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Title: Using Biomarkers in Population Research Biomarkers are use


1
Methodological Issues in Using Biomarker Data for
Demographic Research
  • Eleanor Brindle
  • CSDE Biodemography Core
  • Jane Shofer
  • Anita Rocha
  • CSDE Statistics Core

April 4th, 2006
2
Methodological Issues
  • I. Biomarker methods
  • Introduction to biomarkers and their use in
    population research
  • Brief overview of techniques commonly used to
    measure biomarkers
  • Introduction to the kinds of measurement error in
    those techniques
  • II. Statistical methods useful for biomarker
    data
  • Incorporating known measurement error into power
    analyses
  • Dealing with repeated measures issues (frequently
    encountered in biomarker data)

3
I. Biomarker Methods
  • What is a biomarker
  • How are biomarkers measured
  • What underlying process do you really want to
    know about, and what are you really measuring?
  • For example, cortisol does many things. Are you
    measuring cortisol to learn about metabolism or
    stress? Chronic or acute stress?
  • White coat effect, binding proteins and receptors
    (bioactive or not), metabolites, other
    potentially complicating factors
  • For example, Vitamin A levels can be affected by
    immune status
  • Sampling issuesfrequency, diurnal patterns,
    fluid type
  • Dictated by biology, technology and your
    questions
  • Measurement error types
  • Sensitivity, specificity, accuracy, precision

4
II. Statistical Considerations for Biomarker Data
  • Power
  • Take advantage of having well-characterized
    measurement error
  • Repeated measures
  • Often encounter non-independence in biomarker data

5
Biomarker Methods
  • What is a biomarker
  • How are biomarkers measured
  • What underlying process do you really want to
    know about, and what are you really measuring?
  • Sampling issuesfrequency, diurnal patterns,
    fluid type
  • Measurement error types

6
Using Biomarkers in Population Research
  • What is a biomarker?
  • Has had different meanings, but is now widely
    used to indicate any marker of underlying biology
    you care to measure.
  • Common goal in biodemography is to integrate
    biological, behavioral, and social/cultural
    levels of analysis.
  • A biomarker in this field is generally something
    that tells you about something else
  • Unlike in biology, the biomarker itself is rarely
    of interest in this field.

7
Using Biomarkers in Population Research
  • Biomarkers are used to estimate
  • health, disease
  • hidden heterogeneity frailty, risk
  • nutritional status
  • behaviors (smoking, drugs of abuse)
  • exposure to environmental contaminants
  • population differences in disease prevalence or
    risk factors
  • markers of aging or other biological events
    (puberty)

8
Using Biomarkers in Population Research
  • Biomarkers
  • blood pressure
  • anthropometrics (height, weight, limb length)
  • molecules in the blood, urine or saliva
  • Hormones, micro- or macronutrients, disease
    markers, toxins, environmental contaminants, etc.
  • Immunoassays commonly used, but there are many
    other methods
  • lung function
  • pulse rate or pattern
  • brain activity
  • genetic markers
  • disease risk, aging, behaviors, relatedness of
    populations

9
Using Biomarkers in Population Research
  • Why biomarkers instead of self-reports?
  • Self reports not useful for undiagnosed or
    sub-clinical health problems
  • Biomarkers may have advantages where self reports
    are likely to be subjective (i.e. stress) or
    inaccurate (i.e. smoking, BMI)
  • Difference between subject perception and
    biomarker results may be interesting in and of
    itself (such as for health or stress)
  • Even perfect self-reports can only tell part of
    the story

10
Examples of Studies Using Biomarkers
  • National Health and Nutrition Examination Survey
    (NHANES)
  • The National Longitudinal Study of Adolescent
    Health (AddHealth)
  • MacArthur Successful Aging Study
  • Coronary Artery Risk Development in Young Adults
    Study (CARDIA)
  • Social and Environmental Biomarkers of Aging
    Study (SEBAS)
  • Framingham Heart Study
  • Whitehall Civil Servants Study
  • Hypertension Detection and Follow-up Program
  • Womens Health Initiative (WHI)
  • Study of Womens Health Across the Nation (SWAN)
  • Melbourne Womens Midlife Health Project (MWMHP)
  • Cebu Longitudinal Health and Nutrition Survey
    (CLHNS)
  • The Health and Retirement Study (HRS)

