American Journal of Epidemiology
Copyright O 1996 by The Johns Hopkins University School of Hygiene and Public Health
All rights reserved
Vol. 143, No. 5
Printed In U.SA.
Association of Serum Total Cholesterol with Coronary Disease and All-Cause
Mortality: Multivariate Correction for Bias Due to Measurement Error
Carlos Iribarren, 12 Dan Sharp,3 Cecil M. Burchfiel,3 Ping Sun,1 and James H. Dwyer1
Measurement error in the exposure under investigation is an important but often ignored source of bias in
observational studies. The authors examined the impact of measurement error in the association between total
serum cholesterol and 16-year coronary heart disease and all-cause mortality in a cohort of 6,137 middle-aged
men of Japanese descent in the Honolulu Heart Program (1973-1988). A Cox regression model that enables
modeling of survival time with correction for measurement errors in multiple covariates was employed. After
controlling for age, body mass index, systolic blood pressure, smoking status, alcohol consumption, dietary
cholesterol, and total calorie intake, a difference of one standard deviation (38 mg/dL) in total cholesterol was
associated with a significant increase in the risk of coronary disease death (uncorrected hazard ratio = 1.35).
After correction for measurement errors in total cholesterol and covariates (except smoking and age), the
estimated hazard ratio increased to 1.65 (a 22% increase). A U-shaped relation was observed between total
cholesterol levels and the risk of all-cause mortality. This association was then examined with a quadratic
model and with a two-slope or V-shaped regression model. In the quadratic fit, the magnitude of the quadratic
total cholesterol term increased threefold after the adjustment for measurement error. In the V fit, the hazard
ratio of all-cause death corresponding to a change in one standard deviation above 214 mg/dL (the nadir of
the V) was 1.15, and increased to 1.49 (by 29%) after the correction. The corresponding hazard ratio of a
change in one standard deviation below 214 mg/dL was 1.11, and increased to 1.37 (by 23%) after the
correction. The authors conclude that the impact of elevated total cholesterol on the risk of coronary disease
and all-cause mortality may be greater than previously estimated with standard methods of analysis. In
addition, the correction for measurement error in total cholesterol and covariates did not explain the excess
mortality associated with low total cholesterol. More research is needed to elucidate the fundamental issues
underlying the U-shaped association, i.e., confounding versus causal implications. Am J Epidemiol 1996;143:
463-71.
bias (epidemiology); cohort studies; coronary disease; mortality; regression analysis; risk factors
A common problem in observational studies is that
measured biologic or behavioral risk factors are only
surrogate indicators of the individual's true level of
exposure (1). A well-known consequence of the error
in measurement is that the slope of the simple regression of y (disease) on x (exposure) is attenuated (2, 3).
This phenomenon has been called "regression dilution
bias" by MacMahon et al. (4).
Because total serum cholesterol concentrations are
subject to intraindividual fluctuations and to laboratory error (5, 6), it follows that the univariate relation
of total cholesterol level with mortality will be subject
to the effect of regression dilution bias. In consequence, previous estimates of the relation of total
cholesterol with risk of coronary heart disease or allcause mortality may be attenuated relative to the true
extent of the association (7-9). However, when multivariate models are used and two or more variables
included in the model are measured with error, the
situation becomes more complex and the observed
regression coefficients may underestimate or overestimate the corresponding true regression coefficients
(3). Recently, a number of papers have appeared (3,
10-13) that describe methods to assess and correct for
measurement error.
Received for publication January 23,1995, and In final form May
30, 1995.
Abbreviations: Cl, confidence interval; ICD-8, International Classification of Diseases, 8th revision; SE, standard error.
1
Institute for Health Promotion and Disease Prevention Research, Department of Preventive Medicine, University of Southern
California School of Medicine, Los Angeles, CA.
2
Present address: Division of Epidemiology, School of Public
Health, University of Minnesota, Minneapolis, MN.
3
Honolulu Epidemiology Research Unit, Division of Epidemiology and Clinical Applications, National Heart, Lung and Blood Institute, Bethesda, MD.
Correspondence to Dr. James H. Dwyer, Institute for Prevention
Research, USC School of Medicine, 1540 Alcazar St., CHP 205, Los
Angeles, CA 90033.
463
464
Iribarren et al.
The aim of this report is to present two empirical
examples of a method for correcting for measurement
error bias using multiple Cox proportional hazards
regression. The method is an extension of a logistic
procedure described by Rosner et al. (13). In the first
example, and as previously shown in the Lipid Research Clinics Mortality Follow-up Study (14) and the
British United Provident Association Study (15), we
hypothesized that the crude (uncorrected) association
of elevated total cholesterol with the risk of coronary
disease death is an underestimation of the true extent
of the hazard of elevated total cholesterol. The second
example involved the application of the correction
procedure to the U-shaped relation of total cholesterol
with all-cause mortality. We hypothesized that the
quadratic relation and thus both arms of a V-shaped fit
will become steeper after the correction. It is anticipated that measurement error is not a likely explanation of the excess death rate in cohort members with
low total cholesterol.
mined by the same method, but sera specimens were
processed in a different laboratory (Kuakini Medical
Center, Honolulu, Hawaii). Deaths during the period
1973-1988 were then ascertained through hospital surveillance, state health department records, and newspaper obituaries. The underlying cause of death was
assigned by a mortality review panel, and coded following the eighth revision of the International Classification of Diseases (ICD-8) (21).
