Basic epidemiologic analysis with Stata Biostatistics 212 Lecture

Basic epidemiologic analysis with Stata Biostatistics 212 Lecture 5

Housekeeping • Questions about Lab 4? – Extra credit puzzle • Lab 3 issues – Make sure your do file executes – Make sure your do file opens the dataset • Final Project – by the last session you should: – – Have dataset imported into Stata Clean up the variables you will use Sketch out (paper and pencil) a table and a figure Be ready to write analysis do files

Today. . . • What’s the difference between epidemiologic and statistical analysis? • Interaction and confounding with 2 x 2’s • Stata’s “Epitab” commands • Adjusting for many things at once • Logistic regression • Testing for trends

Epi vs. Biostats • Statistical analysis – Evaluating the role of chance • Epidemiologic analysis – Analyzing and interpreting clinical research data in the context of scientific knowledge – – – Directionality of causes Mediation vs. confounding Prediction vs. causal inference Clinical importance of effect size “Cost” of a type I and type II error

Epi vs. Biostats • Epi –Confounding, interaction, and causal diagrams. – What to adjust for? – What do the adjusted estimates mean? C A B A C B

2 x 2 Tables • “Contingency tables” are the traditional analytic tool of the epidemiologist Outcome + + a b Exposure - c d OR = (a/b) /(c/d) = ad/bc RR = a/(a+b) / c/(c+d)

2 x 2 Tables • Example Coronary calcium + Binge drinking + 106 585 691 - 186 2165 2351 292 2750 3042 OR = 2. 1 (1. 6 – 2. 7) RR = 1. 9 (1. 6 – 2. 4)

2 x 2 Tables • Example Can we say that binge drinking CAUSES atherosclerosis? Coronary calcium + Binge drinking + 106 585 691 - 186 2165 2351 292 2750 3042 OR = 2. 1 (1. 6 – 2. 7) RR = 1. 9 (1. 6 – 2. 4)

2 x 2 Tables • There is a statistically significant association, but is it causal? Male Binge drinking Coronary calcium • Does male gender confound the association?

2 x 2 Tables • Men more likely to binge – 34% of men, 14% of women • Men have more coronary calcium – 15% of men, 7% of women

2 x 2 Tables • But what does confounding look like in a 2 x 2 table? • And how do you adjust for it?

2 x 2 Tables • But what does confounding look like in a 2 x 2 table? • And how do you adjust for it? – Stratify – Examine strata-specific estimates (for interaction) – Combine estimates if appropriate (if no interaction) • Weighted average of strata-specific estimates

2 x 2 Tables • First, stratify… + Binge 374 - + 106 585 - 186 2165 In men CAC + + 89 Binge - 118 CAC RR = 1. 94 (1. 55 -2. 42) In women CAC + - (34%) 801 (15%) RR = 1. 50 (1. 16 -1. 93) + 17 Binge - 68 211 (14%) 1364 (7%) RR = 1. 57 (0. 94 -2. 62)

2 x 2 Tables • …compare strata-specific estimates… In men CAC + + 89 Binge - 118 374 In women CAC + (34%) 801 + 17 Binge - 68 (15%) RR = 1. 50 (1. 16 -1. 93) • (they’re about the same) 211 (14%) 1364 (7%) RR = 1. 57 (0. 94 -2. 62)

2 x 2 Tables • …and then “combine” the estimates. In men CAC + Binge + 89 374 - 118 801 RR = 1. 50 (1. 16 -1. 93) In women CAC + Binge + 17 211 - 68 1364 RR = 1. 57 (0. 94 -2. 62) RRadj = 1. 51 (1. 21 -1. 89)

Binge + - + 106 585 - 186 2165 In men CAC + Binge + 89 374 - 118 801 RR = 1. 94 (1. 55 -2. 42) In women CAC + - (34%) Binge (15%) + 17 211 - 68 1364 (14%) (7%) RR = 1. 50 (1. 16 -1. 93) RR = 1. 57 (0. 94 -2. 62) RRadj = 1. 51 (1. 21 -1. 89)

