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Methodological Issues in Using Biomarker Data for Demographic Research. Eleanor Brindle CSDE Biodemography Core Jane Shofer Anita Rocha CSDE Statistics Core. April 4 th , 2006. Methodological Issues…. I. Biomarker methods Introduction to biomarkers and their use in population research

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Methodological issues in using biomarker data for demographic research

Methodological Issues in Using Biomarker Data for Demographic Research

Eleanor Brindle

CSDE Biodemography Core

Jane Shofer

Anita Rocha

CSDE Statistics Core

April 4th, 2006


Methodological issues
Methodological Issues… Demographic Research

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)


I biomarker methods
I. Biomarker Methods Demographic Research

  • 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 issues—frequency, diurnal patterns, fluid type

    • Dictated by biology, technology and your questions

  • Measurement error types

    • Sensitivity, specificity, accuracy, precision


Ii statistical considerations for biomarker data
II. Statistical Considerations for Biomarker Data Demographic Research

  • Power

    • Take advantage of having well-characterized measurement error

  • Repeated measures

    • Often encounter non-independence in biomarker data


Biomarker methods
Biomarker Methods Demographic Research

  • 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 issues—frequency, diurnal patterns, fluid type

  • Measurement error types


Using biomarkers in population research
Using Biomarkers in Population Research Demographic 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.


Using biomarkers in population research1
Using Biomarkers in Population Research Demographic 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)


Using biomarkers in population research2
Using Biomarkers in Population Research Demographic 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


Using biomarkers in population research3
Using Biomarkers in Population Research Demographic 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


Examples of studies using biomarkers

National Health and Nutrition Examination Survey (NHANES) Demographic Research

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

Women’s Health Initiative (WHI)

Study of Women’s Health Across the Nation (SWAN)

Melbourne Women’s Midlife Health Project (MWMHP)

Cebu Longitudinal Health and Nutrition Survey (CLHNS)

The Health and Retirement Study (HRS)

Examples of Studies Using Biomarkers


Links to more
Links to more Demographic Research

NIH and CDC sites:

http://www.nih.gov/icd/

http://www.nia.nih.gov/ResearchInformation/ScientificResources/

http://resresources.nci.nih.gov/categorydisplay.cfm?catid=9

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_large.htm

http://www.cdc.gov/nchs/datawh.htm

http://www.cdc.gov/nchs/express.htm




Participation in cultural activities by risk and cortisol group
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 activity’s 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.


Methodological issues in using biomarker data for demographic research
NHANES groupNational 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


  • Nhanes biomarkers

    Triglycerides group

    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

    Hepatitis AntiHBs

    Hepatitis A, B, C, D

    HbSAg

    Selenium

    Chlamydia (urine)

    Gonorrhea (urine)

    NHANESBiomarkers

    • 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

    • Cadmium

    • Erythrocyte protoporphyrin

    • RBC folate

    • Serum folate

    • Glycohemoglobin

    • Mercury (hair)

    • Mercury (blood)

    • Mercury (urine)

    • CD4

    • WBC/DNA

    • VOC (blood)

    • Iron

    • TIBC

    • Ferritin

    • Vitamin B12

    • C-reactive protein

    • Helicobacter pylori

    • Cryptosporidium

    • Vitamin A/E/Carotenoids

    • Vitamin C

    • Measles/Varicella/Rubella

    • Cotinine

    • Chemistry panel

    • Bone alkaline phosphatase

    • Toxoplasma

    • Total cholesterol

    • HDL

    • LDL

    • Acrylamide


    Add health
    Add Health group

    • 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…”


    Biomarker methods1
    Biomarker Methods group

    • 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 issues—frequency, diurnal patterns, fluid type

    • Measurement error types


    Biomarker measurement
    Biomarker Measurement group

    • 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


    Immunoassays
    Immunoassays group

    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.


    Methodological issues in using biomarker data for demographic research

    Immunoassays group

    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)


    Methodological issues in using biomarker data for demographic research

    Immunoassays group

    • 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).


