How to use data to get The Right Answer

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How to use data to getThe Right Answer

• Donna Spiegelman
• Departments of Epidemiology and Biostatistics
• Harvard School of Public Health
• stdls_at_channing.harvard.edu

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• - Standard designs analysis sometimes not
• adequately controlling for
• - confounding
• - information bias
• - selection bias
• Wrong answer?
• - Agreed We can be doing a better job
• - Not agreed HOW

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Confounding What do we do?
industry standard END of
mainstream epi methods
collect data on known suspected time-varying
confounders
MSMs, G-causal algorithm
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Confounding outstanding problems

• unmeasured confounding
• known or suspected confounders
• unknown confounders

Fact 47 of US breast cancer incidence
explained by known risk factors (Madigan et al.,
JNCI, 19871681-1695) r2 in most epi regressions
(blood pressure, serum hormones) 20-40
(Pediatric Task Force on BP Control in Children,
Pediatrics, 2004 Hankinson, personal
communication)
Undiscovered genes? Unimagined environmental
factors? Complex non-linear interactions?
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Solution to confounding by unknown risk
factors randomization
VERY limited applicability Outstanding
questions a few strong risk factors or many
weak ones? many rare ones or a few common ones?
modeling of scenarios do biases cancel?
NEW IDEAS NEEDED
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Unmeasured confounding by known or suspected risk
factors We can use the data to get the right
answer! Design two-stage Stage 1 (Di, Ei,
C1i), i 1, . . . , n Stage 2 (Di, Ei, C1i,
C2i), i 1, . . . , n2 (Di, Ei, C1i, . ), i
n2 1, . . . , n1 n2 n1 n2 Analysis
MLE of 2-stage likelihood References
Weinberg Wacholder, 1990 Zhao Lipsitz,
1992 Robins et al., 1994 many others
Cain Breslow, AJE, 1988
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f (D E, C1, C2 ß) pdf of complete data Pr (I
D, E, C1), I 1 if in stage 2, 0 otherwise f
(D, I E, C1 ß,?) Pr (I D, E, C1) f
(D E, C1, c2) f (c2 E, C1) d c2
likelihood of 2-stage design Stage 1
log f (D, I E, C1 , ?) Stage
2
log f (D E, C1, C2 ) Stage
2 log f (C2 E, C1 ?
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Example Kyle Steenland retrospective cohort
study of lung cancer in
(Steenland Greenland, AJE 2004160384-392) f
(D E, C) E silica, C smoking f (D E)
f (D E, C j) Pr (C j E) Pr (C j
Ei) where
relation to occupational silica exposure
n1 silica workers in retrospective cohort study
n2 silica workers in 1987 smoking prevalence
study n3 NHIS participants on general
population smoking rates in 1986 n4 ACS
prospective cohort data on smoking lung cancer
Likelihood (silica 1987 smoking data US
smoking data ACS lung cancer smoking data)
silica 1987
silica smoking date log f(Di Ei)
log
ACS
US
r1,, R levels of exposure s1,, S levels of
smoking
could treat as known

• assume distribution of smoking during entire
  period 1987

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Obstacles software? Offsets weights in
PROC GENMOD training? funding?
Result The right answer? Is
it worth it?
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INFORMATION BIAS What do we usually do?
NOTHING! What can we do?
Design
Analysis main
study/validation study
measurement error methods MS/EVS, MS/IVS,
IVS References Carroll, Ruppert, Stefanski,
1995, Chapman Hall Rosner et al., AJE, 1990,
1992 Spiegelman, Reliability studies
Validation studies Robins et
al., JASA, 1994
Encyclopedia of Biostatistics
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EXAMPLE FRAMINGHAM HEART STUDY MAIN STUDY - 1731
men free of CHD (non-fatal MI, fatal
CHD) At exam 4 - Followed for 10 years
for CHD Incidence (163 events, cumulative
incidence 9.4) REPRODUCIBILITY STUDY - 1346
men with all risk factors information at exams
23 (subgroup of 1731 men) - Risk factors in
main study Age, BMI, Serum Cholesterol, Serum
Glucose, Smoking, SBP - Risk factors in
reproducibility study Serum Cholesterol, BMI,
Serum Glucose, SBP, Smoking
?
?
?
?
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Example (from Rosner, Spiegelman, Willett AJE,
1992) Framingham Heart Study Reliability study
(n 1346 men)
Subject is observed valve at time j
Subject is true mean
Reliability
Coefficients CHOL
75 GLUC 52
BMI 95 SBP
72
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Assumptions 1. Measurement error model
within
between
2. Disease incidence model log
3.

