# Why Evidence for the Fetal Origins of Adult Disease Might Be a Statistical Artifact: The “Reversal Paradox” for the Relation between Birth Weight and Blood Pressure in Later Life

**Abstract**

Some researchers have recently questioned the validity of associations between birth weight and health in later life. They argue that these associations might be due in part to inappropriate statistical adjustment for variables on the causal pathway (such as current body size), which creates an artifactual statistical effect known as the "reversal paradox." Computer simulations were conducted for three hypothetical relations between birth weight and adult blood pressure. The authors examined the effect of statistically adjusting for different correlations between current weight and birth weight and between current weight and adult blood pressure to assess their impact on associations between birth weight and blood pressure. When there was no genuine relation between birth weight and blood pressure, adjustment for current weight created an inverse association whose size depended on the magnitude of the positive correlations between current weight and birth weight and between current weight and blood pressure. When there was a genuine inverse relation between birth weight and blood pressure, the association was exaggerated following adjustment for current weight, whereas a positive relation between birth weight and blood pressure could be reversed after adjusting for current weight. Thus, researchers must consider the reversal paradox when adjusting for variables that lie within causal pathways.

27 Am J Epidemiol 2005;161:27–32

American Journal of Epidemiology

Copyright © 2005 by the Johns Hopkins Bloomberg School of Public Health

All rights reserved

Vol. 161, No. 1

Printed in U.S.A.

DOI: 10.1093/aje/kwi002

ORIGINAL CONTRIBUTIONS

Why Evidence for the Fetal Origins of Adult Disease Might Be a Statistical Artifact:

The “Reversal Paradox” for the Relation between Birth Weight and Blood Pressure in

Later Life

Yu-Kang Tu

1,2

, Robert West

1

, George T. H. Ellison

3

, and Mark S. Gilthorpe

1

1

Biostatistics Unit, Centre for Epidemiology and Biostatistics, University of Leeds, Leeds, United Kingdom.

2

Leeds Dental Institute, University of Leeds, Leeds, United Kingdom.

3

St. George’s Hospital Medical School, London, United Kingdom.

Received for publication March 11, 2004; accepted for publication June 3, 2004.

Some researchers have recently questioned the validity of associations between birth weight and health in later

life. They argue that these associations might be due in part to inappropriate statistical adjustment for variables

on the causal pathway (such as current body size), which creates an artifactual statistical effect known as the

“reversal paradox.” Computer simulations were conducted for three hypothetical relations between birth weight

and adult blood pressure. The authors examined the effect of statistically adjusting for different correlations

between current weight and birth weight and between current weight and adult blood pressure to assess their

impact on associations between birth weight and blood pressure. When there was no genuine relation between

birth weight and blood pressure, adjustment for current weight created an inverse association whose size

depended on the magnitude of the positive correlations between current weight and birth weight and between

current weight and blood pressure. When there was a genuine inverse relation between birth weight and blood

pressure, the association was exaggerated following adjustment for current weight, whereas a positive relation

between birth weight and blood pressure could be reversed after adjusting for current weight. Thus, researchers

must consider the reversal paradox when adjusting for variables that lie within causal pathways.

birth weight; blood pressure; computer simulation; confounding factors (epidemiology); statistics

Inverse associations observed between low birth weight

and markers of chronic disease in later life have generated

what is termed the “fetal origins of adult disease hypothesis”

(1, 2). The idea is that an unfavorable environment, or insults

during fetal life, might induce lifetime effects on the subse-

quent development of body systems and hence give rise to

major disease processes such as hypertension (2), diabetes

(3), arteriosclerosis (4), asthma (5), and obesity (6). Over the

last decade, many studies have been undertaken in many

parts of the world to examine these proposed relations (7).

Although some researchers have questioned the biologic

basis of the hypothesis as well as its clinical importance, the

concept that low birth weight is an independent risk factor

for a range of chronic diseases in later life is now widely

recognized as scientifically plausible and linked to poor fetal

nutrition (8). One consequence of this seemingly plausible

mechanism is that the fetal origins hypothesis is increasingly

viewed as an important issue for public health and preven-

tive medicine (9).

Nonetheless, two recent articles outlined substantive chal-

lenges to the fetal origins hypothesis (7, 8). One article raised

concerns about the statistical methodology used and the

improper interpretation of epidemiologic analyses invoked

in support of the hypothesis (8). The second article suggested

that the inverse association between birth weight and adult

diseases might “chiefly reflect the impact of random error”

in the measurement of birth weights, as well as “selective

emphasis on particular results” (by which they meant publi-

cation bias in favor of analyses describing inverse relations

between birth weight and adult blood pressure), and “inap-

propriate adjustment for current weight and for [other]

confounding factors” (7, p. 659). A recent meta-analysis also

Correspondence to Dr. Yu-Kang Tu, Biostatistics Unit, Centre for Epidemiology and Biostatistics, University of Leeds, 30/32 Hyde Terrace,

Leeds, LS2 9LN, United Kingdom (e-mail: y.k.tu@leeds.ac.uk).

by guest on November 6, 2015http://aje.oxfordjournals.org/Downloaded from

28

Tu et al.