The principal endpoints for this analysis were deaths
due to coronary disease (rubrics 410-414 of the
ICD-8) and all-cause mortality. Less than 2 percent of
the cohort was lost to follow-up during the study
period. Of the total 8,006 men enrolled in the study,
231 had prevalent coronary disease, 68 had cerebrovascular disease, and 58 had cancer at the time of
baseline measurements, and were excluded from the
study. Of the remaining 7,515 men, 1,378 had missing
values in total cholesterol and/or study covariables, or
did not attend examination 3. Thus, the final sample
for analysis comprised 6,137 participants.
MATERIALS AND METHODS
The cohort
Statistical analysis
The Honolulu Heart Program was established in
1965-1968 with the examination of 8,006 JapaneseAmerican men born between 1900 and 1919 and who
lived on the island of Oahu, Hawaii. About 12 percent
of the cohort were migrant farmers from southern
Japan. The principal focus of the study has been the
identification of predictors of coronary disease and
stroke. Specifics of the design, study population, and
methodological procedures have been previously published (16, 17). On entry into the study (1965-1968)
and during the third examination 6 years later (1971—
1974), the following data were obtained from each
subject: sociodemographic factors, individual and
family medical history, weight, height, blood pressure,
non-fasting total cholesterol, as well as cigarette
smoking and alcohol consumption habits. At each
examination, blood pressure was measured once by a
physician and twice by a trained nurse, and the average of the three readings was used in the analysis.
Usual diet was assessed at the first examination with
the 24-hour dietary recall method (18). In 1970, a
random sample of 261 men were invited to participate
in a dietary intake validation study involving the completion of 7-day dietary records. The purpose of this
validation study was to assess within-person variability of nutrient intake (19). In 1965-1968, non-fasting
total cholesterol concentrations were measured by the
Autoanalyzer N-24A method (Technicon Instruments
Corp., Tarrytown, New York) at the US Public Health
Service Laboratory in San Francisco, California (20).
In 1971-1974, non-fasting total cholesterol was deter-
We first obtained descriptive statistics and Pearson
correlations among the study variables. Age-adjusted
mortality rates for coronary disease and all causes
were computed by quintiles of total cholesterol using
the direct method with the entire cohort as the standard
population.
To model survival time as a function of total cholesterol, we used the Cox proportional hazards model
(22, 23). Hazard ratios and 95 percent confidence
intervals are given for corresponding increases of one
standard deviation in each continuous predictor variable and for contrasted levels of categorical predictors.
To remove the effect of age, regression models were
stratified on age at baseline (in individual's years, and
assumed to contain no error).
Tests for linear or quadratic (U-shaped) associations
between total cholesterol and mortality outcomes were
performed with age-adjusted Cox regression on linear
total cholesterol only and with age-adjusted Cox regression of linear plus total cholesterol squared terms,
respectively. A U-shaped relation indicates that the
risk across the independent variable (in this case, total
cholesterol) is elevated at low and at high values of the
predictor and is minimum at the middle range.
One way to parametrize a quadratic risk relation is
to fit a "two-piece" or "V-shaped" regression line to
the data. This parametrization has been described in
the literature as "broken" or "piece-wise" regression
(24). The nadir or breakpoint of the "V" was estimated
as the minimum of the U-curve (25), and was equal to
214 mg/dL.
Am J Epidemiol
Vol. 143, No. 5, 1996
Measurement Error Bias in Cholesterol-Mortality Relations
To correct for the effect of measurement error in
total cholesterol and selected life-style (alcohol consumption, dietary cholesterol, and total calorie intake)
and physiologic characteristics (body mass index and
systolic blood pressure), we employed a multivariate
method described by Rosner et al. (13), and a matrixbased algorithm developed by Dwyer and Sun (Institute for Prevention Research, Department of Preventive Medicine, University of Southern California,
unpublished). The Dwyer-Sun program is a generalization of the Rosner method that applies to different
forms of regressions: linear, probit, logistic, and proportional hazards. In the current analysis, smoking
status (past, continuing smoking, and quitting, relative
to never smokers) was also included in the multivariate models, but no attempt was made to correct for
possible errors in the ascertainment of smoking status.
We entered a categorical variable for alcohol abstinence (presumed fully accurate), because abstainers
have been shown to be a group with compromised
health (26). The Dwyer-Sun algorithm yields measurement error corrected point and confidence limit estimates of proportional hazards regression coefficients
with covariates assumed to be measured with or without error. This analytic approach requires the availability of estimates of between- and withinperson components of variance. These are usually
determined via analysis of repeated measures or by
validation studies. In our analysis, we used two observations of total cholesterol and covariates (examinations 1 and 3, 6 years apart), and two observations of
dietary cholesterol and total calorie intake (one the
baseline 24-hour dietary recall, and the other the average of seven consecutive daily food records supplied
by a random subsample of 261 cohort members about
2 or 3 years later).
