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midterm2011sol

# midterm2011sol - NAME_SOLUTIONS PUBH 7430 Midterm...

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NAME: __________ SOLUTIONS __________________ PUBH 7430 – Midterm examination November 3, 2011 This exam runs from 9:45 a.m. until 11:00 a.m. There are 5 questions, for a total of 80 points. There is an (optional) BONUS question worth 5 additional points at the end of Question 1. Closed book, closed notes. Write all your answers on the exam paper. Where appropriate, show your work. Good luck!

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Question 1 [ 26 + 5 points ] A venous catheter with antibacterial coating is being tested to see if it reduces colonization of the catheter with bacteria, compared with a standard catheter. Patients in an intensive care unit receive multiple catheters over time; which catheter a patient gets is determined by randomization at baseline (i.e. a patient always gets the same type of catheter). The response variable is the presence (1) or absence (0) of bacterial colonization in the catheter and the treatment variable is 1 for the coated catheter and 0 for the standard catheter. a) [ 5 points ] In these data, which observations would expect to be correlated? Which would you expect to be independent? We would expect observations on the same individual (i.e. colonization outcomes over time) to be correlated. We would expect observations on different individuals to be independent, provided any common external factors (eg. nursing staff) do not affect the outcome. b) [ 21 points, 3 points per part ] The following tables summarize the effect of treatment as estimated from 1) a GEE logistic regression model with exchangeable working correlation matrix, and 2) a random effects logistic regression model with random intercept. 1) GEE logistic regression model Estimate 95% CI p-value Treatment (coated cath) -0.79 (-1.63, 0.05) 0.07 2) Random effects logistic regression model w/ random intercept Estimate 95% CI p-value Treatment (coated cath) -0.54 (-0.97, -0.11) 0.03
i) For the GEE model, write down: - The assumed mean model for observation i from cluster j logit(p ij ) = β 0 + β 1 x treatment ij - The assumed variance function Var(Y ij | trt ij ) = p ij (1-p ij ) - The assumed working correlation matrix for a cluster (individual) who received three catheters 1 ρ ρ ρ 1 ρ ρ ρ 1 ii) Write a sentence interpreting the treatment effect from the GEE model. The odds ratio comparing treatment to control is exp(-0.79) = 0.45. Hence the odds of having bacterial colonization are 55% lower with the coated catheter than the standard catheter (95% CI: 80% lower to 5% higher). The treatment effect is not significant at the 0.05 level (p = 0.07). iii) Does an exchangeable working correlation matrix seem like a reasonable assumption for these data? Why or why not? One could argue that an exchangeable correlation structure is reasonable since the likelihood of catheter colonization is determined mainly by the unique characteristics (eg. immune system) of each patient. Hence the time at which each successive catheterization was performed is unlikely to influence the correlation between the outcomes.

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midterm2011sol - NAME_SOLUTIONS PUBH 7430 Midterm...

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