Am J Epidemiol 2005;161:27–32

indicated that the relation between blood pressure and birth

weight might suffer publication bias because small studies

were more likely to report stronger inverse associations (10).

Indeed, although a number of retrospective studies have

found a direct relation between birth weight and adult health

outcomes, others have found that a significant relation

emerged only after adjusting for subsequent body size

(notably current adult weight or body mass index) in the

statistical analyses. It is the latter that forms the focus of this

article.

The inappropriate use of statistical adjustment(s) for so-

called confounders is an important source of potential bias

among observational studies of the fetal origins of adult

disease hypothesis. We sought to demonstrate how adjust-

ment for current body mass (or any similar measure of

current body size) is inappropriate because it is not a true

“confounder” but part of the causal pathway between birth

weight and adult blood pressure. The resulting phenomenon

has been given the generic name the “reversal paradox” (or

the “amalgamation paradox”) (11), although it is perhaps not

widely known as either. Whatever the name, the reversal

paradox makes it very challenging to correctly interpret the

findings of observational studies of the causal links between

fetal growth and adult disease where covariates are inappro-

priately treated as confounders.

Because the inverse association between birth weight and

blood pressure is considered the most statistically consistent

of the associations between birth weight and health in later

life (7), our article adopts this example for illustration.

Nevertheless, what follows is essentially applicable to all

health outcomes in later life and to any other descriptive

epidemiologic analyses in which similar statistical adjust-

ments are undertaken inappropriately.

MATERIALS AND METHODS

To avoid complicating the issues surrounding adjustment

for multiple confounders, such as age and gender, we

decided to consider only a single hypothetical sample

comprising adult males of equal age. Synthetic data for these

men were generated for three variables—birth weight,

current adult weight, and adult systolic blood pressure—and

for three scenarios in which there is 1) no direct relation

between birth weight and blood pressure (i.e., the Pearson

correlation between birth weight and blood pressure is 0); 2)

a modest inverse relation between birth weight and blood

pressure (i.e., the Pearson correlation between birth weight

and blood pressure is –0.05); and 3) a modest positive rela-

tion between birth weight and blood pressure (i.e., the

Pearson correlation between birth weight and blood pressure

is 0.05). Mean values for the three variables and their stan-

dard deviations were derived from the literature (12) and

from the results of surveys conducted by the United

Kingdom Department of Health (http://www.doh.gov.uk):

birth weight = 3.38 kg (standard deviation, 0.57 kg), current

weight = 82.60 kg (standard deviation, 14.75 kg), and

systolic blood pressure = 130.0 mmHg (standard deviation,

11.2 mmHg).

Since the effects of the reversal paradox depend on the

pairwise correlations of birth weight, current weight, and

blood pressure, each scenario was simulated for a range of

different assumptions. To illustrate the impact of the reversal

paradox on changes in the relation between birth weight and

blood pressure after statistically adjusting for current weight,

we assumed three different values for the birth weight–

current weight correlation (0.15, 0.25, and 0.35) and four

different values for the current weight–blood pressure corre-

lation (0.15, 0.25, 0.35, and 0.45). The range of correlation

values adopted was motivated by typical values encountered

in the literature. The theoretical basis of these simulations is

outlined in the Appendix.

With adult blood pressure as the outcome variable, we

estimated a median value for the partial regression coeffi-

cient with birth weight after adjusting for current adult

weight, using simulations based on a sample of 500

persons—the mid-range sample size of previous empirical

studies (7)—and with 1,000 iterations for each scenario. All

simulations and statistical evaluations were performed by

using the statistical package R, version 1.7.1 (13). For each

scenario, the function “mvrnorm” in the MASS package in R

was used to generate multivariate normal data using the

mean values, standard deviations, and given correlation

matrix for the three variables birth weight, current weight,

and blood pressure (14).

RESULTS

Scenario 1: the correlation between blood pressure and

birth weight is 0

When the Pearson correlation between blood pressure and

birth weight was 0, the simple (bivariate) regression coeffi-

cient of birth weight, for blood pressure regressed on birth

weight, was unsurprisingly close to 0. In contrast, when

current weight was included in the model, the regression

coefficient for birth weight became negative, and the magni-

tude of this coefficient increased as the birth weight–current

weight and blood pressure–current weight correlations

increased (table 1). When both of the latter correlations were

set to 0.15, the estimated effect of a 1-kg increase in birth

weight was a 0.42-mmHg reduction in adult blood pressure.