The method of Rosner et al. (13) for measurement
error correction involves four steps. First, uncorrected
or crude Cox regression coefficients are estimated for
each study outcome using the main study data (examination 1 and 24-hour dietary recall). Second, a multivariate linear model is performed in which the repeated and validation substudy data (examination 3
and average of 7-daily food records) are correlated
with individually paired data from the main study.
Third, the corrected regression estimates are obtained
by weighting the unadjusted coefficients by the
variance-covariance matrix relating the main study
variables with the repeated or validation study variables. Finally, the variance of the corrected estimate is
calculated using formulas based on the multivariate
delta method (3, 27) (also called the method of statistical differentials), and asymptotic 100(1 — a) percent
Am J Epidemiol
Vol. 143, No. 5, 1996
465
confidence limits for the corrected regression coefficients are derived as /3* ± Z\-an (var fi*)m. The
var O*) is the estimated variance and a is the type I
error (a = 0.05 in the current analysis). Var (0*)
includes a component attributable to the estimation of
the repeated correlations, and is obtained by expanding the risk function in a truncated Taylor series (27).
Because the linear model was adequate to describe
the relation of total cholesterol with coronary disease
mortality, example 1 is based on the correction for
measurement error in linear total cholesterol and covariates. The relation between total cholesterol and
all-cause mortality is U-shaped, and therefore example
2 comprises two different approaches: first, a multivariate quadratic model (linear total cholesterol, total
cholesterol squared, plus covariates); and second, a
segmented multivariate V-shaped regression model
(converging near the estimated total cholesterol value
of minimal mortality, plus covariates).
RESULTS
Table 1 presents descriptive statistics of all the predictor variables in the main sample of 6,137 men,
TABLE 1. Descriptive statistics of study variable* among a
cohort of 6,137 middle-aged men of Japanese descent In the
Honolulu Heart Program*
Malnsampk 3 (/l = 6,137)
Non-dietary
variables
Age (years), mean (SDt)
Serum cholesterol (mg/dL),
mean (SD)
Body mass index (kg/m*),
mean (SD)
Systolic blood pressure
(mmHg), mean (SD)
Current smokers (%)
Alcohol consumption
(oz/montht), mean (SD)
Alcohol abstainers (%)
At baseline
(1965-1968)
At examination 3
(1971-1974)
53.9 (5.4)
59.9
(5.4)
218 (36)
216
(36)
23.9 (3.0)
23.7 (3.0)
133 (20)
45.3
136 (20)
34.2
13.6 (23.6)
35.5
13.5 (24.4)
30.8
Dietary validation sample (n = 261)
Dietary
variables
Dietary cholesterol
(mg/day), mean (SD)
Total calorie Intake (Kcal/
day), mean (SD)
24-hour dietary
recall
(1965-1968)
7-day
dietary records
(1970)
542 (317)
528 (182)
2,318 (662)
2,300 (511)
* Men with prevalent coronary disease, stroke, or cancer at
baseline, or with missing values on study covariates at baseline or
examination 3 variables are excluded.
t SD, standard deviation.
$ 1 oz = 28.35 g.
466
Iribarren et al.
Example 1: total cholesterol and coronary
mortality
together with the intake of dietary cholesterol and total
calories in the validation sample of 261 men. There
were slight reductions in average levels of serum cholesterol and body mass index, and a small increase in
average systolic blood pressure from examination 1 to
examination 3. The standard deviations of dietary cholesterol and total calorie intake measured by 7-day
dietary records were appreciably smaller than the corresponding standard deviations of the same dietary
variables measured with a 24-hour dietary recall (18.2
vs. 31.2 and 727 vs. 511, respectively). Results in table
1 also indicate a smaller proportion of current smokers
and a tendency toward less alcohol abstinence in examination 3.
Total cholesterol at baseline showed a weak positive
correlation with body mass index (r = 0.12), systolic
blood pressure (r = 0.07) and dietary cholesterol (r =
0.06), and a weak negative correlation with alcohol
consumption (r = —0.05). Autocorrelations (i.e., correlation of a variable at examination 1 with the same
variable at examination 3) were high for body mass
index (r = 0.89) and alcohol consumption (r = 0.72),
and moderate for total cholesterol (r = 0.61) and
systolic blood pressure (r = 0.64). The correlation
between dietary cholesterol and total calories from the
24-hour dietary recall method and the same variables
measured by 7-day records were r = 0.33 and r =
0.46, respectively, in the 261 participants in the collection of 7-day dietary records.
There were 197 documented coronary disease
deaths, comprising about 13 percent of all deaths and
50 percent of all cardiovascular disease deaths. Ageadjusted coronary disease mortality rates per 100 men
increased consistently with the level of total cholesterol: 1.7 (<189 mg/dL), 2.7 (189-207 mg/dL), 3.2
(208-226 mg/dL), 3.1 (227-247 mg/dL), and 5.9
(>247 mg/dL), respectively (p linear trend = 0.0001).
