1 / 35

Lecture 14: Logistic regression

Lecture 14: Logistic regression. risk. 30. 30. 2  2 table (contingency table). Depression. No depression. 10. 20. Divorce . 1. 29. No divorce. a+b. c+d. 2  2 table (contingency table). Disease. Healthy. a. b. Exposed. c. d. Not-exposed. Risk ( absolute).

teddy
Download Presentation

Lecture 14: Logistic regression

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 14: Logistic regression

  2. risk 30 30 22 table (contingency table) Depression No depression 10 20 Divorce 1 29 No divorce

  3. a+b c+d 22 table (contingency table) Disease Healthy a b Exposed c d Not-exposed

  4. Risk (absolute) • Proportion of individuals initially healthy who contracted the disease during a given periode • The observation period must be the same for everyone • Given as a proportion (0-1), or a percentage (0-100%) • Estimation of the risk • For exposed • For non-exposed

  5. Relative risk • Ratio of the risk for the exposed to the risk for the non-exposed (no unit) • Interpretation • RR>1: exposition increases the risk • RR=1: exposition does not modify the risk • RR<1: exposition decreases the risk • When RR<1, relative risk reduction (in %)may be presented RR = Re / Rne RRR = (1-RR)*100

  6. Caveat • Relative risk does not provide any information on the importance of the compared risks • RR = 3 peut correspondre à: • Re = 45% Rne = 15% • Re = 3% Rne = 1% • Re = 0.006% Rne = 0.002% • …

  7. Risk difference • Difference between the risks of the exposed and non-exposed individuals • Given as a proportion or a percentage • Interpretation • DR>0: exposition increases the risk • DR=0: exposition does not modify the risk • DR<0: exposition decreases the risk DR = Re – Rne

  8. H0: Re = Rne 2 test Test and estimation • Null hypothesis: no effect of exposition: • RR = 1 • DR = 0 • It is also possible to compute a standard-error for each of these statistics, and to obtain a confidence interval

  9. BMJ 2003;327:1254-7

  10. RR=1.53

  11. Prevalence of smoking in an freshman class Prevalence • Proportion of individuals having a disease (or presenting a characteristic) at a given moment • Moment is defined by • Date (eg: 19 october 2011) • Event (eg: at birth)

  12. Incidence rate • Risk of contracting a disease during one time unit • Numerator: new cases • Denominator: sum of the time-person at risk • Person-years • Person-days • …

  13. Comparison with prospective study: case control study… • Allows to studyvery rare conditions (e.g., autism, suicide) • Can be made more quickly • Requiresless observations (cost) • Allows to test severalriskfactors for the outcome • But… • Does not allow to compute a risk, or an incidence rate (question: why) • Risk of bias in the measure of risk factor • Difficult to chooseappropriate control • Can onlystudy one condition at a time

  14. We take only a sample We take everyone Case control study Case Control The sums: a+b and c+d have no sense! a b Exposed Impossible to compute risk and relative risk c d Non-exposed

  15. Solution: odds ratio • Transform a proportion in odds • Transform odds in proportion:

  16. denominator numerator b/d a/c exposition odds Cas control study Case Control a b Exposed c d Non-exposed

  17. Disease odds a/b c/d b/d a/c Exposition odds Prospective study Disease Healthy a b Exposed c d Non-exposed

  18. Signification a-b-c-d

  19. odds ratio Disease odds Exposition odds Property of odds ratio • Exposition odds ratio = disease odds ratio Odds ratio are the same, computed from a prospective study or a case control study

  20. Odds ratio and relative risk • When the condition is rare, (a<<b et c<<d), OR is approximately equal to RR

  21. 573 patients with facial clefts • 763 controls • Exposition: • Taking more than 400 mg of folic acid supplements BMJ 2007; 334:464-470

  22. Results Odds ratio for folic acid < 400 mg

  23. Why not compute the RR? • The prevalenceis not correct since the goal of the case-control design is to have as many cases as controls. • Thus, a/(a+b)does not makesense.

  24. Interpretation of odds ratio • Similar to relative risk: • OR>1: IV is associated with DV (e.g., exposition is associated with disease) • OR=1: IV is not associated with DV • OR<1: IV is negatively associated with DV • Folicacid and facial cleft: • Not takingfolicacidsupplements(>400 mg)increases the risk of facial cleft (by 40%)

  25. Continuous IV • Compare means of cases and controls (t test) • Divide the IV in several categories and compute an odds ratio for each category • Model:

  26. Model: linear regression Proportion of males >100% male Distribution of the residuals [y - (a+bx)] is not normal female This is not the right method! Proportion of females <0%

  27. Logistic regression • The DV must be transformed • Y: probability that sex=1 (female), instead of 0 (male) • “logit” odds!

  28. Interpretation of « b » • In linear regression: • b: mean change of Y expected for an increase of one unit of X • By analogy, logistic regression: • b: mean change of logit(Y=1) expected for an increase of one unit of X eb= odds ratio ofY for one unit of X

  29. Odds ratio and logistic regression coefficients • Dependent variable: Y = 1 (case) or = 0 (control) • Independent variable: X = 1 (exposed) or = 0 (non-exposed) • Model: logit(y) = a + bx • Equation among exposed: logit(yexp) = a + b*1 = a + b • Equation among non-exposed: logit(ynon-exp) = a + b*0 = a • Equation for b = (a + b) – a = logit(yexp) – logit(ynon-exp)

  30. Example weight - sex • Weight in 4 categories: • odds ratio = 8.9 • Odds of being a man is multiplied by 8.9 for each increase to a higher category of weight • Weight in kilos: • odds ratio = 1.2 • Odds of being a man is multiplied by 1.2 for each additional kilo de poids

  31. adjusted for height Adjusted for weight Multiple IVs • Example: • Results: • Odds ratio for one additional kg: 1.15 (p<0.001) • Odds ratio for one additional cm: 1.20 (p<0.001)

  32. Conclusions • Case-control study: design to examine associations between risk factors and disease • Mostly for rare disease • Efficient and cost effective • Odds ratio: measure of association – often similar to relative risk • Logistic regression: modeling method for binary dependent variables

  33. Multilevel logistic regression This is a random intercept multilevel logistic regression

  34. Correct judgment of normality • Statistical normality test (KS) was correct for 71.4% of the distributions. • Only 57.1% for AD and JB. • Levene test correct in both cases (because data were normally distributed) • You were correct for 71.4% of the distributions, but your errors were not the same as the statistical tests. • All of you correctly found the bimodal distribution • You were not influenced by sample size

More Related