With the birth weight–current weight correlation increased

to 0.35 and the blood pressure–current weight correlation

increased to 0.45, the estimated effect of a 1-kg increase in

birth weight was a 3.51-mmHg reduction in adult blood

pressure.

Scenario 2: the correlation between blood pressure and

birth weight is –0.05

When a modest inverse relation between birth weight and

blood pressure was adopted, the theoretical value of the

simple (bivariate) regression coefficient of birth weight, for

blood pressure regressed on birth weight, was –0.98 mmHg/

kg. This value can be derived by multiplying the correlation

coefficient by the ratio of standard deviation for blood

pressure to that of the standard deviation for birth weight

(–0.05 × [11.2 ÷ 0.57]), and the results of the simulations

were very close to this (ranging from –0.95 to –1.01; table 2).

When the birth weight–current weight and blood pressure–

by guest on November 6, 2015http://aje.oxfordjournals.org/Downloaded from

Reversal Paradox for Fetal Origins Hypothesis 29

Am J Epidemiol 2005;161:27–32

current weight correlations were both 0.15, the estimated

effect of a 1-kg increase in birth weight was a 1.48-mmHg

reduction in adult blood pressure, similar to that estimated by

a previous meta-analysis (7). With the birth weight–current

weight correlation increased to 0.35 and the blood pressure–

current weight correlation increased to 0.45, increasing birth

weight by 1 kg yielded a 4.47-mmHg reduction in adult

blood pressure.

Scenario 3: the correlation between blood pressure and

birth weight is 0.05

When a modest positive relation between birth weight and

blood pressure was adopted, the theoretical value of the coef-

ficient of birth weight, for blood pressure regressed on birth

weight, was 0.98 mmHg/kg (0.05 × [11.2 ÷ 0.57]), as antici-

pated from the symmetry of scenario 3 with scenario 2; refer

to table 3. When the birth weight–current weight and blood

pressure–current weight correlations were both 0.15, a 1-kg

increase in birth weight was associated with a 0.55-mmHg

increase in adult blood pressure. When the birth weight–

current weight and blood pressure–current weight correla-

tions were both 0.25, the regression coefficient was reversed,

and increasing birth weight by 1 kg became associated with

a 0.26-mmHg reduction in adult blood pressure. With the

birth weight–current weight and blood pressure–current

weight correlations increased to 0.35 and 0.45, respectively,

the estimated effect of a 1-kg increase in birth weight was a

2.41-mmHg reduction in adult blood pressure.

DISCUSSION

For categorical variables within the field of probability

and statistical science, the reversal paradox is best known as

“Yule’s paradox” or “Simpson’s paradox.” George U. Yule

noticed this phenomenon as early as 1903 (15), when he

referred to a paper published by Karl Pearson et al. dating

from 1899 (16). The issue was later mentioned in a 1951

paper by Edward H. Simpson on the way in which the rela-

tion between two variables changed after a third variable was

factored into a two-by-two contingency table (17). When

such data are analyzed by regression methods, the reversal

paradox is more often referred to as “Lord’s paradox,”

particularly within the behavioral sciences (18), ever since

Frederic M. Lord published his 1967 paper on this phenom-

enon with respect to the use of analysis of covariance (19).

Within any generalized linear modeling framework, this

phenomenon is more generally known in the statistical liter-

ature as the “suppression effect,” with the third variable

termed a “suppressor” (20, 21). Thus, in whatever form and

under whatever name, the reversal paradox has been recog-

nized ever since the statistical methods of correlation and

regression became established. Indeed, the paradox was

discussed in 1910 by Karl Pearson and Arthur C. Pigou,

Professor of Political Economics at Cambridge University in

the United Kingdom, when they debated the role of parental

alcoholism and its impact on the performance of children

(11). However labeled, the paradox has been extensively

explored in the statistical literature, especially in the behav-

TABLE 1. Association between birth weight and adult blood pressure in simple regression models and multiple regression models

after adjustment for adult body weight in scenario 1*

* The bivariate correlation between birth weight and blood pressure is 0.

† CI, confidence interval.

‡ The expected regression coefficient should be 0 (0 × [11.2 ÷ 0.57]).

Simple regression

coefficient (mmHg/kg)

Birth weight–

current weight

correlation

Multiple regression coefficient (mmHg/kg): blood pressure–current weight correlation

0.15 0.25 0.35 0.45

Median 95% CI† Median 95% CI Median 95% CI Median 95% CI Median 95% CI

0.02‡ –1.69, 1.77 0.15 –0.42 –2.13, 1.31 –0.75 –2.40, 0.97 –1.05 –2.66, 0.60 –1.35 –2.87, 0.22

0.07‡ –1.79, 1.74 0.25 –0.77 –2.49, 1.04 –1.31 –2.99, 0.47 –1.79 –3.43, –0.19 –2.36 –3.91, –0.73

0.01‡ –1.76, 1.82 0.35 –1.17 –2.94, 0.71 –1.95 –3.69, –0.11 –2.74 –4.44, –0.96 –3.51 –5.14, –1.86

TABLE 2. Association between birth weight and adult blood pressure in simple regression models and multiple regression models

after adjustment for adult body weight in scenario 2*

* The bivariate correlation between birth weight and blood pressure is –0.05.