Table 2 presents the uncorrected and measurement
error corrected multivariate hazard ratios of coronary
disease death associated with differences of one standard deviation in continuous variables, and the corresponding hazards of former smokers, continuing
smokers, and quitters, relative to never smokers. The
risk from alcohol abstinence is given in relation to any
alcohol consumption.
A difference of one standard deviation (38 mg/dL)
of total cholesterol was associated with a 1.35 "crude"
increase in coronary disease mortality. When the correction for measurement error was performed, the hazard increased to 1.65 (a 22 percent increase). The
association of systolic blood pressure with the risk of
death from coronary disease was also considerably
augmented after the correction for measurement error
(1.57 uncorrected vs. 1.98 corrected). Dietary cholesterol was a weak (and non-statistically significant)
TABLE 2. Coronary disease mortality among a cohort of 6,137 middle-aged men of Japanese descent,
the Honolulu Heart Program, 1973-1988: uncorrected and corrected multivariate hazard ratios (95%
confidence Intervals (Cl)) (n = 197 coronary disease deaths)*
Predictor
vanflCMas
(1 SD change)
Serum cholesterol (38 mg/dL)
Body mass index (3.1 kg/m*)
Systolic blood pressure (21
mmHg)
Alcohol consumption (24 oz/
month§)
Dietary cholesterol (300 mg/day)
Total calories (700 Kcal/day)
Past smoking vs. never smoking
Continuing smoking vs. never
smoking
Quitting smoking vs. never
smoking
Alcohol abstinence vs. any
alcohol
Hazard ratlot (95% Cl)
%
Uncorrected
Corrected
Changed
1.35(1.19-1.54)
1.20(1.04-1.38)
1.65(1.34-2.03)
1.19 (1.01-1.40)
+22.2
-0.8
1.57(1.38-1.78)
1.98(1.64-2.39)
+26.1
0.87 (0.72-1.06)
1.05(0.91-1.22)
0.96(0.82-1.12)
1.22(0.81-1.84)
0.81 (0.59-1.12)
1.26(0.56-2.80)
0.96(0.59-1.56)
1.25(0.82-1.90)
-6.8
+20.0
0.0
+2.4
2.22(1.54-3.22)
2.20(1.48-3.27)
-0.1
2.32(1.48-3.63)
2.08(1.31-3.31)
-10.3
1.39(1.01-1.90)
1.38(0.96-1.98)
-0.7
* Men with prevalent coronary disease, stroke, or cancer at baseline are excluded.
t Hazard ratios are estimated for 1 SD (standard deviation) Increase in continuous variables, and relative to
never smokers and any alcohol consumption, respectively, for smoking status and alcohol abstinence.
+. % change is estimated as ((corrected - uncorrected)/uncorrected) x 100.
§ 1 oz = 28.35 g.
Am J Epidemiol
Vol. 143, No. 5, 1996
Measurement Error Bias in Cholesterol-Mortality Relations
positive risk factor for fatal coronary disease. It is
noteworthy that the relative risk associated with an
increase of 300 mg/day in dietary cholesterol (holding
the total calorie intake constant) rose from 1.05 to 1.26
after the multivariate correction for measurement error
bias (about 20 percent increase). However, this deattenuation was accompanied by an extremely wide 95
percent confidence interval, including unity. Conversely, correction for errors of measurement did not
have an appreciable impact on the direct relation between body mass index and the inverse relation of
alcohol consumption with the risk of coronary death.
Among the variables assumed to contain no error, it
was found that smoking quitters, continuing smokers
(in relation to never smokers), and abstainers from
alcohol (in relation to any alcohol consumption) were
at increased risk of coronary disease mortality.
error (SE) = 0.0OOOO93; t = 3.6). To facilitate the
interpretation of the U-shaped relation, we estimated
the hazard ratios for changes of 1 standard deviation
(SD) (38 mg/L) above and below the nadir of the V
(that is, the intersection of the slopes at 214 mg/dL)
using a V-shaped regression model (table 3). An increase of 38 mg/dL above 214 mg/dL was associated
with a hazard ratio of 1.15. A decrease of 38 mg/dL
from the breaking point of the V predicted a hazard
ratio of 1.11. Corresponding corrected estimates were
about 29 percent higher for the hazard derived from
the right slope (total cholesterol change toward higher
level), and 23 percent higher for the hazard derived
from the left slope (total cholesterol change toward
lower level).
When the correction was applied to the multivariate
quadratic model, the coefficient for total cholesterol
squared became about three times larger (/3 =
0.000113; SE = 0.000044; t = 2.5).
