1 / 39

Cohort studies: Statistical analysis

Cohort studies: Statistical analysis. Jan Wohlfahrt Department of Epidemiology Research Statens Serum Institut. Contents. A research question and a wrong answer What kind of data is needed How to analyse data Confounder adjustment Poisson regression Cox regression.

argus
Download Presentation

Cohort studies: Statistical analysis

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. Cohort studies:Statistical analysis Jan Wohlfahrt Department of Epidemiology Research Statens Serum Institut

  2. Contents • A research question and a wrong answer • What kind of data is needed • How to analyse data • Confounder adjustment • Poisson regression • Cox regression Danish Epidemiology Science Centre, Copenhagen, Denmark

  3. 1.1. A research question Do MMR vaccination increase the risk of autistic disorder ? Danish Epidemiology Science Centre, Copenhagen, Denmark

  4. 1.1. Material • All children born 1991 to 98 (537.000 children). • Registerbased information on MMR vacn. (441.000) and autistic disorder (412 cases). Inform. on autisme: Danish Psychiatric Central Register Danish Civil Registration System Inform. on MMR Danish National Board of Health Cohort Danish Epidemiology Science Centre, Copenhagen, Denmark

  5. 1.2. A wrong answer I What is the proportion of children with autism in vacn and non-vacn in the cohort before end of 2000(end of follow-up)? Relative risk = 0.079/0.064= 1.23. Danish Epidemiology Science Centre, Copenhagen, Denmark

  6. 1.2. A wrong answer II • The simple comparison of proportion is not correct, because: • autism may be diagnosed before MMR • no age-adjustment, time under risk not taken into account, • Conclusion: Compare person-time under risk, not the number of persons under risk. Danish Epidemiology Science Centre, Copenhagen, Denmark

  7. 2. What kind of data is needed

  8. 2.1. Information on time • Time of study-entrance (1yr birthdate) • Time of status-change (date of vaccination) • Time of outcome (date of autism) • Time of study-exit (date of autism, death, emigration, disappearance, end of study) Danish Epidemiology Science Centre, Copenhagen, Denmark

  9. 2.2 Datalines . Not before end of 2000

  10. 2.3 Data as livelines

  11. 3. How to analyse data

  12. 3.1 Cox vs. Poisson regresssion • Poisson regression in large datasets with time-dependent variables • Cox regression in small datasets

  13. 3.2 Livelines

  14. 3.3 Contribution of pyrs

  15. 3.4 Contribution of pyrs

  16. 3.5 Data reduction

  17. 3.6 Rate ratio calculation (Incidence) rate = number of new autistic cases per year = cases/pyrs Rate ratio = RR+vacn vs –vacn = rate+vacn/rate-vacn= 1.40

  18. 4. Confounder Adjustment

  19. 4.1 The lexis-diagram

  20. 4.2 Person-years by age and period

  21. 4.3 Person-years by age and period (9 ages) x (9 periods) x (two vacn.) =162 groups e.g. Age period vacn pyrs cases 4 1996 yes 54626 9

  22. 4.4 Relative rates by age and period 1 in thousands, 2 per 100000 yr

  23. 5. Poisson Regression

  24. 5.1 Regression analysis of the rates log(rate) = const + aI(vacn) + bI(5-9) + cI(96-00) I(vacn) = 1 if vacn, 0 otherwise I(5-9) = 1 if 5-9 years, 0 otherwise I(96-00) = 1 in period 1996-2000, 0 otherwise For non-vacn. children in 1997 aged 6 log(rate) is modelled by: const+b+c.

  25. 5.2 Log-linear Poisson regression (I) log(rate) = log((nr of cases)/pyrs) = log(nr of cases) - log(pyrs) i.e. log(nr of cases) = log(pyrs) + log(rate) log(rate) = const + aI(vacn) + bI(5-9) + cI(96-00) log(nr of cases) = log(pyrs) + const + aI(vacn) + bI(5-9) + cI(96-00)

  26. 5.3 Log-linear Poisson regression (II) • log(nr of cases) = • log(pyrs) + const + aI(vacn) + bI(5-9) + cI(96-00) •  The number of case is Poisson-distributed. • log of the number of cases is modelled with a linear-function • log(pyrs) is considered known for every cell and is called an offset

