Statistical methods in longitudinal studies

Jouko Miettunen, PhD

Department of Psychiatry

University of Oulu

e-mail: jouko.miettunen@oulu.fi

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Topics of this presentation

Logistic regression analysis Survival analysis Analysis of variance Random regression analysis Structural equation modeling Latent class analysis Imputing missing data

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Logistic regression analysis (1)

Most common modeling method to analyze confounders in epidemiology, especially in longitudinal studies

Outcome variable should be dichotomized (no/yes, healthy/sick)

Exposure variables can be both dichotomized or continuous

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Variables in logistic regression

Include sociodemographic variables, e.g. sex, social class

Include previous known risk factors Especially if statistically significant in

the model Do not include too many variables

Depends on data size and distribution of variables

Do not include intercorrelating variables

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Example data set

Northern Finland 1966 Birth Cohort

Women who were living in the provinces of Oulu and Lapland and were due to deliver during 1966

N = 12,058 live births N = 10,934 living 1997 in Finland Data on biological, socio-economic and health

conditions collected prospectively from pregnancy up to the age of 35 years

Data from several registers and e.g. from large follow-ups at 14 and 31 years

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Example question

Northern Finland 1966 Birth Cohort

What predicts rehospitalization in psychoses? N = 158 hospital treated cases Exposure variables

sex father’s social class (1980) familial risk onset age length of first hospitalization diagnosis (schz / other psychosis)

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SPSS Output (1)

Categorical Variables Codings

48 ,000 ,000

96 1,000 ,000

14 ,000 1,000

133 ,000

25 1,000

93 1,000

65 ,000

108 1,000

50 ,000

94 1,000

64 ,000

I,II

III,IV

V

Fathers social class 1980

no

yes

Parent has psychotic dg 1972-2000

male

female

Sex

schizophrenia

other psych

Diagnosis

< 1 month

> 1 month

Length of first hospitalization

Frequency (1) (2)

Parameter coding

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SPSS Output (2)

Variables in the Equation

1,048 ,375 7,805 1 ,005 2,852 1,367 5,948

-,559 ,366 2,331 1 ,127 ,572 ,279 1,172

-,047 ,043 1,199 1 ,274 ,954 ,876 1,038

,839 ,385 4,740 1 ,029 2,314 1,087 4,926

,651 2 ,722

,309 ,392 ,622 1 ,430 1,362 ,632 2,934

,109 ,647 ,028 1 ,866 1,115 ,314 3,960

,612 ,513 1,423 1 ,233 1,845 ,675 5,045

,488 1,100 ,197 1 ,657 1,629

Length of 1st hospital.(1)Sex(1)

Onset age

Diagnosis(1)

FSC 1980

FSC 1980(1)

FSC 1980(2)

Parental psych(1)

Constant

B S.E. Wald df Sig. Exp(B) Lower Upper

95,0% C.I.for EXP(B)

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Survival analysis (1) Examines time between two events, e.g.

from birth to illness onset from illness onset to death from end of treatment to

rehospitalization

Kaplan-Meier model estimates probability of events in each time point

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Survival analysis (2)

Required information Event (0,1) Time to event (days, months,…) or to

censoring Data is censored due to

End of follow-up time Loss of contact Or e.g. other dead than that of interest

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Example questionNorthern Finland 1966 Birth Cohort

What predicts age of suicide? People alive and living in Finland at 16 years (N=10,934) Data till end of 2001

58 (0.5%) suicides 140 (1.3%) other deaths 10,736 (98.2%) alive

Predictor variable: family type at birth (full, single)

12log rank test, p=0.002

Test Statistics for Equality of Survival Distributions

Survival Functions

age (years)

3530252015

Cum

Sur

viva

l

1,000

,999

,998

,997

,996

,995

,994

,993

,992

,991

,990

,989

family type 1966

full

full-censored

single

single-censored

SPSS Output (1)

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Survival analysis (3) Difference or trend in difference

between groups should be about the same across time, at least curves shouldn’t cross (if statistically tested)

Can be done also with small samples Curve can be presented as survival or

as hazard function

References, e.g. Parmar & Machin: Survival analysis. A practical approach. John Wiley & Sons, 1995.