Systolic blood pressure and alcohol consumption
were significant risk factors for all-cause mortality
among men of the Honolulu cohort. After the correction, the risk associated with these variables increased
by a moderate amount (11 percent for systolic blood
pressure and 6 percent for alcohol consumption). No
impact on all-cause mortality was observed for body
mass index, dietary cholesterol, and total calorie intake. On the other hand, all smoking categories (rela-
Example 2: total cholesterol and all-cause
mortality
There were a total of 1,490 deaths in the 16 years of
follow-up among the study subjects. Age-adjusted
mortality rates (per 100 persons) by quintiles of total
cholesterol at baseline were 25.5, 22.0, 22.1, 25.4, and
26.3, respectively, evidencing a quadratic relation of
all-cause mortality with the level of total cholesterol
(/3 for total cholesterol squared = 0.0000339; standard
TABLE 3. All-cause mortality among a cohort of 6,137 middle-aged men of Japanese descent, the
Honolulu Heart Program, 1973-1988: uncorrected and corrected multivariate hazard ratios (95%
confidence Intervals (Cl)) (n = 1,490 deaths)*
Predictor
vaiiiimoo
(1 SD change)
Serum cholesterol
+38 mg/dL above 214 mg/dL
-38 mg/dL below 214 mg/dL
Body mass Index (3.1 kg/m*)
Systolic blood pressure (21
mmHg)
Alcohol consumption (24 oz/
month§)
Dietary cholesterol (300 mg/day)
Total calories (700 calories)
Past smoking vs. never smoking
Continuing smoking vs. never
smoking
Quitting smoking vs. never
smoking
Alcohol abstinence vs. any
alcohol
Hazard ratlot (95% Cl)
%
Uncorrected
Corrected
Change^
1.15(1.07-1.24)
1.11 (1.00-1.22)
1.02(0.96-1.07)
1.49 (1.21-1.84)
1.37(1.06-1.76)
1.00(0.94-1.07)
+29.5
+23.4
-0.02
1.25(1.19-1.31)
1.39(1.28-1.49)
+11.2
1.10(1.04-1.16)
1.02(0.97-1.08)
0.92 (0.87-0.97)
1.18 (1.02-1.37)
1.17(1.06-1.29)
1.08(0.81-1.45)
0.84(0.70-1.01)
1.17(1.00-1.36)
-6.3
+5.8
-8.6
+2.4
2.10(1.84-2.40)
1.98(1.70-2.29)
-0.8
1.78(1.50-2.11)
1.70(1.42-2.04)
-4.5
1.22(1.08-1.36)
1.25(1.10-1.43)
+2.0
• Men with prevalent coronary disease, stroke, or cancer at baseline are excluded.
t Hazard ratios are estimated for 1 SD (standard deviation) change in continuous variables, and relative to
never smokers and any alcohol consumptton, respectively, for smoking status and alcohol abstinence.
+. % change is estimated as ((corrected - uncorrected)/uncorrected) x 100.
§ 1 oz = 28.35 g.
Am J Epidemiol
Vol. 143, No. 5, 1996
467
468
Iribarren et al.
tive to never smokers) and alcohol abstinence were
important determinants of death.
DISCUSSION
The aim of this analysis was to reduce the effect of
measurement error in the association between total
cholesterol and coronary disease mortality and between total cholesterol and all-cause mortality in the
Honolulu Heart Program. The corrected relative risk
estimates can be interpreted as the true measure of
association given that only random (unbiased) but not
systematic (biased) within-person errors were present
in total cholesterol and related confounders (body
mass index, systolic blood pressure, alcohol consumption, dietary cholesterol, and total calorie intake).
The sources of random within-person error in the
assessment of total cholesterol level are well documented. They consist of within-person seasonal (28),
day-to-day (29), or diurnal variation (30), as well as
possible technical errors in the laboratory (e.g., omissions in the protocol, variability of reagents, or faulty
instruments). The principal source of systematic error
in total cholesterol is actual physiologic change due to
life-style modification or disease.
Within-person random error and consequent regression dilution are closely related to the phenomenon of
regression toward the mean, a problem first described
by Galton (31) after he observed the stature of parents
and their offspring. Galton concluded that the stature
of the offspring tended toward values closer to the
mean population height. Regression toward the mean
in total cholesterol level implies that extreme readings
at baseline are more likely than not to shift toward
central values at a subsequent reexamination. This
phenomenon can be illustrated in the Honolulu cohort.
Men with total cholesterol values in the lowest quintile
at baseline had a mean total cholesterol concentration
of 170 mg/dL in 1965-1968, but the same men had a
mean value of 186 mg/dL at examination 3. Similarly,
the mean total cholesterol concentration in men in the
highest quintile at baseline was 272 mg/dL, and had
regressed 6 years later to 249 mg/dL.
In corroboration of the first hypothesis of the study,
we noted an increase in the hazard ratio of fatal coronary disease associated with a difference of 38 mg/dL
in total cholesterol after correction for measurement
error (from 1.35 to 1.65, a 22 percent increase). A
systolic blood pressure higher by 21 mmHg was associated with a crude 1.6 hazard ratio. However, when
measurement errors were accounted for, the hazard
ratio for the same difference in systolic blood pressure
was estimated to be about 2.0 (26 percent change in
the hazard ratio). The increased importance of blood
pressure as a coronary disease risk factor after correction for measurement error has been reported by
MacMahon et al. (4).
