How to use data to get “The Right Answer” Donna Spiegelman Departments of Epidemiology and Biostatistics Harvard School of Public Health stdls@channing.harvard.edu  Standard designs & analysis sometimes not adequately controlling for  confounding  information bias
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Donna Spiegelman
Departments of Epidemiology and Biostatistics
Harvard School of Public Health
stdls@channing.harvard.edu
 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
What do we do?
“industry standard” END of mainstream epi methods
collect data on known & suspected timevarying confounders
MSMs, Gcausal algorithm
Fact: ~ 47% of US breast cancer incidence explained by known risk factors (Madigan et al., JNCI, 1987:16811695)
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 nonlinear interactions?
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
Unmeasured confounding by known or suspected risk factors:
We can use the data to get ‘the right answer’!
Design: twostage
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 2stage likelihood
References:
Weinberg & Wacholder, 1990; Zhao & Lipsitz, 1992;
Robins et al., 1994; + many others
Cain & Breslow, AJE, 1988
f (D  E, C1, C2; β) pdf of complete data
Pr (I  D, E, C1), I = 1 if in stage 2, 0 otherwise
f (D, I  E, C1; β,θ) =
Pr (I  D, E, C1) f (D  E, C1, c2) f (c2  E, C1) d c2
likelihood of 2stage design =
Stage 1
log [f (D, I  E, C1; , θ)]
Stage 2
+log [f (D  E, C1,C2; )]
Stage 2
+ log [f (C2  E, C1; θ ]
Example: Kyle Steenland – retrospective cohort study of lung cancer in
(Steenland & Greenland, AJE 2004;160:384392)
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
r=1,…, R levels of exposure
s=1,…, S levels of smoking
could treat as known
software?Offsets + weights in PROC GENMOD
training?
funding?
Result: The right answer?
Is it worth it?
What do we usually do?
NOTHING!
What can we do?
DesignAnalysis
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
FRAMINGHAM HEART STUDY
MAIN STUDY
 1731 men free of CHD
(nonfatal 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 2+3 (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
Example: (from Rosner, Spiegelman, Willett; AJE, 1992)
Framingham Heart Study
Reliability study: (n = 1346 men)
Subject i’s observed valve at time j
Subject i’s true mean
Reliability Coefficients
CHOL 75%
GLUC 52%
BMI 95%
SBP 72%
1. Measurement error model
within
between
2. Disease incidence model
log
3.
4. Reliability substudy “representative” of main study
― For one variable measured with unbiased, additive error
Z=X + 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)
Step 2. Estimate reliability coefficient from reliability substudy (n2 subjects,
r replicates)
Need same # of replicates per subject
where
TOTAL
withinperson variance (estimated)
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
10year 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)
4554
AGE 3.21 (1.95, 5.29)
2.85 (1.72, 4.74)
5564
AGE 4.30 (2.06, 8.98)
3.73 (1.67, 8.35)
6569
General framework for estimation and inference in failure time regression models
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
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)
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; 91:629634.
SmithWarner 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, ZeleniuchJacquotte A, Hunter DJ. Types of dietary fat and breast cancer: a pooled analysis of cohort studies. International Journal of Cancer 2001; 92:767774.
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 AfricanAmerican and EuropeanAmerican women? Ethnicity and Disease 1999; 8:331339.
RichEdwards 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.
KohBanerjee 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 9year gain in wais circumference among 15,587 men. Am J Clin Nutr 2003; 78:719727.
KohBanerjee 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 8year weight gain among men. In press, Am J Clin Nutr, 2004.
Keshaviah AP, Weller EA, Spiegelman D. Occupational exposure to methyl tertiarybutyl ether in relation to key health symptom prevalence: the effect of measurement error correction. Environmetrics, 2002; 14:573582.
Thurston SW, Williams P, Hauser R, Hu H, HernandezAvila 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 (r=0.19)
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 (r=0.82)
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.
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
So why are methods underutilized?
No validation data
Insufficient training of statisticians & epidemiologists
Either/or about assumptions
Quantitative correction for selection bias:
DesignAnalysis
main study/’selection’ study ML
SPE EE
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 EE
Let I=1 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 ), i=1, …, 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; i=1, …, n1
REPEATED SUBJECT = ID / TYPE = IND;
For dependent censoring, (a.k.a. biased loss to followup)
Assumes

Methods EXIST for efficient study design and valid data analysis when standard design with standard analysis gives the wrong answer

Why do epidemiologists routinely adjust for one source of bias only?
(confounding by measured risk factors)

Barriers to utilization