† CI, confidence interval.

‡ The expected regression coefficient should be –0.98 (–0.05 × [11.2 ÷ 0.57]).

Simple regression

coefficient (mmHg/kg)

Birth weight–

current weight

correlation

Multiple regression coefficient (mmHg/kg): blood pressure–current weight correlation

0.15 0.25 0.35 0.45

Median 95% CI† Median 95% CI Median 95% CI Median 95% CI Median 95% CI

–1.01‡ –2.75, 0.70 0.15 –1.48 –3.20, 0.25 –1.79 –3.48, –0.10 –2.08 –3.70, –0.45 –2.39 –3.93, –0.83

–0.95‡ –2.87, 0.69 0.25 –1.86 –3.62, –0.10 –2.38 –4.11, –0.67 –2.87 –4.67, –1.29 –3.41 –5.00, –1.84

–0.96‡ –2.58, 0.66 0.35 –2.32 –4.13, –0.51 –3.10 –4.86, –1.36 –3.87 –5.59, –2.17 –4.47 –6.26, –3.01

by guest on November 6, 2015http://aje.oxfordjournals.org/Downloaded from

30

Tu et al.

Am J Epidemiol 2005;161:27–32

ioral sciences (22, 23), yet comparatively few of these anal-

yses acknowledge that they are in fact different

manifestations of the same phenomenon; that is, they are all

just one paradox.

Moreover, while the original definition and naming of the

reversal paradox drew on the notion that the direction of any

relation between two variables is reversed after a third vari-

able is introduced, it may nevertheless be generalized to

scenarios in which the relation between two such variables is

enhanced, not reversed nor reduced, after a third variable is

introduced. This difference is not widely appreciated, which

is perhaps why the impact of the reversal paradox is not

always recognized in empirical, rather than theoretical,

statistical analyses. However, the potential problem of statis-

tical adjustment in the fetal origins hypothesis has been

known for some time. Paneth et al. (24, 25) specifically

addressed the issue of “overcontrolling” for current body

mass index when analyzing the relation between birth weight

and disease risk in later life. To illustrate the reversal

paradox and explore this point further, we used simulations

of hypothetical data to mimic three scenarios pertaining to

the fetal origins hypothesis for adult blood pressure. For

those interested in the statistical theory underpinning these

ideas, refer to the Appendix.

The reversal paradox invokes bias due to the inappropriate

“controlling” of alleged confounders that are not in fact “true

confounders” (26). The concept of what constitutes a

confounder has been revised in recent years, with greater

emphasis given to the definition of “causality” in the associ-

ations among outcomes, exposures, and confounders.

Detailed expositions on this issue have emerged only

recently (27–29), and these stricter, revised definitions of

what constitutes a confounder may not have been dissemi-

nated, or universally accepted, throughout the discipline of

epidemiology. Consequently, the reason why the reversal

paradox is a problem in some instances and not others may

be more of a philosophical issue than a statistical one.

Indeed, the principal issue of statistical adjustment pertinent

to the fetal origins hypothesis is the one surrounding the

causal pathway and the position within it of current adult

body weight as an alleged confounder. If one defines a

causal pathway as the chain of events or factors leading in

sequence to an outcome, it only makes sense to examine an

outcome in relation to any one point along the causal

pathway (27, 30).

We differentiated between two different, but complemen-

tary causal pathways: 1) low birth weight affecting blood

pressure directly (e.g., poor nutrition in utero having an irre-

versible impact on the subsequent development of cardio-

vascular systems); and 2) low birth weight affecting blood

pressure via birth weight’s impact on current weight (e.g.,

through a genetic link between size at birth and current adult

body size), which in turn is causally related to high blood

pressure (i.e., birth weight → current weight → blood pres-

sure). In the latter model, it is sensible to examine either the

relation between birth weight and adult blood pressure or the

relation between current weight and adult blood pressure, in

isolation. It is not sensible to examine the relation between

birth weight and adult blood pressure while controlling for

current weight, because adult weight lies on the causal

pathway between the outcome (blood pressure) and the

exposure (birth weight). To statistically “adjust” for current

weight while exploring the impact of birth weight on adult

blood pressure invokes the reversal paradox.

In a slightly different formulation of the fetal origins

hypothesis, some researchers have argued that persons of a

relatively low birth weight and a relatively high adult body

size (be it weight, height, or body mass index) ought to be

considered a “high-risk” group for cardiovascular disease in

later life (31). Indeed, this is another possible interpretation

of the statistical models commonly used in analyses

exploring the fetal origins hypothesis. However, as

discussed previously, it is not appropriate to include current

weight as a confounder in these analyses if the relation

between birth weight and adult blood pressure is the primary

interest because weight gain, like current adult weight, is in

the causal pathway from birth weight to adult blood pressure.