• Pr (Di) is small
• Measurement error independent of disease status

4. Reliability substudy representative of main
study
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The Procedure ? For one variable measured with
unbiased, additive error ZX U, where Corr
(X,U) 0 simplest case Step 1. Run a
logistic regression of D on Z, U in main
study logit
Measured with
Measured without
error
error (1)
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Step 2. Estimate reliability coefficient from
reliability substudy (n2 subjects,
r replicates)
Need same of replicates per subject
where
within-person variance (estimated)
TOTAL
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Step 3. Correct.
corrected
uncorrected
MAIN STUDY
RELIABILITY STUDY
This contributes much less.

(Donner, Intl Stat Review, 1986)
95 C.I. for odds ratio
biological meaningful comparison, e.g. 90
percentile 10 percentile
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10-year cumulative incidence of CHD (163 events
/ 1731 men)
Results

2.91 (1.62, 5.24)
CHOL 2.21 (1343, 3.39)
100mg/dl
1.75 (0.87, 3.52)
GLUC 1.27 (0.97, 1.66)
34mg/dl
1.49 (0.92, 2.43)
BMI 1.64 (1.04, 2.58)
9.7kg/m2
3.93 (2.19, 7.05)
SBP 2.80 (1.85, 4.24)
49mmHg
1.69 (1.16, 2.47)
SMOKE 1.70 (1.17, 2.47)
(cig/day)
30 cig/day
1.89 (1.16, 3.07)
AGE 2.05 (1.27, 3.33)
45-54
AGE 3.21 (1.95, 5.29)
2.85 (1.72, 4.74)
55-64
AGE 4.30 (2.06, 8.98)
3.73 (1.67, 8.35)
65-69
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General framework for estimation and inference in
failure time regression models

• Main study/validation study studies

The data
(Di, Ti, Xi, Vi), i 1, . . ., n1 main study
subjects
(Di, Ti, xi, Xi, Vi), i n1 1, . . ., n1 n2
validation study subjects
where
Ti survival time
Di 1 if case at Ti, 0 o.w.
xi perfect exposure measurement
Xi surrogate exposure measurement for x
Vi other perfectly measured covariate data
- assume sampling into validation study is at
random
Spiegelman and Logan, submitted
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Effect of radon exposure on lung cancer mortality
rates UNM uranium miners
Mortality RR(95 CI)
100 WLM 500 WLM
Uncorrected 3.52 (0.658)
1.4 (1.3, 1.6) 5.8 (3.1, 11) EPL
5.00 (1.00) 1.7
(1.4, 2.0) 12 (4.6, 32)