11
Links to more
  • NIH and CDC sites
  • http//www.nih.gov/icd/
  • http//www.nia.nih.gov/ResearchInformation/Scienti
    ficResources/
  • http//resresources.nci.nih.gov/categorydisplay.cf
    m?catid9
  • http//apps.nhlbi.nih.gov/popstudies/
  • http//www.clinicaltrials.gov/
  • http//www.niaid.nih.gov/daids/aidsdata.htm
  • http//pubs.niaaa.nih.gov/publications/datasys.htm
  • http//www.nichd.nih.gov/resources/resources.htm
  • http//www.nichd.nih.gov/about/cpr/dbs/res_ss_larg
    e.htm
  • http//www.cdc.gov/nchs/datawh.htm
  • http//www.cdc.gov/nchs/express.htm

12
Using Biomarkers in Population Research
13
Using Biomarkers in Population Research
14
Participation in cultural activities by risk and
cortisol group
Using Biomarkers in Population Research
Low and high salivary cortisol groups based on
bottom and top 25. Y axis Geometric mean for
risk behaviors and attitudes X axis Summary
score, average participation in cultural
activities during the past year activities and
degree of activitys importance on 1-5 scale
Schechter et al. 2006 Gender differences in
salivary cortisol and measures of bicultural
identity in a sample of Native American youth.
Annual Meeting of the Human Biology Association,
Anchorage, Alaska.
15
NHANESNational Health and Nutrition Examination
and Surveyfrom the National Center for Health
Statistics, part of the CDC
  • NHANES I 1971 to 1975, N 32,000
  • NHANES II 1976-1980, N 27,800
  • NHANES III 1988-1994, N 34,000
  • Starting with NHANES 1999-2000, the survey is now
    conducted yearly
  • each year N 7000 interviews, about 5000 exams
  • Demographic data, interviews and exams for all
    phases
  • Exam and laboratory components provide data on a
    wide range of biomarkers

16
NHANES Biomarkers
  • Albumin (urine)
  • Arsenic (urine)
  • Creatinine (urine)
  • NTX
  • Iodine (urine)
  • BV/Trich
  • MRSA
  • VOC exposure monitor
  • Pthalates (7)
  • Organophosphates metabolites
  • Metals (13)
  • Nonpersistent pesticides
  • Persistent pesticides
  • Phytoestrogens (8)
  • PAHs (16)
  • Dioxins
  • Lead dust
  • Complete blood count
  • Lead
  1. Mercury (hair)
  2. Mercury (blood)
  3. Mercury (urine)
  4. CD4
  5. WBC/DNA
  6. VOC (blood)
  7. Iron
  8. TIBC
  9. Ferritin
  10. Vitamin B12
  11. C-reactive protein
  12. Helicobacter pylori
  13. Cryptosporidium
  14. Vitamin A/E/Carotenoids
  15. Vitamin C
  16. Measles/Varicella/Rubella
  17. Cotinine
  18. Chemistry panel
  19. Bone alkaline phosphatase
  • Triglycerides
  • HIV antibody
  • Insulin/c-peptide
  • Herpes 1 and 2 antibody
  • Syphilis
  • HPV antibody
  • PSA
  • FSH/LH
  • Latex
  • Vitamin D
  • TSH/TH
  • Parathyroid hormone
  • Transferrin receptor
  • Surplus sera
  • Vitamin B6
  • Homocysteine
  • Methyl malonic acid
  • Glucose plasma
  • Fibrinogen

17
Add Health
  • Biological specimens collected in Wave III
  • HIV tests (20,745 oral swabs)
  • Sexually transmitted infection tests (12,548
    urine specimens)
  • DNA (2612 saliva specimens)
  • genotyping of full siblings or twins in the same
    household
  • To facilitate analyses that differentiate
    between parental, social, and genetic influence

18
Biomarker Methods
  • What is a biomarker
  • How are biomarkers measured
  • What underlying process do you really want to
    know about, and what are you really measuring?
  • Sampling issuesfrequency, diurnal patterns,
    fluid type
  • Measurement error types

19
Biomarker Measurement
  • Often standard clinical methods are useful for
    population research (blood pressure, infectious
    and non-infectious disease, lung function, etc.)
  • Normal biological variation and sub-clinical
    conditions are often of interest in research, and
    clinical tools are not always well-suited to
    address these things
  • Immunoassays, HPLC, GC/MS, and other similar
    methods can be optimized for use in population
    research
  • Diagnostic value not always needed
  • Cost, practicality, and efficiency may be more
    important