Nonetheless, the same statistical model is useful and appro-

priate if the relation between adult blood pressure and

current weight is the primary interest; the precision of esti-

mating the association between adult blood pressure and

current weight can be enhanced by including birth weight in

the analyses. This asymmetric utility of adjusting for

“confounding” occurs because the adult body weight of

some adults is likely to be greater because they were born

heavier. For these adults, their greater body weight may not

be associated with the factors that

give rise to higher adult

TABLE 3. Association between birth weight and adult blood pressure in simple regression models and multiple regression models

after adjustment for adult body weight in scenario 3*

* The bivariate correlation between birth weight and blood pressure is 0.05.

† CI, confidence interval.

‡ The expected regression coefficient should be 0.98 (0.05 × [11.2 ÷ 0.57]).

Simple regression coefficient

(mmHg/kg)

Birth weight–

current weight

correlation

Multiple regression coefficient (mmHg/kg): blood pressure–current weight correlation

0.15 0.25 0.35 0.45

Median 95% CI† Median 95% CI Median 95% CI Median 95% CI Median 95% CI

0.97‡ –0.76, 2.63 0.15

0.55

–1.17, 2.18 0.24 –1.43, 1.84 –0.05 –1.68, 1.49 –0.36 –1.93, 1.13

1.00‡ –0.89, 2.77 0.25

0.26

–1.50, 1.94 –0.26 –2.02, 1.38 –0.74 –2.51, –0.93 –1.32 –2.95, 0.22

0.95‡ –0.72, 2.60 0.35

–0.06

–1.85, 1.69 –0.85 –2.65, 0.90 –1.64 –3.40, 0.04 –2.41 –4.08, –0.79

by guest on November 6, 2015http://aje.oxfordjournals.org/Downloaded from

Reversal Paradox for Fetal Origins Hypothesis 31

Am J Epidemiol 2005;161:27–32

blood pressure but with their greater size at birth (which

might, for example, be genetically determined). Under these

circumstances, the association between adult blood pressure

and current weight will be attenuated, and adjusting for birth

weight deals with the way in which the relation between

adult blood pressure and current weight would otherwise be

diluted. Nevertheless, it should be stressed that, in this

analytic model, the relation between adult blood pressure

and birth weight does not have any empirical utility.

In the epidemiologic literature, body size measurements

(be they body weight, body height, or body mass index) are

frequently considered confounders for health-related

outcomes, presumably because there are well-known allo-

metric relations between body size and function (32).

However, there appears to be no consistent practice in the

literature as to when and how such variables should (or

should not) be “controlled for,” and most studies do not offer

any justification for their choice of confounders. For

instance, a recent study of the fetal origins hypothesis that

adjusted for current body weight and body mass index simul-

taneously found a significant negative relation between birth

weight and adult systolic blood pressure, even though there

was no significant (simple, bivariate) correlation between

them prior to adjustment (33). Furthermore, because body

weight is the numerator of body mass index, including both

variables in the analyses simultaneously means that they will

have undergone mathematical coupling (34, 35). A recently

published meta-analysis, along with other studies, shows

that removing the adjustment for current weight (or a compa-

rable measure of current body size) reduces the association

between birth weight and adult blood pressure (7); in some

instances, the association is no longer statistically significant

(36). Our scenario 2 might therefore be closest to reality.

Note that the estimated effect size in this simulated study,

or in any empirical study, is affected by the sample ratio of

the blood-pressure standard deviation to that of the birth-

weight standard deviation. If this ratio is large in any partic-

ular study, for instance, when the adult age range is wide and

thereby yields a wider range of adult blood pressures, the

effect size (i.e., the extent of bias) caused by the reversal

paradox will be exaggerated. On the other hand, if the

sample ratio of blood-pressure standard deviation to birth-

weight standard deviation is small, as, for instance, among

studies of children or young adults in which blood-pressure

variation tends to be smaller than among older adults, the

effect size caused by the reversal paradox will be dimin-

ished. Nevertheless, testing the significance of an associa-

tion is affected by sample size, and it is well known that even

a small effect size will be statistically significant if the

sample size is large enough. Most studies examining the fetal

origins of adult blood pressure have sufficiently large

samples to yield statistical significance for relatively small

effect sizes. Thus, the exaggerating effect of the reversal

paradox tends to give the misleading impression that the

relation between blood pressure and birth weight, after

adjustment for current weight, is not only statistically signif-

icant (because of the power available to detect the biased

difference from 0) but also biologically and clinically signif-

icant (as a result of the biased effect size caused or enhanced

by the reversal paradox).

