University:
Boston University
Course:
QST SM 101 | Introduction to Management
Academic year:

2022
Views:

37

Pages:

19
Author:

pubicswprv

Applied Logistic Regression: SAS Coding Tips to Enhance Interpretation of Modeling and Output Analysis of Categorical or Event Outcomes Boston University Slideshow Title Goes Here  Outcome (dependent variable): dichotomous (yes/no, event)  Study design: either comparing groups on dichotomous outcome, or association with dichotomous outcome; Cross-sectional or Cohort or Case-Control or RC Trial  The independent variable(s) can be measurement or categorical A Little Refresher University Slideshow Title Goes Here Boston The logistic model is based on the odds of an event occurring: Based on the odds or probability, px/(1-px) log(odds(x))=log (px/1-px)=β0 + βx logit(P)=β0 + βx The Odds Ratio (x1 vs x2)= px1/(1-px1) px2/(1-px2) The Odds Ratio Boston University Slideshow Title Goes Here Sharon misses yoga class Cherry Garcia Ice Yes (1) Cream No (0) Total Yes (1) 7 3 10 No (0) 4 6 10 Total 11 9 20 OR of Cherry Garcia Boston University Slideshow Title Goes Here  The probability of Sharon having Cherry Garcia when she skips yoga is 7/11 or 0.63 . The odds from this probability are (p/ 1-p) or 0.63/0.36= 1.75  The probability of Sharon having CG when she attends class 3/9 or 0.33. The odds from this probability are 0.33/0.66= 0.50  OR= 1.75/ 0.5 = 3.50 A Simple SAS Example Boston University Slideshow Title Goes Here  Perhaps we want to look at the association between CHD and age  CHD is coded as 1=yes 0=no  Age is a measurement Independent variable Boston University Slideshow Title Goes Here The "SIMPLE" option gives summary statistics The (event = '1') is an efficient way of specifying the probability modeled (vs. using the descending option ) proc logistic data=chdage simple; model chd (event='1') = age;run; The Be sure your output is modeling the event of interestent Boston University Slideshow Title Goes Here Response Profile Ordered Value chd 1 0 Total Frequency 57 2 1 Probability modeled is chd=1. 43 The The SAS Units Statement tement Boston University Slideshow Title Goes Here  The SAS UNITS statement - When we have a continuous IV often the value of a 1 unit change in x will not be very biologically interesting or clinically meaningful proc logistic data=chdage simple; model chd (event='1') = age/ clodds = wald; units age= sd 5 10; run; The The SAS Units Statement tement Boston University Slideshow Title Goes Here  The SAS UNITS statement - When we have a continuous IV often the value of a 1 unit change in x will not be very biologically interesting or clinically meaningful proc logistic data=chdage simple; model chd (event='1') = age/ clodds = wald; units age= sd 5 10; run; Output from the Units Statement Boston University Slideshow Title Goes Here Descriptive Statistics for Continuous Variables Variable age chd 0 Mean 39.175439 Standard Deviation 10.201755 1 51.279070 9.979325 25.000000 69.000000 Total 44.380000 11.721327 20.000000 69.000000 Minimum 20.000000 Maximum 64.000000 Odds Ratio Estimates and Wald Confidence Intervals Effect Age (1 SD) Unit 11.7213 Estimate 3.670 95% Confidence Limits 2.112 age 1.0000 1.117 1.066 1.171 age 5.0000 1.741 1.376 2.204 age 10.0000 3.032 1.892 4.859 6.378 Reference Group Coding Boston University Slideshow Title Goes Here Let us consider data from a study designed to identify risk factors associated with giving birth to a baby weighing less than 2500 grams (LBW) Race is categorized as White=1 Black=2 and Other=3 We will consider Indicator variables for Race RACE WHITE 0 0 (White=1 , Black=2, Other=3 codes in dataset) BLACK 1 0 OTHER 0 1 What are the Odds of having a Low Birth Weight Baby Based on Race? Boston University Slideshow Title Goes Here proc logistic data=work.lbw simple; class race/ param=ref ref=first; model low (event='1')= LWT RACE ; run; White Coded as 1 Becomes our Reference Group Boston University Slideshow Title Goes Here Class Level Information Class RACE Probability modeled is LOW=1. Value 1=white Design Variables 0 0 2=Black 1 0 3=Other 0 1 Odds Ratio Estimates Effect LWT Point Estimate 0.985 95% Wald Confidence Limits 0.973 0.997 RACE 2 vs 1 2.948 1.133 7.672 RACE 3 vs 1 1.617 0.804 3.253 SAS defaults to Deviation from Means Coding Boston University Slideshow Title Goes Here  If the parameter statements are not used- sas will default to deviation from the means coding  This expresses effect as the deviation of the group mean from the overall mean. Class Level Information Design Class Value Variables RACE 1 -1 -1 2 1 0 3 0 1 Back to some math • Due to the S shape of the logistic distribution one must use the natural log (ln) to account for the shape • ln(P)=β0 + βx • The odds ratio is equal to exp(B) • So we may need to exponentiate our beta coefficient or slope to get the odds ratio exp(1.08)=2.94 and conversely ln(2.94)=1.08 Example with Proc Genmod Boston University Slideshow Title Goes Here proc genmod data=work.lbw descending; class race (ref='1')/ param=ref; model low = lwt race /dist=bin type3 link=logit ; estimate "Black vs White" race 1 0 / exp; run; White=1 0 0 0 Black=2 0 1 0 Other=3 0 0 1 Of Here Maximum Likelihood Parameter Estimates Boston University SlideshowAnalysis Title Goes Parameter Intercept LWT Wald 95% Confidence Limits 0.8452 -0.8507 2.4622 Wald ChiSquare 0.91 Pr > ChiSq 0.3404 DF 1 Estimate 0.8058 1 -0.0152 0.0064 -0.0278 -0.0026 5.59 0.0181 RACE 2 1 1.0811 0.4881 0.1245 2.0376 4.91 0.0268 RACE 3 1 0.4806 0.3567 -0.2185 1.1797 1.82 0.1778 0 1.0000 0.0000 1.0000 1.0000 Scale Contrast Estimate Results Mean Label Black vs White Exp(Black vs White) L'Beta Mean Confidence L'Beta Standard Estimate Limits Estimate Error Alpha 0.7467 0.5311 0.8847 1.0811 0.4881 0.05 2.9478 1.4387 0.05 Confidence Limits 0.1245 2.0376 1.1326 7.6724 ChiSquare 4.91 Pr > ChiSq 0.0268