2 x 2 Tables • How do we do this with Stata? – Tabulate – output not exactly what we want. – The “epitab” commands • Stata’s answer to stratified analyses cs, cc csi, cci tabodds, mhodds

2 x 2 Tables • Example – demo using Stata cs cac binge, by(male) cs cac modalc, by(racegender) cc cac binge

2 x 2 Tables • Example of Confounding. cs cac binge, by(male) male | RR [95% Conf. Interval] M-H Weight ---------+------------------------0 | 1. 570175. 9402789 2. 622042 9. 339759 1 | 1. 497071 1. 164201 1. 925117 39. 53256 ---------+------------------------Crude | 1. 938954 1. 551487 2. 423187 M-H combined | 1. 511042 1. 205656 1. 89378 ---------------------------------Test of homogeneity (M-H) chi 2(1) = 0. 027 Pr>chi 2 = 0. 8700

2 x 2 Tables • Example of Effect Modification. cs cac modalc, by(racegender) racegender | RR [95% Conf. Interval] M-H Weight ---------+------------------------Black women |. 75888. 3595892 1. 601547 8. 043758 White women |. 8960739. 4971477 1. 61511 11. 07552 Black men | 1. 945668 1. 114927 3. 3954 8. 304878 White men |. 9279831. 66551 1. 293974 29. 45557 ---------+------------------------Crude | 1. 30072 1. 023022 1. 653798 M-H combined | 1. 046446. 8225915 1. 331218 ---------------------------------Test of homogeneity (M-H) chi 2(3) = 6. 245 Pr>chi 2 = 0. 1003

2 x 2 Tables • Inmediate commands – csi, cci – No dataset required – just 2 x 2 cell frequencies csi a b c d csi 106 186 585 2165 (for cac binge)

Multivariable adjustment • Binge drinking appears to be associated with coronary calcium – Association partially due to confounding by gender • What about race? Age? SES? Smoking?

Multivariable adjustment manual stratification # 2 x 2 tables Crude association 1 Adjust for gender 2 Adjust for gender, race 4 Adjust for gender, race, age 68 Adjust for “” + income, education 816 Adjust for “” + smoking 2448

Multivariable adjustment cs command • cs command – Does manual stratification for you • Lists results from every strata • Tests for overall homogeneity • Adjusted and crude results – Demo cs cac binge, by(male black age)

Multivariable adjustment cs command • cs command – Does manual stratification for you • Lists results from every strata • Tests for overall homogeneity • Adjusted and crude results – Demo cs cac binge, by(male black – Can’t interpret interactions! age)

Multivariable adjustment mhodds command • mhodds allows you to look at specific interactions, adjusted for multiple covariates – Does same stratification for you – Adjusted results for each interaction variable – P-value for specific interaction (homogeneity) – Summary adjusted result • Demo mhodds cac binge age, by(racegender)

Multivariable adjustment mhodds command • mhodds allows you to look at specific interactions, adjusted for multiple covariates – Does same stratification for you – Adjusted results for each interaction variable – P-value for specific interaction (homogeneity) – Summary adjusted result • Demo mhodds cac binge • But strata get thin! age, by(racegender)

Multivariable adjustment logistic command • Assumes logit model – Await biostats class for details! – Coefficients estimated, no actual stratification – Continuous variables used as they are

Multivariable adjustment logistic command Basic syntax: logistic outcomevar [predictorvar 1 predictorvar 2 predictorvar 3…]

Multivariable adjustment logistic command If using any categorical predictors: logistic outcomevar [i. catvar 2…] Creates “dummy variables” on the fly If you forget, Stata won’t know they are categorical, and you’ll get the wrong answer!