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SPSS Output (2)Hazard Function

age (years)

3530252015

Cum

Haz

ard

,012

,010

,008

,006

,004

,002

0,000

family type 1966

full

full-censored

single

single-censored

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Example question (2)

Age of suicide and family type Possible confounding variables

sex social class 1966 (I-II,III-IV,V) average school mark at 14 psychiatric diagnosis (no, yes) crime (no, violent, non-violent)

Cox regression analysis

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Cox regression analysis

SPSS Output (3)

Categorical Variable Codings

5425 1

5222 0

10197 0

450 1

783 0 0

7823 1 0

2041 0 1

1975 1

8672 0

10019 0 0

200 1 0

428 0 1

1=male

2=female

Sex

0=healthy

1=any dg

Psych dg

1=I,II

2=III,IV

3=V

Fathers SocialClass 1966

1=single

2=full

Family type1966

0=no crimes

1=violent

2=nonviolent

Criminality

Frequency (1) (2)

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Cox regression analysis

SPSS Output (4)

Variables in the Equation

,812 ,340 5,720 1 ,017 2,253 1,158 4,383

2,463 ,303 66,085 1 ,000 11,740 6,483 21,260

,728 ,287 6,429 1 ,011 2,072 1,180 3,637

1,514 2 ,469

,451 ,715 ,398 1 ,528 1,570 ,386 6,377

,536 ,436 1,513 1 ,219 1,710 ,727 4,018

-,276 ,164 2,825 1 ,093 ,759 ,550 1,047

3,398 2 ,183

,239 ,454 ,276 1 ,600 1,269 ,521 3,093

-1,011 ,625 2,613 1 ,106 ,364 ,107 1,239

SEX

PSYCH DG

FAM TYPE

FSC 1966

FSC 1966(1)

FSC 1966(2)

SCHOOL MARK

CRIMES

CRIMES(1)

CRIMES(2)

B SE Wald df Sig. Exp(B) Lower Upper

95,0% CI for Exp(B)

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Analysis of variance

ANOVA One continuous outcome (dependent) variable

MANOVA Several continuous outcome variables

Repeated measurements ANOVA Same measurements are made several times on

each subject ANOVA, MANOVA and rANOVA

Only categorical predictors ANCOVA, MANCOVA, rANCOVA

Also continuous predictors

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Example question

Difference in size of hippocampus Northern Finland 1966 Birth Cohort

Follow-up study 1999-2001 Schizophrenia patients (N=56) vs.

healthy controls (N=104) Repeated measurements ANCOVA

Measurements of right and left side were thought as repeated measurements

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Example tableSchizophrenia and Comparison subjectsHippocampus volumes

F Sig.

Model 1Within effect: side 20.3 < 0.001Diagnosis 1.2 0.28Gender 6.5 0.01Model 2Within effect: side 0.81 0.37Covariate: brain vol. 35.0 < 0.001Diagnosis < 0.01 0.89Gender 0.7 0.41Familial psychosis 1.9 0.17Perinatal risk 0.8 0.38Handedness 0.3 0.61

Tanskanen et al. Schizophrenia Research (in press)

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Random regression analysis Random regression analysis = Random-effects (multilevel) models = …

Allow presence of missing data Allow time-varying covariates Allow subjects measured at different

timepoints Takes into account several levels of

subjects (multilevel analysis)

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Random regression analysis Available software

SAS Proc Mixed Stata (GLLAMM) Specific multilevel modeling software

MLWin• http://multilevel.ioe.ac.uk/index.html

HLM• http://www.ssicentral.com/hlm/hlm.htm

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Random regression analysis References

Goldstein et al. Tutorial in biostatistics. Multilevel modelling of medical data. Stat Med, 21, 3291-315, 2002.

Hedeker & Mermelstein. Application of random-effects regression models in relapse research, Addiction, 91, S211-30, 1996.

Sharma et al. A longitudinal study of plasma cortisol and depressive symptomatology by random regression analysis. Biol Psychiatry 31, 304-14, 1992.

Tilling et al. A new method for predicting recovery after stroke. Stroke 32, 2867-73, 2001.