Total calorie intake had a weak protective effect on
coronary death risk, a circumstance that was unchanged after correction for measurement error. On
the other hand, the corrected risk associated with an
increase of 300 mg/day of dietary cholesterol was 20
percent greater than the uncorrected risk (1.26 vs.
1.05). Because the blood level of total cholesterol is
likely to be in the causal pathway of the dietary
cholesterol-coronary disease relation, we also estimated the risk of coronary disease death associated
with this nutrient without adjusting for total cholesterol in the multivariate model. The corresponding
crude estimate was 1.07 (95 percent CI 0.92-1.24) and
the corrected estimate was 1.32 (95 percent CI 0.592.93).
Connor and Connor (32) demonstrated a significant
correlation between cholesterol intake and death rates
from arteriosclerotic and degenerative heart disease in
24 countries. In the Western Electric Study (33), the
Ireland - Boston Diet-Heart Study (34), and the
Zutphen Study (35), dietary cholesterol was an independent risk factor of coronary disease mortality. In
the Honolulu Heart Program, dietary cholesterol intake was significantly higher among incident cases of
definite coronary disease (nonfatal myocardial infarction, coronary disease death, or sudden death within
one hour of coronary disease-type chest pain) after 10
years of follow-up than among non-cases (36). Other
studies, however, have failed to find associations between dietary lipids and the risk of coronary disease
within defined populations (37). Interestingly, our corrected results support the evidence a role of dietary
cholesterol in the development of coronary disease, as
previously reported in ecologic and population-based
data.
A controversy exists about the U-shaped association
between total cholesterol and all-cause mortality, arising from a (causal) positive association between high
total cholesterol and atherosclerotic disease, and a
negative association (of uncertain nature) between low
total cholesterol and nonatherosclerotic conditions
(apparently in men but not in women) (38). In this
paper, we focused on the potential impact of measurement error in this U-shaped association between total
cholesterol and mortality. Regression dilution bias has
been cited as an unlikely mechanism behind the Ushaped association between total cholesterol and allcause mortality (39) because, if present, it may increase rather than reduce the U-shape of the
association. The current analysis is an empirical demAm J Epidemiol
Vol. 143, No. 5, 1996
Measurement Error Bias in Cholesterol-Mortality Relations
onstration of this hypothesis. However, this analysis
does not address the other fundamental issues underlying the U-shaped relation, namely confounding by
other risk factors, reverse causality by undetected or
prevalent disease, potential interaction mechanisms, or
causal implications.
A reanalysis of the Honolulu data (40) and a recent
comprehensive review of the area (41) suggest that the
excess mortality linked to low total cholesterol may be
attributable to a failure to adequately control for diseases and behaviors (i.e., heavy smoking) leading to
reduced total cholesterol level and eventually to death.
On the other hand, Jacobs (42) has discussed potential
etiologic implications of low total cholesterol in intracranial hemorrhage, pulmonary disease, and infections.
A few methodological shortcomings of the current
analysis should be pointed out. First, within-person
variability in serum cholesterol and the covariates
was assumed to be solely due to random fluctuation.
In reality, however, it is likely that systematic together with random fluctuations in serum cholesterol
and related risk factors may have occurred. For example, since the repeated measures used in this analysis were taken an average of 6 years apart, it is
likely that some true biologic change may have
taken place. If this is the case, the correction procedure is anticonservative and may actually have led
to overcorrection of the risk estimates. Second, all
the exposures need to conform to the normal or
Gaussian distribution. All of the variables used in
the analysis were approximately normal, with the
exception of alcohol consumption. As a check of robustness in this instance, the continuous alcohol intake variable was logarithmically transformed and
the models reestimated. The risk estimates and confidence intervals were very similar. Finally, in the
case of the dietary variables, it was necessary to assume that the errors from the two dietary measures
(24-hour dietary recall and the average of the 7-day
records) were uncorrelated (e.g., that they fluctuate
randomly with respect to each other). This assumption implies that participants who completed both
the 24-hour and the 7-day dietary records were unlikely to either overreport or underreport their dietary intake in both occasions. The random error in
dietary measures includes actual variation over time,
imprecise recall of foods consumed, and errors in
portion size, as well as random recording and data
entry errors (43).
In the current analysis, we chose to include only
dietary cholesterol and total calories because of the
high intercorrelation (i.e., multicollinearity) of macronutrients, which makes it difficult to separate out
Am J Epidemiol
Vol. 143, No. 5, 1996
469
independent effects of fat, protein, carbohydrate, or
dietary cholesterol in multivariate models (19, 36).
Recently, several studies have been published that
employ methods to correct for exposure measurement
error in chronic disease epidemiology: colon cancer
and diet (44); breast cancer and dietary fat, calories,
and alcohol (13); blood pressure, stroke, and coronary
disease (4); and total cholesterol and risk of coronary
disease (14, 15, 45). As recognized by a recent review
on this topic (3), a much wider application of these
methods, particularly in the area of nutritional epidemiology, is desirable.