Frequently, statistical methodology in studies of the fetal

origins hypothesis is at risk of the reversal paradox, thereby

bringing into question the validity and reliability of some of

the purported evidence. It is thus difficult, if not impossible,

to compare results across studies where so many varied

attempts have been made to control for confounders, without

consistent reasoning concerning the choice of these

confounders. This difficulty does not invalidate the fetal

origins hy

pothesis per se; rather, it implies that any direct

interpretation of inverse relations between birth weight and

any adult condition, while adjusting for current adult body

measurements, cannot be taken to mean that birth weight has

a direct impact on the adult outcome. For our hypothetical

example, a more appropriate interpretation is that, if all

babies grew to the same size in adulthood, lower-birth-

weight babies would, on average, have higher blood pressure

in adulthood. Yet, this conclusion is counterfactual since

low-birth-weight babies will, on average, be smaller than

heavy-birth-weight babies in adulthood; there is a positive

correlation between birth weight and adult weight, as studies

supporting the fetal origins hypothesis have shown.

As an understated and poorly recognized issue, the

reversal paradox, in whatever form it takes, has the potential

to severely affect data analyses undertaken in empirical

research, which increasingly rely on the methods of general-

ized linear modeling of observational (i.e., nonrandomized)

data. Our simulations highlight this issue with respect to the

fetal origins of adult disease hypothesis, where the paradox

is perhaps instrumental in generating a great deal of the

evidence cited within the hypothesis’ burgeoning orthodoxy.

However, the aim of this article was not to refute the fetal

origins hypothesis but to remind epidemiologists that, to

arrive at the correct interpretation of evidence supporting or

refuting this hypothesis, one must fully understand the statis-

tical methods used and the implications of making statistical

adjustment for “confounders.”

REFERENCES

1. Barker DJ. The fetal origins of hypertension. J Hypertens Suppl

1996;14:S117–S120.

2. Huxley RR, Shiell AW, Law CM. The role of size at birth and

postnatal catch-up growth in determining systolic blood pres-

sure: a systematic review of the literature. J Hypertens 2000;18:

815–31.

3. Barker DJ, Eriksson JG, Forsen T, et al. Fetal origins of adult

disease: strength of effects and biological basis. Int J Epidemiol

2002;31:1235–9.

4. Hahn P. Effect of litter size on plasma cholesterol and insulin

and some liver and adipose tissue enzymes in adult rodents. J

Nutr 1984;114:1231–4.

5. Yuan W, Basso O, Sorensen HT, et al. Fetal growth and hospi-

talization with asthma during early childhood: a follow-up

study in Denmark. Int J Epidemiol 2002;31:1240–5.

6. Leon DA, Koupilova I, Lithell HO, et al. Failure to realise

growth potential in utero and adult obesity in relation to blood

pressure in 50 year old Swedish men. BMJ 1996;312:401–6.

7. Huxley RR, Neil A, Collins R. Unravelling the fetal origins

hypothesis: is there really an inverse association between birth-

weight and subsequent blood pressure? Lancet 2002;360:

by guest on November 6, 2015http://aje.oxfordjournals.org/Downloaded from

32

Tu et al.

Am J Epidemiol 2005;161:27–32

659–65.

8. Lucas A, Fewtrell MS, Cole TJ. Fetal origins of adult disease—

the hypothesis revisited. BMJ 1999;319:245–9.

9. Law CM. Significance of birth weight for the future. Arch Dis

Child Fetal Neonatal Ed 2002;86:F7–F8.

10. Schluchter MD. Publication bias and heterogeneity in the rela-

tionship between systolic blood pressure, birth weight, and

catch-up growth—a meta analysis. J Hypertens 2003;21:273–9.

11. Stigler SM. Statistics on the table. Cambridge, MA: Harvard

University Press, 1999.

12. Hennessy E, Alberman E. Intergenerational influences affect-

ing birth outcome. II. Preterm delivery and gestational age in

the children of the 1958 British birth cohort. Paediatr Perinat

Epidemiol 1998;12(suppl 1):61–75.

13. R Development Core Team. R: a language and environment for

statistical computing, version 1.7.1. Vienna, Austria: R Foun-

dation for Statistical Computing, 2003.

14. Ripley BD, Venables WN. Modern applied statistics with S. 4th

ed. New York, NY: Springer Verlag, 2002.

15. Yule GU. Notes on the theory of association of attributes in sta-

tistics. Biometrika 1903;2:121–34.

16. Pearson K, Lee A, Bramley-Moore L. Mathematical contribu-

tions to the theory of evolution: VI—genetic (reproductive)

selection: inheritance of fertility in man, and of fecundity in

thoroughbred racehorses. Philos Trans R Soc London A 1899;

192:257–330.

17. Simpson EH. The interpretation of interaction in contingency

tables. J R Stat Soc (B) 1951;13:238–41.