Homepage of Don Hedeker: http://tigger.uic.edu/~hedeker/

Homepage of Sophia Rabe-Hesketh (GLLAMM) http://www.gllamm.org/sophia.html

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Structural Equation Modeling

Combination of factor analysis and regression

Continuous and discrete predictors and outcomes

Relationships among measured or latent variables

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Caringorientation

Expertiseorientation

Lifeorientation

Catalytic-co-operational

nursing

Controllingnursing

Confirmingnursing

•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=.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)

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Structural Equation Modeling

References Bentler & Stein. Structural equation models in

medical research. Stat Methods Med Res 1: 159–181, 1992.

Bollen. Structural equations with latent variables. John Wiley & Sons, Inc, New York, 1989.

Finch & West. The investigation of personality structure: statistical models. J Res Pers 31: 439–485, 1997.

MacCallum & Austin. Applications of structural equation modeling in psychological research. Annu Rev Psychol 51: 201–226, 2000.

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Latent class analysis

Specific statistical method developed to group subjects according to selected characteristics

Classifies subjects to groups Identifies characteristics that indicate

groups

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Example: Anti-Social Behavior

Damaged property Fighting Shoplifting Stole <$50 Stole >$50 Use of force Seriously threaten Intent to injure

Use Marijuana Use other drug Sold Marijuana Sold hard drugs ‘Con’ somebody Stole an Automobile Broken into a building Held stolen goods Gambling Operation

National Longitudinal Survey of Youth (NLSY) Respondent ages between 16 and 23 Background information: age, gender and ethnicity N=7,326

17 antisocial dichotomously scored behavior items:

Reference:http://www.ats.ucla.edu/stat/mplus/seminars/lca/default.htm

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Example: Anti-Social Behavior

Damage Property

Fighting Shoplifting Stole <$50 Gambling. . .

Male

Race

Age

C

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Example: Anti-Social Behavior probabilities

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Relationship between class probabilities and age by gender

Females Males

16 17 18 19 20 21 22 23 (age) 16 17 18 19 20 21 22 23

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Summary of four classes: Property Offense Class (9.8%) Substance Involvement Class (18.3%) Person Offenses Class (27.9%) Normative Class (44.1%)   

Classification Table:

1 2 3 4

1 0.854 0.031 0.070 0.040

2 0.041 0.917 0.040 0

3 0.058 0.021 0.820 0.100

4 0.038 0 0.080 0.880

Example: Anti-Social Behavior

Rows:Average latent class probability for most likely latent class membership

Columns: Latent class

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Latent class analysis

References Muthén & Muthén. Integrating person-centered

and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcohol Clin Exp Res, 24, 882-91, 2000.

http://www.ats.ucla.edu/stat/mplus/seminars/lca/default.htm

More references and examples Homepage of Mplus software:

www.statmodel.com

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Missing data Major problem in longitudinal studies Usually data is not missing at random One “solution”

Compare included and excluded cases Not very good! Smaller sample size give less power

(change to get low p-values)

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Imputing single missing data With mean of sample (or subsample)

Gives less variability to data

Nearest neighbour imputation Gives less variability to data

Use regression techniques to predict missing data

Mean of variables of same subject measuring

appr. same thing e.g. in psychological scales

Now “missing value analysis” also in SPSS

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Multiple imputation Requires special software

SAS/STAT (PROC MI & PROC MIANALYZE) S-PLUS (MICE) SOLAS for Missing Data Analysis 3.0

References Kmetic et al. Multiple imputation to account for

missing data in a survey: estimating the prevalence of osteoporosis. Epidemiology, 13, 437-44, 2002.

McCleary. Using multiple imputation for analysis of incomplete data in clinical research. Nurs Res, 51, 339-43, 2002.

Streiner. The case of the missing data: methods of dealing with dropouts and other research vagaries. Can J Psychiatry, 47, 68-75, 2002.

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General references in Finnish

Metsämuuronen. Tutkimuksen tekemisen perusteet ihmistieteissä (2003)

Nummenmaa et al. Tutkimusaineiston analyysi (1997)

Uhari & Nieminen. Epidemiologia & Biostatistiikka (2001)

SPSS, SAS, etc. manuals