    Biomarker methods2
    Biomarker Methods group

    • 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 issues—frequency, diurnal patterns, fluid type

    • Measurement error types


    Using biomarkers in population research4
    Using Biomarkers in Population Research group

    • 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?


    Using biomarkers in population research5
    Using Biomarkers in Population Research group

    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?


    Using biomarkers in population research6
    Using Biomarkers in Population Research group

    • “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


    Example estradiol and obesity
    Example: Estradiol and obesity group

    • 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 150:161-71.


    Biomarker methods3
    Biomarker Methods group

    • 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 issues—frequency, diurnal patterns, fluid type

      • Dictated by biology, technology and your questions

    • Measurement error types



    Longitudinal biomarker data
    Longitudinal biomarker data group

    One woman, daily urine samples across six months for each of five years. (Data are from the BIMORA study of the menopausal transition.)


    Cross sectional biomarker data
    Cross-sectional biomarker data group

    • 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


    Diurnal patterns in cortisol
    Diurnal Patterns in Cortisol group

    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.


    Collection methods
    Collection Methods group

    Dried blood spot collection

    Typically one prick with a small lancet will produce 4 blood spots—enough to assay several different biomarkers


    Collection methods1
    Collection Methods group

    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


    Collection methods2
    Collection Methods group

    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


    Biomarker methods4
    Biomarker Methods group

    • 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 issues—frequency, diurnal patterns, fluid type

    • Measurement error types

      • Sensitivity, specificity, accuracy, precision


    Types of error in biomarker measures where error comes from and what it looks like
    Types of error in biomarker measures: groupwhere 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


    Sensitivity and specificity
    Sensitivity and Specificity group

    • 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


    Sensitivity and specificity immunoassays
    Sensitivity and Specificity: groupImmunoassays


    Sensitivity and specificity qualitative discrete tests
    Sensitivity and Specificity: groupQualitative (discrete) tests

    Loong (2003) Understanding sensitivity and specificity with the right side of the brain. BMJ 327:716-9


    Sensitivity and specificity in qualitative data
    Sensitivity and Specificity in Qualitative Data group

    • 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)


    Sensitivity and specificity in qualitative data1
    Sensitivity and Specificity in Qualitative Data group

    • 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)


    Sensitivity and specificity1
    Sensitivity and Specificity group

    • 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


    Sensitivity and specificity2
    Sensitivity and Specificity group

    TN = true negative

    TP = true positive

    FN = false negative

    FP = false positive


    Methodological issues in using biomarker data for demographic research

    Sensitivity and Specificity group

    TNF = true negative fraction

    TPF = true positive fraction

    FNF = false negative fraction

    FPF = false positive fraction

    http://www.anaesthetist.com/mnm/stats/roc/


    Methodological issues in using biomarker data for demographic research

    Sensitivity and Specificity group(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)


    Sensitivity and specificity examples from addhealth
    Sensitivity and Specificity groupExamples from AddHealth

    Sensitivity = 665  673 = 0.9881

    Specificity EIA only = 2880  2897 = 0.9941

    Specificity EIA & WB = 2893  2897 = 0.9986


    Sensitivity and specificity3
    Sensitivity and Specificity group

    • AddHealth HIV tests have sensitivity of 98.80% and specificity of 99.86%. Now what?

    • 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


    Methodological issues in using biomarker data for demographic research

    Sensitivity and Specificity group

    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.


    Sensitivity and specificity for reference later
    Sensitivity and Specificity group(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)


    Methodological issues in using biomarker data for demographic research

    Sensitivity and Specificity group

    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.


    Types of error in biomarker measures where error comes from and what it looks like1
    Types of error in biomarker measures: groupwhere 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


    Methodological issues in using biomarker data for demographic research

    Accuracy and Precision group(bias and variability)

    Of a test:

    Chard (1995) An introduction to radioimmunoassay and related techniques. Elsevier: Amsterdam


    Accuracy and precision bias and variability
    Accuracy and Precision group(bias and variability)

    Of a marker:


    Accuracy and precision
    Accuracy and Precision group

    • 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 you’re 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


    Accuracy and precision1
    Accuracy and Precision group

    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.