18. Wainer H. Adjusting for differential base rates: Lord’s paradox

again. Psychol Bull 1991;109:147–51.

19. Lord FM. A paradox in the interpretation of group compari-

sons. Psychol Bull 1967;68:304–5.

20. Horst P. The role of prediction variables which are independent

of the criterion. In: Horst P, ed. The prediction of personal

adjustment. New York, NY: Social Science Research Council,

1941:431–6.

21. Lynn HS. Suppression and confounding in action. Am Stat

2003;57:58–61.

22. Hand D. Deconstructuring statistical questions. J R Stat Soc (A)

1994;157:317–56.

23. Lindley DV. Linear hypothesis: fallacies and interpretive prob-

lems (Simpson’s paradox). In: International encyclopaedia of

the social and behavioural sciences. Oxford, United Kingdom:

Elsevier Sciences, 2003:8881–4.

24. Paneth N, Susser M. Early origin of coronary heart disease (the

“Barker hypothesis”). BMJ 1995;310:411–12.

25. Paneth N, Ahmed F, Stein AD. Early nutritional origins of

hypertension: a hypothesis still lacking support. J Hypertens

1996;14:S121–S129.

26. Kirkwood BR, Sterne JA. Medical statistics. 2nd ed. London,

United Kingdom: Blackwell, 2003.

27. Jewell NP. Statistics for epidemiology. London, United King-

dom: Chapman & Hall, 2004.

28. Vandenbroucke JP. The history of confounding. Soz Praven-

tivmed 2002;47:216–24.

29. Hernan MA, Hernandez-Diaz S, Werler MM, et al. Causal

knowledge as a prerequisite for confounding evaluation: an

application to birth defects epidemiology. Am J Epidemiol

2002;155:176–84.

30. McNamee R. Confounding and confounders. Occup Environ

Med 2003;60:227–34.

31. Power C, Li L, Manor O, et al. Combination of low birth weight

and high adult body mass index: at what age is it established

and what are its determinants? J Epidemiol Community Health

2003;57:969–73.

32. Schmidt-Nielson K. Scaling: why is animal size so important?

New York, NY: Cambridge University Press, 1984.

33. Stocks NP, Davey Smith G. Blood pressure and birthweight in

the first year university student aged 18–25. Public Health

1999;113:273–7.

34. Tu YK, Gilthorpe MS, Griffiths GS. Is reduction of pocket

probing depth correlated with the baseline value or is it ‘mathe-

matical coupling’? J Dent Res 2002;81:722–6.

35. Tu YK, Maddick IH, Griffiths GS, et al. Mathematical coupling

can undermine the statistical assessment of clinical research:

illustration from the treatment of guided tissue regeneration. J

Dent 2004;32:133–42.

36. Gunnarsdottir I, Birgisdottir BE, Benediktsson R, et al. Rela-

tionship between size at birth and hypertension in a genetically

homogeneous population of high birth weight. J Hypertens

2002;20:623–8.

APPENDIX

Denoting adult blood pressure by BP, birth weight by BW,

and current weight by CW, and assuming that the three vari-

ables follow a trivariate normal distribution, we may write

BW = a

1

+ b

1

CW + e

1

and BP = a

2

+ b

2

CW + e

2

. The uncon-

ditional covariance between BW and BP is thus

b

1

b

2

var(CW) + cov(e

1

, e

2

). If both BW and BP are positively

correlated with CW, then b

1

and b

2

must both be positive,

and hence so is their product. Thus, the only way to obtain a

zero covariance between BW and BP—that is, a zero

bivariate correlation between them, as was imposed in

scenario 1—is for cov(e

1

, e

2

) to be negative. Now, if we look

at cov(BW, BP) while conditioning on CW (as in a regres-

sion model that includes both CW and BW as predictors), the

conditional covariance is equal to cov(e

1

, e

2

), which we have

just indicated must be negative. The sign of the coefficient of

BW as determined by cov(BW, BP) must therefore be nega-

tive in the model that includes CW, provided that both BW

and BP are positively correlated with CW and that BW and

BP are also uncorrelated.

If we denote growth weight by GW, as per Lucas et al. (8),

the following models could be rearranged:

BP = β

0

+ β

1

BW + β

2

CW, (1)

and

BP = β

0

+ β

1

BW + β

2

(BW + GW)

= β

0

+ (β

1

+ β

2

)BW + β

2

GW. (2)

In model 2, the regression coefficient for birth weight is

attenuated because β

2

is always positive. In other words,

whenever weight gain after birth (i.e., growth weight) is

adjusted for, the inverse association between birth weight

and blood pressure will be less than that obtained while

“controlling” for current weight. However, the two

approaches—controlling for current weight or growth

weight—are no different from a statistical viewpoint since

birth weight is contained in some aspect within current adult

weight. The difficult question then arises: which coefficient

is the more accurate estimate of the contribution of birth

weight to adult blood pressure?

