus.utk.edu/stat/Stat579/Logistic%20Regression.pdf • Etc: Google “logistic regression”

  8. Case Control Studies in Logistic Regression • http://www.oxfordjournals.org/our_journals/tropej/online/ma_chap11.pdf • How is a case-control study performed? • What is the outcome and what is the predictor in the regression setting?

  9. Recall the simple 2x2 example • Odds ratio for 2x2 table can be used in case-control studies • Similarly, the logistic regression model can be used treating ‘case’ status as the outcome. • It has been shown that the results do not depend on the sampling (i.e., cohort vs. case-control study).

  10. Example: Case control study of HPV and Oropharyngeal Cancer • Gillison et al. (http://content.nejm.org/cgi/content/full/356/19/1944) • 100 cases and 200 controls with oropharyngeal cancer • How was the sampling done?

  11. Data on Case vs. HPV > table(data$hpv16ser, data$control) 0 1 0 186 43 1 14 57 > epitab(data$hpv16ser, data$control) $tab Outcome Predictor 0 p0 1 p1 oddsratio lower upper p.value 0 186 0.93 43 0.43 1.00000 NA NA NA 1 14 0.07 57 0.57 17.61130 8.99258 34.49041 4.461359e-21

  12. Multiple Logistic Regression • This is not ‘randomized’ study • there are lots of other predictors that may be associated with the cancer • Examples: • smoking • alcohol • age • gender

  13. Fit the model: • Write down the model • assume main effects of tobacco, alcohol and their interaction • What is the likelihood function? • What are the MLEs?

  14. How do we interpret the results? • Is there an effect of tobacco? • Is there an effect of alcohol? • Is there an interaction?

  15. Interpreting the interaction • What is the OR for smoker/non-drinker versus a non-smoker/non-drinker? • What is the OR for a smoker/drinker versus a non-smoker/drinker?

  16. How can we assess if the effect of smoking differs by HPV status?

  17. How likely is it that someone who smokes and drinks will get oropharyngeal cancer? • How can we estimate the chance?

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