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# CAT ANALYSIS EPIDEM EPI 536

UW

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This 19 page Class Notes was uploaded by Garry Marvin on Wednesday September 9, 2015. The Class Notes belongs to EPI 536 at University of Washington taught by Staff in Fall. Since its upload, it has received 35 views. For similar materials see /class/191973/epi-536-university-of-washington in Epidemiology at University of Washington.

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Date Created: 09/09/15

Midterm Review BIOSTEPI 536 October 28 2008 Hypothesis testing Purpose to ask whether the true value of the parameter is likely to have been different from some test value Likelihood Ratio Test Score Test Wald Test If individual model terms represent dummy variables which test should you use Types of models Saturated Full Reduced Null How can you tell if one model is nested within another Why is this important Example esophageal cancer risk You are interested in studying the effect of alcohol consumption on the risk of esophageal cancer after adjusting for age Age age is coded as O 2444 1 45 64 2 65 Alcohol alc is coded as O 039 1 40 792 80119 3 120 gramsday Q Write out the formula for the logit and stata command for model with categorical age and ordinal alcohol Q Write out the formula for the logit and stata command for model with categorical age and ordinal alcohol A logitU 30 310861 320862 636110 Stata code xi logit cc iage alc Is the model with logitp 3031alc nested in the model with logitp 3031alc132a0233alcs To show nesting do one of the following Rewrite full model as reduced model plus extra terms that can be set to zero as done in previous discussion Rewrite reduced model so that it contains all terms in full model and compare coefficients Note that alc alc12a023alc3 Then reduced model is Iogitltpgt Boslalc 3031alc12alc23a03 3031alc1231a02331alc3 Models will be equal if 3030 31261 322261 and BB36139 Akkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Xi logit cc alc iage iage Iage0 2 naturally coded Iage0 omitted Logistic regression Number of obs 975 LR chi23 24800 Prob gt chi2 00000 Log likelihood 37074599 Pseudo R2 02506 co Coef Std Err Pgtz 95 Conf Interval alc 1092815 102185 0000 8925358 1293094 Iage1 2341755 3528545 0000 1650172 3033337 Iage2 2981249 3760928 0000 2244121 3718377 cons 4636974 3686775 0000 5359568 3914379 estimates store glinear WHAT IS THE LR chi2 3 24800 testing Akkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Xi logit cc alc iage iage Iage0 2 naturally coded Iage0 omitted Logistic regression Number of obs 975 LR chi23 24800 Prob gt chi2 00000 Log likelihood 37074599 Pseudo R2 02506 co Coef Std Err z Pgtz 95 Conf Interval alc 1092815 102185 1069 0000 8925358 1293094 Iage1 2341755 3528545 664 0000 1650172 3033337 Iage2 2981249 3760928 793 0000 2244121 3718377 cons 4636974 3686775 1258 0000 5359568 3914379 estimates store glinear The LR chi23 24800 is a test of the parameters in this model compared to the null model If you needed to determine the loglikelihood value of the null model you could calculate it from the information given on this slide 248 2x 37o7 X 4948 Bkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Xi logit cc ialc iage ialc Ialc0 3 naturally coded Ialc0 omitted iage Iage0 2 naturally coded Iage0 omitted Logistic regression Number of obs 975 LR chi25 25407 Prob gt chi2 00000 Log likelihood 36770864 Pseudo R2 02568 cc Coef Std Err z Pgtz 95 Conf Interval Ialc1 1420253 2433156 584 0000 9433629 1897143 Ialc2 1998396 2749044 727 0000 1459593 2537198 Ialc3 3676903 3718568 989 0000 2948078 4405729 Iage1 2423755 3609901 671 0000 1716227 3131283 Iage2 3080279 3842215 802 0000 2327219 383334 cons 4849649 3946009 1229 0000 5623053 4076246 estimates store dummy LR 1kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk lrtest glinear dummy Likelihood ratio test LR chi22 607 Assumption glinear nested in dummy Prob gt chi2 00480 Using Model A interpret the following Cons Alo lage1 Using Model A interpret the following Cons log odds of esophageal cancer among individuals in the lowest age group and lowest alcohol exposure group Alc log odds ratio for esophageal cancer risk comparing any two adjacent categories of alcohol exposure 120 vs 4079 or 4079 vs 039 adjusting for age lage1 log odds ratio comparing individuals in aged 4564 to 2444 holding alcohol level constant Q Is there evidence of a linear trend for alcohol group Q Is there evidence of a linear trend for alcohol group A Yes there is strong evidence for a linear trend for the alcohol group using the Wald statistic from the output for Model A and the grouped linear alcohol term Q Would you recommend using the grouped linear term or the dummy variable categorization for alcohol exposure Why Q Would you recommend using the grouped linear term or the dummy variable categorization for alcohol exposure Why A Using the likelihood ratio test from the output testing the grouped linear model vs the dummy variable model we would reject the null hypothesis and conclude that the dummy variable categorization for alcohol appears to be most appropriate Q How would you go about testing if age is statistically significantly associated with esophagealcancernsk Q Can you do this with the given data If yes do so if not explain why not and how you would perform the test Q How would you go about testing if age is statistically significantl associated with esophageal cancer ris A Test using the likelihood ratio test Q Can you do this with the given data If yes do so if not explain why not and how you would perform the test A No we do not have the log likelihood value of a model with only alcohol either grouped linear or categorical 2log likelihood reduced log likelihood full Reduced model model with only alcohol Full model model with alcohol and categorical age

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