1. Statistical methods in longitudinal studies Jouko Miettunen, PhD Department of Psychiatry University of Oulu e-mail: jouko.miettunen@oulu.fi

2. 2 Topics of this presentation n Logistic regression analysis n Survival analysis n Analysis of variance n Random regression analysis n Structural equation modeling n Latent class analysis n Imputing missing data

3. 3 Logistic regression analysis (1) n Most common modeling method to analyze confounders in epidemiology, especially in longitudinal studies n Outcome variable should be dichotomized (no/yes, healthy/sick) n Exposure variables can be both dichotomized or continuous

4. 4 Variables in logistic regression n Include sociodemographic variables, e.g. sex, social class n Include previous known risk factors u Especially if statistically significant in the model n Do not include too many variables u Depends on data size and distribution of variables n Do not include intercorrelating variables

5. 5 Example data set Northern Finland 1966 Birth Cohort n Women who were living in the provinces of Oulu and Lapland and were due to deliver during 1966 n N = 12,058 live births n N = 10,934 living 1997 in Finland n Data on biological, socio-economic and health conditions collected prospectively from pregnancy up to the age of 35 years n Data from several registers and e.g. from large follow-ups at 14 and 31 years

6. 6 Example question Northern Finland 1966 Birth Cohort n What predicts rehospitalization in psychoses? n N = 158 hospital treated cases n Exposure variables u sex u father’s social class (1980) u familial risk u onset age u length of first hospitalization u diagnosis (schz / other psychosis)

7. 7 SPSS Output (1)

8. 8 SPSS Output (2)

9. 9 Survival analysis (1) n Examines time between two events, e.g. u from birth to illness onset u from illness onset to death u from end of treatment to rehospitalization n Kaplan-Meier model estimates probability of events in each time point

10. 10 Survival analysis (2) n Required information uEvent (0,1) uTime to event (days, months,…) or to censoring uData is censored due to FEnd of follow-up time FLoss of contact FOr e.g. other dead than that of interest

11. 11 Example question Northern Finland 1966 Birth Cohort n What predicts age of suicide? n People alive and living in Finland at 16 years (N=10,934) n Data till end of 2001 u 58 (0.5%) suicides u 140 (1.3%) other deaths u 10,736 (98.2%) alive n Predictor variable: u family type at birth (full, single)

12. 12 log rank test, p=0.002 Test Statistics for Equality of Survival Distributions SPSS Output (1)

13. 13 Survival analysis (3) n Difference or trend in difference between groups should be about the same across time, at least curves shouldn’t cross (if statistically tested) n Can be done also with small samples n Curve can be presented as survival or as hazard function n References, e.g. u Parmar & Machin: Survival analysis. A practical approach. John Wiley & Sons, 1995.

14. 14 SPSS Output (2)

15. 15 Example question (2) Age of suicide and family type n Possible confounding variables u sex u social class 1966 (I-II,III-IV,V) u average school mark at 14 u psychiatric diagnosis (no, yes) u crime (no, violent, non-violent) n Cox regression analysis

16. 16 Cox regression analysis SPSS Output (3)

17. 17 Cox regression analysis SPSS Output (4)

18. 18 Analysis of variance n ANOVA u One continuous outcome (dependent) variable n MANOVA u Several continuous outcome variables n Repeated measurements ANOVA u Same measurements are made several times on each subject n ANOVA, MANOVA and rANOVA u Only categorical predictors n ANCOVA, MANCOVA, rANCOVA u Also continuous predictors

19. 19 Example question Difference in size of hippocampus n Northern Finland 1966 Birth Cohort u Follow-up study 1999-2001 n Schizophrenia patients (N=56) vs. healthy controls (N=104) n Repeated measurements ANCOVA u Measurements of right and left side were thought as repeated measurements

20. 20 Example table Schizophrenia and Comparison subjects Hippocampus volumes F Sig. Model 1 Within effect: side20.3< 0.001 Diagnosis1.20.28 Gender6.50.01 Model 2 Within effect: side0.81 0.37 Covariate: brain vol.35.0< 0.001 Diagnosis< 0.01 0.89 Gender0.7 0.41 Familial psychosis1.90.17 Perinatal risk0.80.38 Handedness0.30.61 Tanskanen et al. Schizophrenia Research (in press)

21. 21 Random regression analysis n Random regression analysis = Random-effects (multilevel) models = … u Allow presence of missing data u Allow time-varying covariates u Allow subjects measured at different timepoints u Takes into account several levels of subjects (multilevel analysis)

22. 22 Random regression analysis n Available software u SAS Proc Mixed u Stata (GLLAMM) u Specific multilevel modeling software F MLWin http://multilevel.ioe.ac.uk/index.html F HLM http://www.ssicentral.com/hlm/hlm.htm