Multivariable adjustment logistic command Demo logistic logistic cac cac binge male black age binge male black age i. smoke binge##i. racegender age i. smoke modalc##racegender

Multivariable adjustment logistic command Demo. xi: logistic cac binge male black age i. smoke _Ismoke_0 -2 (naturally coded; _Ismoke_0 omitted) Logistic regression Log likelihood = -852. 99988 Number of obs LR chi 2(6) Prob > chi 2 Pseudo R 2 = = 3036 211. 95 0. 0000 0. 1105 ---------------------------------------cac | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] -------+--------------------------------binge | 1. 387573. 1985355 2. 29 0. 022 1. 048251 1. 836736 male | 3. 253031. 4608839 8. 33 0. 000 2. 464287 4. 294226 black |. 7282563. 0994953 -2. 32 0. 020. 5571756. 9518674 age | 1. 19833. 025771 8. 41 0. 000 1. 148869 1. 24992 _Ismoke_1 | 1. 357694. 2308651 1. 80 0. 072. 972886 1. 894707 _Ismoke_2 | 2. 120925. 3302698 4. 83 0. 000 1. 563063 2. 87789 ---------------------------------------

logistic command interaction demo. logistic cac modalc##racegender age i. smoke Logistic regression Log likelihood = -739. 54359 Number of obs LR chi 2(10) Prob > chi 2 Pseudo R 2 = = 2795 186. 28 0. 0000 0. 1119 ---------------------------------------cac | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] -------+--------------------------------1. modalc |. 6024889. 2430813 -1. 26 0. 209. 2732258 1. 328546 | racegender | 2 | 1. 018361. 3137632 0. 06 0. 953. 5567262 1. 862783 3 | 1. 601149. 519393 1. 45 0. 147. 8478374 3. 023786 4 | 4. 119486 1. 100853 5. 30 0. 000 2. 439922 6. 955209 | modalc#| racegender | 1 2 | 1. 422897. 7314808 0. 69 0. 493. 5195041 3. 897247 1 3 | 2. 867897 1. 473405 2. 05 0. 040 1. 047736 7. 850102 1 4 | 1. 546468. 7057105 0. 96 0. 339. 6322751 3. 782472 | age | 1. 184036. 0271845 7. 36 0. 000 1. 131937 1. 238534 | smoke | 1. 438413. 2623889 1. 99 0. 046 1. 00603 2. 056629 2 | 2. 464978. 4157232 5. 35 0. 000 1. 771154 3. 430597 ---------------------------------------

Multivariable adjustment logistic command • Pro’s – – Provides all OR’s in the model Accepted approach (mhodds rarely used by statisticians) Can deal with continuous variables (like age) Better estimation for large models? • Con’s – Interaction testing more cumbersome, less automatic – More assumptions – Harder to test for trends

Multivariable adjustment • Format for linear regression, and other types of regression is the same as for logistic regression, except for the initial command: regress outcomevar [predictorvar 1 predictorvar 2 predictorvar 3…] ologit outcomevar [predictorvar 1 predictorvar 2 predictorvar 3…] etc

Testing for trend • Test of trend with tabodds cac alccat -------------------------------------alccat | cases controls odds [95% Conf. Interval] ------+------------------------------0 | 110 1325 0. 08302 0. 06835 0. 10084 <1 | 90 933 0. 09646 0. 07770 0. 11976 1 -1. 9 | 46 295 0. 15593 0. 11429 0. 21275 2+ | 45 193 0. 23316 0. 16856 0. 32252 -------------------------------------Test of homogeneity (equal odds): chi 2(3) = 36. 70 Pr>chi 2 = 0. 0000 Score test for trend of odds: chi 2(1) Pr>chi 2 = = 32. 20 0. 0000

Testing for trends tabodds command • Adjustment for multiple variables possible – tabodds cac alccat, adjust(age male black)

Approaching your analysis • Number of potential models/analyses is daunting – Where do you start? How do you finish? • My suggestion – – – Explore Plan definitive analysis, make dummy tables/figures Do analysis (do/log files), fill in tables/figures Show to collaborators, reiterate prn Write paper

Summary • Make sure you understand confounding and interaction with 2 x 2 tables in Stata • Epitab commands are a great way to explore your data – Emphasis on interaction • Logistic regression is a more general approach, ubiquitous, but testing for interactions and trends is more difficult

In lab today… • Lab 5 – Epi analysis of coronary calcium dataset – Walks you through evaluation of confounding and interaction • Judgment calls – often no right answer, just focus on reasoning. • Reminder – put your answers as comments in the do file * 15 c – 15%, p<. 001