However, this analytical method is not without some
liabilities. It enables the estimation of deattenuated
risk relations, but at the expense of increased variance.
Furthermore, as seen in the examples presented here,
this effect is sensitive to the size of the validation
cohort.
Nevertheless, the question of measurement error
may have important consequences for conducting
epidemiologic research. First, it underscores the need
for reproducibility and validation studies, therefore
establishing some potential new priorities when planning and implementing studies. Second, from an etiologic point of view, measurement error correction may
help clarify causal mechanisms of disease, or may
support existing ones. Finally, correcting for regression dilution bias in associations between risk factors
and disease may have public health implications, because corrected estimates could substantially alter
population attributable risks. Therefore, there is a
growing consensus that the design, implementation,
and analytical phases of future studies should consider
the possibility and consequences of exposure measurement errors.
In conclusion, the example presented here illustrates
the feasibility and the precautions that one should bear
in mind when implementing procedures for measurement error correction. Our data suggest that the influence of elevated serum total cholesterol may have a
more important influence on the risk of coronary heart
disease and all-cause mortality than has been previously estimated with the use of standard methods of
analysis. In addition, correction for measurement error
in total cholesterol and study covariates did not explain the excess mortality associated with low total
cholesterol level. On the contrary, the hazard of low
total cholesterol became larger after the correction.
More experience and careful application of methods
for correcting for measurement error will allow researchers to balance the deattenuation of associations
with the increased uncertainty introduced by the correction procedure.
470
Iribarren et al.
ACKNOWLEDGMENTS
Supported by research contract nos. NO1-HC-02901 and
NO1-HV-02901 from the National Heart, Lung and Blood
Institute.
The authors thank Peter Hannan for his helpful comments
on the manuscript.
18.
19.
20.
REFERENCES
1. Cochran WG. Errors of measurement in statistics. Technometrics 1968;10:637-66.
2. Michalek JE, Tripathi RC. The effects of errors in diagnosis
and measurement on the estimation of the probability of an
event. JASA 1980;75:713-21.
3. Thomas D, Stram D, Dwyer JH. Exposure measurement error:
influence on exposure-disease relationships and methods of
correction. Ann Rev Public Health 1993;14:69-93.
4. MacMahon S, Peto R, Cutler J, et al. Blood pressure, stroke
and coronary heart disease. I. Prolonged differences in blood
pressure: prospective observational studies corrected for the
regression dilution bias. Lancet 1990;335:765-74.
5. Roeback JR, Cook JR, Guess HA, et al. Time-dependent
variability in repeated measurements of cholesterol levels:
clinical implications for risk misclassification and intervention
monitoring. J Clin Epidemiol 1993;46:1159-71.
6. Thompson SG, Pocock SJ. The variability of serum cholesterol measurements: implications for screening and monitoring. J Clin Epidemiol 1990;43:783-9.
7. Kagan A, McGee DL, Yano K, et al. Serum cholesterol and
mortality in a Japanese-American population. Am J Epidemiol
1981;114:11-20.
8. Stemmermann GN, Chyou PH, Kagan A, et al. Serum cholesterol and mortality among Japanese-American men: the
Honolulu (Hawaii) Heart Program. Arch Intern Med 1991;
151:969-72.
9. Frank JW, Reed DM, Grove JS, et al. Will lowering population levels of serum cholesterol affect total mortality? Expectations from the Honolulu Heart Program. J Clin Epidemiol
1992;45:333-46.
10. Prentice RL. Covariate measurement errors and parameter
estimation in a failure time regression model. Biometrika
1982;69:331-42.
11. Rosner B, Willett WC, Spiegelman D. Correction of logistic
regression relative risk estimates and confidence intervals for
systematic within-person measurement error. Stat Med 1989;
8:1051-71.
12. Clayton D. Models for the longitudinal analysis of cohort and
case-control studies with inaccurately measured exposures. In:
Dwyer JH, Feinleib M, Hoffmeister H, eds. Statistical models
for longitudinal studies of health. New York: Oxford University Press, 1992:301-31.
13. Rosner B, Spiegelman D, Willett WC. Correction of logistic
regression relative risk estimates and confidence intervals for
measurement error the case of multiple covariates measured
with error. Am J Epidemiol 1990; 132:734-45.
14. Davis CE, Rifkind BM, Brenner H, et al. A single cholesterol
measurement underestimates the risk of coronary heart disease. An empirical example from the Lipid Research Clinics
Mortality Follow-up Study. JAMA 1990;264:3044-6.
15. Law MR, Wald NJ, Wu T, et al. Systematic underestimation
of association between serum cholesterol concentration and
ischemic heart disease in observational studies: data from the
BUPA study. BMJ 1994;308:363-6.
16. Worth RM, Kagan A. Ascertainment of men of Japanese
ancestry in Hawaii through World War II selective service
registration. J Chronic Dis 1970;23:389-97.