20
Immunoassays
Immunoassays exploit the basic nature of
antibodies to capture, and then quantify,
analytes.
Antibodies allow measurement with excellent
specificity and sensitivity to picomolar (10-12)
concentrations, even when analytes are in a sea
of very closely related molecules.
Antibodies specific to just about any chemical,
hormone, carrier protein, virus, cell, etc. can
be produced.
21
Immunoassays
In the CSDE Biodemography lab, immunoassays are
carried out in the wells of microtiter
plates. Other methods use the same principles to
perform immunoassays in test tubes, on tissue
specimens, on microscope slides, micro-fluidics
discs, etc.
Microtiter plates -plastic dishes with individual
wells in which assays are carried out -wells are
specially made to strongly bind to antibodies
(among other things)
22
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23
Immunoassays
  • Color (or radioactive, fluorescent, etc.)
    response is proportional to concentration (more
    signal, more analyte).
  • Regression using known doses (red circles) of the
    analyte are used to calibrate the assay and
    quantify test samples (blue squares).

24
Biomarker Methods
  • What is a biomarker
  • How are biomarkers measured
  • What underlying process do you really want to
    know about, and what are you really measuring?
  • For example, cortisol does many things. Are you
    measuring cortisol to learn about metabolism or
    stress? Chronic or acute stress?
  • White coat effect, binding proteins and receptors
    (bioactive or not), metabolites, other
    potentially complicating factors
  • For example, Vitamin A levels can be affected by
    immune status
  • Sampling issuesfrequency, diurnal patterns,
    fluid type
  • Measurement error types

25
Using Biomarkers in Population Research
  • Are particular hormones associated with health or
    aging outcomes? Is the relationship causal?
  • Do individuals from different populations vary in
    levels of hormones or other physiological traits?
    Does this have health implications? Clinical
    implications?
  • What is the level of exposure of a population to
    pesticides or other environmental hazards?

26
Using Biomarkers in Population Research
  • Some big questions in the use of biomarker data
  • Are large-scale, cross-sectional surveys useful,
    given that some (all?) markers are dynamic?
  • How should SES be modeled? As a cause or an
    effect?
  • How to model the biology so the choice of which
    markers to use can become less arbitrary
  • How to model and measure stress and health
    markers? What is important? Current status,
    change, history?

27
Using Biomarkers in Population Research
  • Downstream markers specific
  • Example stress will elevate cortisol
  • Upstream markers - non-specific ? trouble
  • Example is elevated cortisol caused by stress?
  • Do we care?
  • If the issue is population health, the goal is to
    understand associations first, not make
    individual predictions

28
Example Estradiol and obesity
  • Estradiol increases with increasing BMI.
  • Sex hormone binding globulin (SHBG) decreases
    with increasing BMI.
  • The combined result is that the effect of BMI on
    bio-available estradiol is much larger than is
    evident when looking at estradiol alone.
  • Important for cancer risk, maybe heart disease

Lukanova et al. (2004) Body mass index,
circulating levels of sex-steroid hormones, IGF-1
and IGF-binding protein-3 a cross-sectional
study in healthy women. European J of Endo
150161-71.
29
Biomarker Methods
  • What is a biomarker
  • How are biomarkers measured
  • What underlying process do you really want to
    know about, and what are you really measuring?
  • Sampling issuesfrequency, diurnal patterns,
    fluid type
  • Dictated by biology, technology and your
    questions
  • Measurement error types

30
Serum and urinary measures of luteinizing hormone
31
Longitudinal biomarker data
  • One woman, daily urine samples across six months
    for each of five years. (Data are from the BIMORA
    study of the menopausal transition.)

32
Cross-sectional biomarker data
  • The Timing of Puberty Among Kenyan Rendille Youth
  • 35 girls aged 10 to 23 years,
  • 303 girls and boys, aged 4 to 10 years.
  • Data show mean concentrations /- 2 SD of two
    reproductive hormones that are relatively low and
    stable before puberty