• 30 attenuation in
• policy implications for

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Nutritional epidemiology Tworoger SS, Eliassen
AH, Rosner B, Sluss P, Hankinson SE. Plasma
prolaction concentrations and risk of
premenopausal breast cancer. In press, Cancer
Research, 2004. Hankinson SE, Willett WC, Michaud
DS, Manson JE, Colditz GA, Longcope C, Rosner B,
Speizer FE. Plasma prolaction levels and
subsequent risk of breast cancer in
postmenopausal women. Journal of the National
Cancer Institute 1999 91629-634. Smith-Warner
SA, Spiegelman D, Adami H, Beeson L, van den
Brandt P, Folsom A, Fraser G, Freudenheim J,
Goldbohm R, Graham S, Kushi L, Miller A, Rohan T,
Speizer FE, Toniolo P, Willett WC, Wolk A,
Zeleniuch-Jacquotte A, Hunter DJ. Types of
dietary fat and breast cancer a pooled analysis
of cohort studies. International Journal of
Cancer 2001 92767-774. Holmes MD, Stampfer MJ,
Wolf AM, Jones CP, Spiegelman D, Manson JE,
Coldditz GA. Can behavioral risk factors explain
the difference in body mass index between
African-American and European-American women?
Ethnicity and Disease 1999 8331-339. Rich-Edward
s JW, Hu F, Michels K, Stampfer MJ, Manson JE,
Rosner B, Willett WC. Breastfeeding in infancy
and risk of cardiovascular disease in adult
women. In press, Epidemiology, 2004. Koh-Banerjee
P, Chu NF, Spiegelman D, Rosner B, Colditz GA,
Willett WC, Rimm EB. Prospective study of the
association of changes in dietary intake,
physical activity, alcohol consumption, and
smoking with 9-year gain in wais circumference
among 15,587 men. Am J Clin Nutr 2003
78719-727. Koh-Banerjee P, Franz M, Sampson L,
Liu S, Jacobs Jr. DR, Spiegelman D, Willett WC,
Rimm EB. Changes in whole grain, bran and cereal
fiber consumption in relation to 8-year weight
gain among men. In press, Am J Clin Nutr, 2004.
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Environmental epidemiology
Keshaviah AP, Weller EA, Spiegelman D.
Occupational exposure to methyl tertiary-butyl
ether in relation to key health symptom
prevalence the effect of measurement error
correction. Environmetrics, 2002 14573-582.
Thurston SW, Williams P, Hauser R, Hu H,
Hernandez-Avila M, Spiegelman D. A comparison of
regression calibration methods for measurement
error in main study/internal validation study
designs. In press, Journal of Statistical
Planning and Inference, 2004.
Fetal lead exposure in relation to birth weight
MS/IVS bone lead vs. cord lead (r0.19)
Weller EA, Milton DK, Eisen EA, Spiegelman D.
Regression calibration for logistic regression
with multiple surrogates for one exposure.
Submitted for publication, 2004.
Metal working fluids exposure in relation to lung
function MS/EVS job characteristics vs.
personal monitors (r0.82)
Horick N, Milton DK, Gold D, Weller E, Spiegelman
D. Household dust endotoxin exposure and
respiratory effects in infants correction for
measurement error bias. In preparation.
Li R, Weller EA, Dockery DW, Neas LM, Spiegelman
D. Association of indoor nitrogen dioxide with
respiratory symptoms in children the effect of
measurement error correction with multiple
surrogates. In preparation.
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SOFTWARE IS AVAILABLE!

• http/www.hsph.harvard.edu/facres/spglmn.html

SAS macros for regression calibration (Rosner et
al., AJE, 1990, 1992 Spiegelman et al., AJCN,
1997 Spiegelman et al, SIM, 2001)
in main study/validation study designs

• STATA (Carroll et al. SIMEX, regression
  calibration)

So why are methods under-utilized?
No validation data Insufficient training of
statisticians epidemiologists Either/or about
assumptions
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Quantitative correction for selection bias
Design Analysis main study/selection
study ML SPE E-E
Note
large overlap w/ missing data literature
when D is missing, potential for selection bias
References
Little Rubin, Wiley, 1986 Scharfstein et al.,
1998 Rotnitzky et al., 1997 Robins et al., 1995
ML
SPE E-E
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Basic idea Let I1 if selected, 0
otherwise, Pr (I E, C) selection
probability Selection study has data on those not
in main study (Di, Ei, Ci (Ci, Ui ), i1, , n2
Surrogates for D, risk factors for D
Mail, phone, house visit to get data
IPW Pr (Ii 1 Di, Ei, Ci)-1 Wi
Use PROC GENMOD w/ robust variance weights Wi
i1, , n1 REPEATED SUBJECT ID
/ TYPE IND
For dependent censoring, (a.k.a. biased loss to
follow-up)
Assumes
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CONCLUSIONS
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Methods EXIST for efficient study design and
valid data analysis when standard
design with standard analysis gives the wrong
answer
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Why do epidemiologists routinely adjust for one
source of bias only?
(confounding by measured risk factors)
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Barriers to utilization

• software gaps
• software unfriendly, no QC
• inadequate training of students practitioners
  (Epi Biostat)
• are two-stage designs fundable _at_ NIH?