17. Belsky JL, Kagan A, Syme DL. Epidemiologic studies of
coronary heart disease and stroke in Japanese men living in
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
Japan, Hawaii and California: research plan. Technical report
no. 12-71. Hiroshima, Japan: Atomic Bomb Casualty Commission, 1971.
Tillotson JT, Kato H, Nichaman MZ, et al. Epidemiology of
coronary heart disease and stroke in Japanese men living in
Japan, Hawaii, and California. Methodology for comparison
of diet. Am J Clin Nutr 1973;26:177-84.
McGee D, Rhoads G, Hankin J, et al. Within-person variability of nutrient intake in a group of Hawaiian men of Japanese
ancestry. Am J Clin Nutr 1982;36:657-63.
Technicon Instruments Corporation. Technicon AutoAnalyzer methodology. Tarrytown, NY: Technicon Corporation, 1965.
National Center for Health Statistics. International classification of diseases, adapted for use in the United States. 8th
revision. Washington, DC: US Department of Health, Education, and Welfare, 1967. (PHS publication no. 1693)
Cox DR. Regression models and life tables (with discussion).
J R Stat Soc 1972;34:187-220.
SAS Institute Inc. SAS/STAT software version 6.09. The
PHREG procedure. Cary, NC: SAS Institute Inc, 1994.
Neter J, Wasserman W, Kutner MH. Applied linear statistical
models. 3rd ed. Boston, MA: Irvan, 1990:370-3.
Aiken LS, West SG. Multiple regression: testing and interpreting interactions. 3rd ed. London: Sage Publications, 1991:
67-78.
Shaper AG. Alcohol and mortality: a review of prospective
studies. Br J Addict 1990;85:837-47.
Fuller WA. Measurement error models. New York: John
Wiley & Sons, 1987, Chapter 1, Appendix lA:85-8.
Bleiler RE, Yearick ES, Schnur SS, et al. Seasonal variation of
cholesterol in serum of men and women. Am J Clin Nutr
1963;12:12-16.
Elveback LR, Weidman WH, Ellefson RD. Day-to-day variability and analytical error in determinations of lipids in children. Mayo Clinic Proc 1980;55:267-9.
Peterson JE, Wilcox AA, Haley MI, et al. Hourly variation in
total serum cholesterol. Circulation 1960;22:247-53.
Galton F. Regression towards mediocrity in hereditary stature.
J Anthropol Inst 1886;15:246-63.
Connor WE, Connor SL. The key role of nutritional factors in
the prevention of coronary heart disease. Prev Med 1972;1:
49-83.
Stamler J, Dyer AR, Shekelle RB, et al. Relationship of
baseline major risk factors to coronary and all-cause mortality,
and to longevity: findings from long-term follow-up of Chicago cohorts. Cardiology 1993;82:191-222.
Kushi LH, Lew RA, Stare FJ, et al. Diet and 20-year mortality
from coronary heart disease: the Ireland-Boston Diet-Heart
Study. N Engl J Med 1985;312:811-18.
Kromhout D, Bosschieter EB, De Lezenne Coulander C. The
inverse relation between fish consumption and 20-year mortality from coronary heart disease. N Engl J Med 1985;312:
1205-9.
McGee DL, Reed DM, Yano K, et al. Ten-year incidence of
coronary heart disease in the Honolulu Heart Program: relationship to nutrient intake. Am J Epidemiol 1984; 119:667-76.
Gordon T, Kagan A, Garcia-Palmieri M, et al. Diet and its
relation to coronary heart disease in three populations. Circulation 1981;63:500-15.
Jacobs DR Jr, Blackburn H, Higgins M, et al. Report of the
Conference on Low Blood Cholesterol: mortality associations.
Circulation 1992;86:lt)46-60.
Hulley SB, Walsh JMB, Newman TB. Health policy on blood
cholesterol. Time to change directions. (Editorial). Circulation
1992;86:1026-9.
Iribarren C, Reed DM, Burchfiel CM, et al. Serum total
cholesterol and mortality: confounding factors and risk modification in Japanese-American men. JAMA 1995;273:
1926-32.
Meilahn EN, Ferrel RE. "Naturally occurring" low blood
cholesterol and excess mortality. Coron Artery Dis 1993;4:
Am J Epidemiol Vol. 143, No. 5, 1996
Measurement Error Bias in Cholesterol-Mortality Relations
843-53.
42. Jacobs DR Jr. Why is low blood cholesterol associated with
risk of nonatherosclerotic disease death? Annu Rev Publ
Health 1993;14:95-114.
43. Willett W. Nutritional epidemiology. New York: Oxford University Press, 1990:272-91.
Am J Epidemiol
Vol. 143, No. 5, 1996
471
44. Armstrong BG, Whittemore AS, Howe GR. Analysis of casecontrol data with covariate measurement error application to
diet and colon cancer. Stat Med 1989;8:1151-63.
45. Dwyer JH, Li L, Curtin R, et al. Correction for non-sampling
measurement error in risk factors for CHD in women from
Framingham. (Abstract). Circulation 1992;85:879.