  27. 5.4 Parameters and rate ratios log(rate) = k + aI(vacn) + bI(5-9) + cI(96-00) rate = exp(k + aI(vacn) + bI(5-9) + cI(96-00)) = exp(k)exp(aI(vacn)exp(bI(5-9))exp(cI(96-00)). For children 5-9 yr in the period 1996-2000: RR+vacn vs -vacn = rate+vacn/rate-vacn = (exp(k)exp(a)exp(b)exp(c)) (exp(k)exp(b)exp(c))   = exp(a)

  28. 5.5 A more complicated model log(rate) = k + aI(vacn) + b1I(1yr) + b2I(2yr) + b3I(3yr) + b4I(4yr) + b5I(5yr) + b6I(6yr) + b7I(7yr) + b8I(8yr) + c1I(92-93) + c2I(94) + c3I(95) + c4I(96) + c5I(97) + c6I(98) +c7I(99) + with non-vacn as the vacn-reference, age=9yr as the age-reference, and period=2000 as the period-reference.

  29. 5.6 SAS-dataset to Poisson regression data mmrdata; input age period vacn cases pyrs; logpyrs=log(pyrs); datalines; 1 92 0 0 20301.68 1 92 1 0 12027.50 . . . . . . . . . . 8 00 0 0 9553.12 8 00 1 2 54829.64 9 00 0 1 4844.91 9 00 1 0 26937.23 ; run;

  30. 5.7 SAS-procedure to Poisson regression proc genmod data=mmrdata; class age period; model cases=age period vacn/ dist=poisson link=log offset= logpyrs ; run;

  31. 5.8 SAS-output Parameter DF Estimate Std Err ChiSquare Pr>Chi INTERCEPT 1 -10.2733 1.0063 104.2281 0.0001 AGE 1 1 0.0720 1.0488 0.0047 0.9453 AGE 2 1 1.6150 1.0137 2.5381 0.1111 AGE 3 1 2.4219 1.0088 5.7637 0.0164 AGE 4 1 2.3435 1.0093 5.3913 0.0202 AGE 5 1 2.0080 1.0118 3.9386 0.0472 AGE 6 1 1.6608 1.0168 2.6679 0.1024 AGE 7 1 1.0864 1.0338 1.1044 0.2933 AGE 8 1 0.4626 1.0966 0.1780 0.6731 AGE 9 0 0.0000 0.0000 . . PERIOD 1992 1 -1.4554 0.7289 3.9869 0.0459 PERIOD 1994 1 -0.6997 0.3148 4.9397 0.0262 PERIOD 1995 1 -0.9527 0.2619 13.2350 0.0003 PERIOD 1996 1 -0.6582 0.2033 10.4808 0.0012 PERIOD 1997 1 -0.3866 0.1728 5.0079 0.0252 PERIOD 1998 1 0.0366 0.1478 0.0614 0.8044 PERIOD 1999 1 0.1157 0.1423 0.6614 0.4161 PERIOD 2000 0 0.0000 0.0000 . . VACN 1 1 -0.1111 0.1348 0.6791 0.4099 VACN 999 0 0.0000 0.0000 . .

  32. 5.9 Confidence-interval RR+vacn vs –vacn = exp(-0.1111) = 0.89 Confidence-interval: RRlower= exp(estimate - 1.96StdErr) RRupper= exp(estimate + 1.96StdErr)   RR+vacn vs -vacn= 0.89 (0.69-1.17)

  33. X.X Time since vaccination 0.8 years 5.9 years

  34. 6. Cox Regression

  35. 6.1 Cox regression

  36. 6.2 Cox regression log(rate) = k + aI(vacn) + b1I(1yr) + b2I(2yr) + b3I(3yr) b4I(4yr) + b5I(5yr) + b6I(6yr) + b7I(7yr) + b8I(8yr) + c1I(92-93) + c2I(94) + c3I(95) + c4I(96) + c5I(97) + c6I(98) +c7I(99) + l(age)

  37. 6.3 Live-lines

  38. 6.4 Data to Cox-regression data coxdata; input @1 intime date7. @9 vactime date7. @17 auttime date7. @25 othtime date7.; datalines; 11sep95 04apr97 17oct97 . 13dec94 . . 24jan00 27jan90 . . . 23jul93 04nov95 01jan98 . 15nov00 . . . 15jun97 03apr99 . 15apr01 03may92 . 06nov95 . ..... run;

  39. 6.5 Cox SAS-program data coxdata2; set coxdata; outtime=min(auttime,othtime,"31dec2000"d); time=(outtime-intime); if auttime=outtime then status=1; else status=0; run; procphreg; model time*status(0)=vacn; if (vactime=. or time<(vactime-intime)) then vacn=0; else vacn=1; run;

More Related