23. 23 Random regression analysis n References u Goldstein et al. Tutorial in biostatistics. Multilevel modelling of medical data. Stat Med, 21, 3291-315, 2002. u Hedeker & Mermelstein. Application of random-effects regression models in relapse research, Addiction, 91, S211-30, 1996. u Sharma et al. A longitudinal study of plasma cortisol and depressive symptomatology by random regression analysis. Biol Psychiatry 31, 304-14, 1992. u Tilling et al. A new method for predicting recovery after stroke. Stroke 32, 2867-73, 2001. u Homepage of Don Hedeker: F http://tigger.uic.edu/~hedeker/ u Homepage of Sophia Rabe-Hesketh (GLLAMM) F http://www.gllamm.org/sophia.html

24. 24 Structural Equation Modeling n Combination of factor analysis and regression n Continuous and discrete predictors and outcomes n Relationships among measured or latent variables

25. 25 Caring orientation Expertise orientation Life orientation Catalytic- co-operational nursing Controlling nursing Confirming nursing male, p=.002 older, p<.0001 no children, p=.048 Swedish, p<.0001 older, p<.0001 no children, p=.036 Finnish, p=.020 younger, p=.0003 sairaanhoit, p=.020 no children, p<.0001 older, p=.034 Swedish, p<.0001 older, p0.002 older, p=.030 + (r=.64) + (r=.11) + (r=.27) + (r=.47) + + + + + + + (r=.22) + (r=.44) + (r=.18) + (r=.19) Orientation to nursing Orientation to learning nursing Example: Nursing orientation Vanhanen-Nuutinen et al. (manuscript)

26. 26 Structural Equation Modeling n References u Bentler & Stein. Structural equation models in medical research. Stat Methods Med Res 1: 159–181, 1992. u Bollen. Structural equations with latent variables. John Wiley & Sons, Inc, New York, 1989. u Finch & West. The investigation of personality structure: statistical models. J Res Pers 31: 439– 485, 1997. u MacCallum & Austin. Applications of structural equation modeling in psychological research. Annu Rev Psychol 51: 201–226, 2000.

27. 27 Latent class analysis n Specific statistical method developed to group subjects according to selected characteristics u Classifies subjects to groups u Identifies characteristics that indicate groups

28. 28 Example: Anti-Social Behavior n Damaged property n Fighting n Shoplifting n Stole <$50 n Stole >$50 n Use of force n Seriously threaten n Intent to injure n Use Marijuana n Use other drug n Sold Marijuana n Sold hard drugs n ‘Con’ somebody n Stole an Automobile n Broken into a building n Held stolen goods n Gambling Operation n National Longitudinal Survey of Youth (NLSY) n Respondent ages between 16 and 23 n Background information: age, gender and ethnicity n N=7,326 17 antisocial dichotomously scored behavior items: Reference: http://www.ats.ucla.edu/stat/mplus/seminars/lca/default.htm

29. 29 Example: Anti-Social Behavior Damage Property FightingShopliftingStole <$50Gambling... Male Race Age C

30. 30 Example: Anti-Social Behavior probabilities

31. 31 Relationship between class probabilities and age by gender FemalesMales 16 17 18 19 20 21 22 23 (age)16 17 18 19 20 21 22 23

32. 32 n Summary of four classes: u Property Offense Class (9.8%) u Substance Involvement Class (18.3%) u Person Offenses Class (27.9%) u Normative Class (44.1%) n Classification Table: 1234 10.8540.0310.0700.040 20.0410.9170.0400 30.0580.0210.8200.100 40.03800.0800.880 Example: Anti-Social Behavior Rows: Average latent class probability for most likely latent class membership Columns: Latent class

33. 33 Latent class analysis n References u Muthén & Muthén. Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcohol Clin Exp Res, 24, 882-91, 2000. u http://www.ats.ucla.edu/stat/mplus/seminars/lca/ default.htm n More references and examples u Homepage of Mplus software: www.statmodel.com

34. 34 Missing data n Major problem in longitudinal studies n Usually data is not missing at random n One “solution” u Compare included and excluded cases F Not very good! F Smaller sample size give less power (change to get low p-values)

35. 35 Imputing single missing data n With mean of sample (or subsample) u Gives less variability to data n Nearest neighbour imputation u Gives less variability to data n Use regression techniques to predict missing data n Mean of variables of same subject measuring appr. same thing u e.g. in psychological scales n Now “missing value analysis” also in SPSS

36. 36 Multiple imputation n Requires special software u SAS/STAT (PROC MI & PROC MIANALYZE) u S-PLUS (MICE) u SOLAS for Missing Data Analysis 3.0 n References u Kmetic et al. Multiple imputation to account for missing data in a survey: estimating the prevalence of osteoporosis. Epidemiology, 13, 437-44, 2002. u McCleary. Using multiple imputation for analysis of incomplete data in clinical research. Nurs Res, 51, 339- 43, 2002. u Streiner. The case of the missing data: methods of dealing with dropouts and other research vagaries. Can J Psychiatry, 47, 68-75, 2002.

37. 37 General references in Finnish n Metsämuuronen. Tutkimuksen tekemisen perusteet ihmistieteissä (2003) n Nummenmaa et al. Tutkimusaineiston analyysi (1997) n Uhari & Nieminen. Epidemiologia & Biostatistiikka (2001) n SPSS, SAS, etc. manuals