33
Diurnal Patterns in Cortisol
Cortisol levels in 8 US adults (male and
female) Shows normal diurnal variation.
Cortisol is well-known as a stress hormone, but
it is also a metabolic hormone.
34
Collection Methods
Dried blood spot collection Typically one prick
with a small lancet will produce 4 blood
spotsenough to assay several different
biomarkers
35
Collection Methods
Salivette Saliva collection method Chew on cotton
swab for 45-60 seconds In the lab we centrifuge
the saliva out of the cotton swab Enough sample
is collected to assay several different biomarkers
36
Collection Methods
Whizpop
Urine collection method Pure cellulose sponge is
held under urine stream In the lab we centrifuge
the urine out of the sponge Enough sample is
collected to assay several different biomarkers
37
Biomarker Methods
  • What is a biomarker
  • How are biomarkers measured
  • What underlying process do you really want to
    know about, and what are you really measuring?
  • Sampling issuesfrequency, diurnal patterns,
    fluid type
  • Measurement error types
  • Sensitivity, specificity, accuracy, precision

38
Types of error in biomarker measureswhere error
comes from and what it looks like
  • sensitivity and specificity
  • quantitative (continuous) data
  • is assay limit of detection good for
    physiological levels
  • is assay sensitive enough to detect small
    differences between samples
  • does it cross react with something else, and do
    we care
  • qualitative (discrete) data
  • For example, pregnancy tests, tests for
    infectious disease, tests for deficient or not in
    a nutrient, test for at risk or not of a
    non-infectious disease, etc.
  • accuracy versus precision
  • How are they different?
  • When is it useful maximize one over the other?
  • Want to know population average level of
    something, choose accuracy
  • Want to find a good marker of another event (ie
    ovulation), choose precision and adjust for known
    bias

39
Sensitivity and Specificity
  • Meanings of sensitivity and specificity differ in
    assay methods literature and epidemiology
    literature
  • In reference to assays
  • sensitivity
  • Usually means smallest dose distinguishable from
    zero (lower limit of detection)
  • sometimes used to describe the ability of an
    assay to reliably detect differences between two
    very similar values
  • specificity is ability of the assay to
    distinguish between very similar molecules


40
Sensitivity and SpecificityImmunoassays
41
Sensitivity and SpecificityQualitative
(discrete) tests
Loong (2003) Understanding sensitivity and
specificity with the right side of the brain.
BMJ 327716-9
42
Sensitivity and Specificity in Qualitative Data
  • Sensitivity The probability of the test finding
    disease among those who have the disease or the
    proportion of people with disease who have a
    positive test result.
  • Sensitivity true positives / (true positives
    false negatives)

43
Sensitivity and Specificity in Qualitative Data
  • Specificity The probability of the test finding
    NO disease among those who do NOT have the
    disease or the proportion of people free of a
    disease who have a negative test.
  • Specificity true negatives / (true negatives
    false positives)

44
Sensitivity and Specificity
  • Distinction between quantitative (or continuous)
    and qualitative (or discrete) is somewhat
    artificial
  • Often, have a quantitative measure that is
    converted to a qualitative measure using a cutoff
    value
  • Moving that cutoff value greatly influences
    sensitivity and specificity

45
Sensitivity and Specificity
TN true negative TP true positive FN false
negative FP false positive
46
Sensitivity and Specificity
TNF true negative fraction TPF true positive
fraction FNF false negative fraction FPF
false positive fraction
http//www.anaesthetist.com/mnm/stats/roc/
47
Sensitivity and Specificity(for reference later)
  • Sensitivity The probability of the test finding
    disease among those who have the disease or the
    proportion of people with disease who have a
    positive test result.
  • Sensitivity true positives / (true positives
    false negatives)
  • Specificity The probability of the test finding
    NO disease among those who do NOT have the
    disease or the proportion of people free of a
    disease who have a negative test.
  • Specificity true negatives / (true negatives
    false positives)
  • Positive Predictive Value (PPV) The percentage
    of people with a positive test result who
    actually have the disease.
  • Positive predictive value true positives /
    (true positives false positives)
  • Negative Predictive Value (NPV) The percentage
    of people with a negative test who do NOT have
    the disease.
  • Negative predictive value true negatives /
    (true negatives false negatives)

48
Sensitivity and SpecificityExamples from
AddHealth
Sensitivity 665 ? 673 0.9881 Specificity EIA
only 2880 ? 2897 0.9941 Specificity EIA WB
2893 ? 2897 0.9986
49
Sensitivity and Specificity
  • AddHealth HIV tests have sensitivity of 98.80
    and specificity of 99.86. Now what?