    Accuracy and precision2
    Accuracy and Precision group

    • 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.


    Methodological issues1
    Methodological groupIssues…

    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)


    Application of coefficients of variation cv
    Application of Coefficients of Variation (CV) group

    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


    Definition of the cv
    Definition of the CV group

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


    Convert cv s to s d s
    Convert CV’s to s.d’s group

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

    Then


    Convert cv s to s d s1
    Convert CV’s to s.d’s group

    Example: Estrogen measurements in women: Bangladesh versus U.S.

    Assume CV(=s.d./mean) for the estrogen assay is 10%.



    Application of cv power analysis
    Application of CV: Power analysis group

    We can use the information from CV to estimate power

    CV  SD  POWER


    Definition of power
    Definition of Power group

    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.


    Precision and power analysis
    Precision and Power analysis group

    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.


    Power analysis
    Power analysis group

    Power is affected by

    • The size of the difference

      Larger difference higher power


    Power analysis1
    Power analysis group

    Power is affected by

    • The size of the difference

    • The size of your sample

      Larger sample  higher power


    Power analysis2
    Power analysis group

    Power is affected by

    • The size of the difference

    • The size of your sample

    • The SD of your difference

      Larger SD  lower power


    Power analysis3
    Power Analysis group

    In biomarker data, where SD’s tend to rise with increasing means, it is best to use the larger SD to determine power to detect differences between 2 groups.


    Repeated measures
    Repeated Measures group

    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


    Repeated measures1
    Repeated Measures group

    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



    Between and within subject variability diurnal patterns in cortisol
    Between and within subject variability: hormones across cycleDiurnal Patterns in Cortisol

    Cortisol levels in 8 US adults (male and female)

    Shows normal diurnal variation—within subject variability

    US7 much higher than US61—between subject variability


    Between and within subject variability effects of aging on estrogen levels
    Between and within subject variability: hormones across cycleEffects 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 12:567-577.


    Repeated measures2
    Repeated Measures hormones across cycle

    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?


    Repeated measures example
    Repeated Measures: Example hormones across cycle

    Simple plot of CRP by cycle day

    Shows strong variation but can’t distinguish from between and within subject variation


    Repeated measures example1
    Repeated Measures: Example hormones across cycle

    Individual plots for each subject

    Can see between and within subject variation

    Better understanding of data


    Repeated measures3
    Repeated Measures hormones across cycle

    Moral: In data with multiple measures per subject, you can miss the structure of the data if you don’t separate out between and within subject variability


    Repeated measures4
    Repeated Measures hormones across cycle

    Example: Daily estrogen (E1G) and progesterone (PDG) measures for 12 women across 1 cycle

    Q: What is the relationship between PDG and E1G?


    Repeated measures example2
    Repeated Measures: Example hormones across cycle

    Scatter plot of logE1G vs. logPDG show an positive correlation between these 2 variables.

    Plot doesn’t take into account repeated measures within subject


    Repeated measures example3
    Repeated Measures: Example hormones across cycle

    Plot by individual subject

    Relationship between PDG and E1G not consistent across subject


    Repeated measures5
    Repeated Measures hormones across cycle

    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(>|t|)

    (Intercept) 8.48438 0.23711 35.783 < 2e-16 ***

    lpdg 0.22253 0.03055 7.283 2.34e-12 ***


    Repeated measures example4
    Repeated Measures: Example hormones across cycle

    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 0.2069190.0760472 325 2.720933 0.0069


    Repeated measures example5
    Repeated Measures: Example hormones across cycle

    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


    Summary of statistical issues
    Summary of statistical issues hormones across cycle

    • Take care in using CV to estimate power (in general use larger CV)

    • Repeated measures often occur in biomarker data—need to account for statistically