test N prev true sick true well sensitivity specificity true false PPV
EIA alone 3,570 0.189 673 2,897 0.9880 0.9941 665 17 0.975
EIA WB 3,570 0.189 673 2,897 0.9880 0.9986 665 4 0.994
  • Sensitivity 665 ? 673 0.9881
  • 8 sick people told they are well
  • Specificity EIA only 2880 ? 2897 0.9941
  • 17 well people told they are sick
  • Specificity EIA WB 2893 ? 2897 0.9986
  • 4 well people told they are sick

50
Sensitivity and Specificity
Number of true positives and false positives is
related to disease prevalence. In the example
below, the test has 95 sensitivity and 95
specificity. All the parameters stay the same,
except the prevalence.
51
Sensitivity and Specificity(for reference later)
  • Prevalence
  • infected population / total N
  • Sensitivity
  • true positives / (true positives false
    negatives)
  • Specificity
  • true negatives / (true negatives false
    positives)
  • Expected positives
  • (prevalence x sensitivity) (1 specificity)
    x (1 prevalence) x N
  • Expected true positives
  • sensitivity x prevalence x N
  • Expected false positives
  • (1 specificity) x (1 prevalence) x N
  • Positive predictive value
  • true positives / (true positives false
    positives)
  • Negative predictive value
  • true negatives / (true negatives false
    negatives)

52
Sensitivity and Specificity
Even tests with very high sensitivity and
specificity (95 and higher are common) can give
large numbers of false positive and false
negative results. Number of correct results
determined by several things, including
prevalence, the distribution of results among
well and sick individuals, and the cutoff value
used to distinguish between healthy and diseased
states.
53
Types of error in biomarker measureswhere error
comes from and what it looks like
  • sensitivity and specificity
  • quantitative data
  • is assay limit of detection good for
    physiological levels
  • is assay sensitive enough to detect small
    differences between samples
  • does it cross react with something else, and do
    we care
  • qualitative data
  • For example, pregnancy tests, tests for
    infectious disease, tests for deficient or not in
    a nutrient, test for at risk or not of a
    non-infectious disease, etc.
  • accuracy versus precision
  • How are they different?
  • When is it useful maximize one over the other?
  • Want to know population average level of
    something, choose accuracy
  • Want to find a good marker of another event (ie
    ovulation), choose precision and adjust for known
    bias

54
Accuracy and Precision(bias and variability)
Of a test
Chard (1995) An introduction to radioimmunoassay
and related techniques. Elsevier Amsterdam
55
Accuracy and Precision(bias and variability)
Of a marker
56
Accuracy and Precision
  • When using existing datasets, real information
    about test accuracy is rarely provided, but
    measures of precision are frequently reported.
  • Usually, quality control (QC) data reported are
    measures of precision.
  • Given that youre likely to know the precision of
    a measurement method, what do you do with it?
  • An example from NHANES data description of lab
    methods for a serum cotinine assay

57
Accuracy and Precision
Quality control data for a serum cotinine assay
from the NHANES lab procedures document Cotinine
is a metabolite of nicotine, and is used to
measure exposure to smoking or second-hand smoke.
58
Accuracy and Precision
  • We know the NHANES serum cotinine assay has CVs
    of 17 to 52. Now what?
  • Unlike some other types of measures, biomarker
    methods often allow measurement error to be
    well-characterized.
  • When designing your own work, include measurement
    error in power analyses.
  • When reading about others studies, be aware of
    this level of error, and how (or if) they dealt
    with it.

59
Methodological Issues
  • I. Biomarker methods
  • Introduction to biomarkers and their use in
    population research
  • Brief overview of techniques commonly used to
    measure biomarkers
  • Introduction to the kinds of measurement error in
    those techniques
  • II. Statistical considerations for biomarker
    data
  • Incorporating known measurement error into power
    analyses
  • Dealing with repeated measures issues (frequently
    encountered in biomarker data)

60
Application of Coefficients of Variation (CV)
  • Often the only information you get regarding the
    precision of an assay is the CV
  • CVs not used much in statistics, but you can use
    the CV to estimate the standard deviation (SD) of
    an assay for a given mean
  • This will be useful when calculating power

61
Definition of the CV
  • Coefficient of Variation (CV) is computed from
    the standard deviation (s.d.) and mean of a
    measurement taken over a sample.

62
Convert CVs to s.ds
  • Coefficient of Variation (CV) is computed from
    the standard deviation (s.d.) and mean of a
    measurement taken over a sample.

Then
63
Convert CVs to s.ds
  • Example Estrogen measurements in women
    Bangladesh versus U.S.
  • Assume CV(s.d./mean) for the estrogen assay is
    10.

64
Convert CVs to s.ds
65
Application of CV Power analysis
  • We can use the information from CV to estimate
    power
  • CV ? SD ? POWER

66
Definition of Power
  • How do we know that the average differences in
    estrogen (or any biomarker) between 2 groups is a
    true difference?
  • Power is the probability that the difference
    between groups is real and not due to random
    noise.

67
Precision and Power analysis
  • Before you undertake any statistical analysis,
    you should determine if you have the power to
    detect the difference you are interested in.
  • Example We are interested in determining if
    estrogen levels are 20 higher in US women than
    in Bangladesh women.

68
Power analysis
  • Power is affected by
  • The size of the difference
  • Larger difference? higher power

69
Power analysis
  • Power is affected by
  • The size of the difference
  • The size of your sample
  • Larger sample ? higher power

70
Power analysis
  • Power is affected by
  • The size of the difference
  • The size of your sample
  • The SD of your difference
  • Larger SD ? lower power

71
Power Analysis
  • In biomarker data, where SDs tend to rise with
    increasing means, it is best to use the larger SD
    to determine power to detect differences between
    2 groups.

72
Repeated Measures
  • Biomarker data may often include repeated
    measures to look at changes in the marker over
    time
  • Issue familiar statistical procedures require
    measurement independence
  • Solution repeated measures must be accounted for
    with appropriate statistics

73
Repeated Measures
  • Statistical models that address repeated measures
    are variously referred to as multi-level models,
    hierarchical models, clustered data models, mixed
    effects models
  • Main issue separating between subject
    variability from within subject variability

74
Between and within subject variability
reproductive hormones across cycle
75
Between and within subject variability Diurnal
Patterns in Cortisol
Cortisol levels in 8 US adults (male and
female) Shows normal diurnal variationwithin
subject variability US7 much higher than
US61between subject variability
76
Between and within subject variabilityEffects
of aging on estrogen levels
Within-woman and between-woman variation
Ferrell et al. (2005) Monitoring reproductive
aging in a five year prospective study aggregate
and individual changes in steroid hormones and
menstrual cycle lengths with age. Menopause
12567-577.
77
Repeated Measures
  • Example C-reactive protein collected from 10
    subjects for up to 12 consecutive collections
    over the course of 2 months (data courtesy of
    Kathy Wander)
  • Q How does mean CRP vary across time?

78
Repeated Measures Example
  • Simple plot of CRP by cycle day
  • Shows strong variation but cant distinguish from
    between and within subject variation

79
Repeated Measures Example
  • Individual plots for each subject
  • Can see between and within subject variation
  • Better understanding of data

80
Repeated Measures
  • Moral In data with multiple measures per
    subject, you can miss the structure of the data
    if you dont separate out between and within
    subject variability

81
Repeated Measures
  • Example Daily estrogen (E1G) and progesterone
    (PDG) measures for 12 women across 1 cycle
  • Q What is the relationship between PDG and E1G?

82
Repeated Measures Example
  • Scatter plot of logE1G vs. logPDG show an
    positive correlation between these 2 variables.
  • Plot doesnt take into account repeated measures
    within subject

83
Repeated Measures Example
  • Plot by individual subject
  • Relationship between PDG and E1G not consistent
    across subject

84
Repeated Measures
  • Simple linear regression (SLR) of LogE1G on
    LogPDG without accounting for repeated measures
    within subject gives following results
  • Coefficients
  • Estimate Std. Error t value Pr(gtt)
  • (Intercept) 8.48438 0.23711 35.783 lt 2e-16
  • lpdg 0.22253 0.03055 7.283 2.34e-12

85
Repeated Measures Example
  • Now do a linear mixed effects (LME) model which
    adjusts for repeated measures within subject
  • Fixed effects le1g lpdg
  • Value Std.Error DF t-value
    p-value
  • (Intercept) 8.651058 0.5942757 325 14.557315
    0.0000
  • lpdg 0.206919 0.0760472 325 2.720933
    0.0069

86
Repeated Measures Example
  • While the estimate of the LogPDG coefficient was
    similar for both models the SE was much larger
    for the LME model than for the SLR model
  • Important to account for within subject
    variability, otherwise may underestimate SE, and
    overestimate model significance

87
Summary of statistical issues
  • Take care in using CV to estimate power (in
    general use larger CV)
  • Repeated measures often occur in biomarker
    dataneed to account for statistically
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