by guest on November 6, 2015http://aje.oxfordjournals.org/Downloaded from

- CitationsCitations182
- ReferencesReferences40

- "Results of the BMI stratification analyses support the argument that BMI needs to be included in the model for adjustment in the analyses related to smoking-central obesity association, especially for normal-weight adults. The phenomenon that the direction of any relation between two variables is reversed after a third variable is introduced is statistically known as " reversal paradox " [36,39]. The reversal paradox makes it very challenging to correctly interpret the findings seen in observational studies. "

[Show abstract] [Hide abstract]**ABSTRACT:**Objectives: Lifestyle factors are well-known important modifiable risk factors for obesity; the association between tobacco smoking and central obesity, however, is largely unknown in the Chinese population. This study examined the relationship between smoking and central obesity in 0.5 million Chinese adults, a population with a low prevalence of general obesity, but a high prevalence of central obesity. Subjects: A total of 487,527 adults (200,564 males and 286,963 females), aged 30-79 years, were enrolled in the baseline survey of the China Kadoorie Biobank (CKB) Study conducted during 2004-2008. Waist circumference (WC) and WC/height ratio (WHtR) were used as measures of central obesity. Results: The prevalence of regular smokers was significantly higher among males (60.6%) than among females (2.2%). The prevalence of central obesity increased with age and BMI levels, with a significant gender difference (females>males). Of note, almost all obese adults (99.4%) were centrally obese regardless of gender. In multivariable regression analyses, adjusting for age, education, physical activity, alcohol use and survey site, regular smoking was inversely associated with BMI in males (standardized regression coefficients, β= -0.093, p<0.001) and females (β= -0.025, p<0.001). Of interest, in the BMI stratification analyses in 18 groups, all βs of regular smoking for WHtR were positive in both genders; the βs showed a significantly greater increasing trend with increasing BMI in males than in females. In the analyses with model adjustment for BMI, the positive associations between regular smoking and WHtR were stronger in males (β= 0.021, p<0.001) than in females (β= 0.008, p<0.001) (p<0.001 for gender difference). WC showed considerably consistent results. Conclusions: The data indicate that tobacco smoking is an important risk factor for central obesity, but the association is gender-specific and depends on the adjustment for general obesity.- "In our study the association between birth weight and SBP was seen without adjustment for current body size in women, but became apparent only after adjusting for current body size in men. Whether adjustment for current body size is appropriate has been the subject of much debate in the literature [7,363738. Weinberg notes that both the adjusted and unadjusted models are mathematically correct, therefore inference depends on the hypothesized causal mechanisms [38]. In the fetal origins paradigm birth weight serves as a proxy for fetal growth and is not itself a 'cause' of adverse adult outcomes; additionally higher birth weight is associated with higher adult body size suggesting that current body size is not the 'causal pathway' in the inverse birth weight BP relationship [36, 38]. "

[Show abstract] [Hide abstract]**ABSTRACT:**Objective: In this study we examined the effects of birth weight (BWT) and early life socioeconomic circumstances (SEC) on systolic and diastolic blood pressure (SBP, DBP) among Jamaican young adults. Study Design and Setting: Longitudinal study of 364 men and 430 women from the Jamaica 1986 Birth Cohort Study. Information on BWT and maternal SEC at child’s birth was linked to information collected at 18-20 years old. Sex-specific multilevel linear regression models were used to examine whether adult SBP/DBP were associated with BWT and maternal SEC. Results: In unadjusted models, SBP was inversely related to BWT z-score in both men (β, -0.82 mmHg) and women (β, -1.18 mmHg) but achieved statistical significance for women only. In the fully adjusted model, one standard deviation increase in BWT was associated with 1.16 mmHg reduction in SBP among men (95%CI 2.15 to 0.17; p=0.021) and 1.34 mmHg reduction in SBP among women (95%CI 2.21 to 0.47; p=0.003). Participants whose mothers had lower SEC had higher SBP compared to those with mothers of high SEC (β, 3.4-4.8 mmHg for men, p<0.05 for all SEC categories, and 1.8-2.1 for women, p>0.05) Conclusion: SBP was inversely related to maternal SEC and BWT among Jamaican young adults. Key words: birth weight, fetal growth, blood pressure, socioeconomic factors, young adult, Jamaica, Black, Caribbean- "The remarkable and complete reversal of association between the average tail lengths of eubacterial and eukaryotic common membrane lipids with their mutually exclusive subsets, shown in Figures 2E and 3E, presented a fascinating statistical anomaly to us. After a substantial literature review, we found that this statistical anomaly, called " Simpson's paradox " (Wagner, 1982), has been reported as a rare phenomenon in biological data, especially clinical data (Tu et al., 2005; Rucker and Schumacher, 2008). To our knowledge, our findings in this work are the first example of Simpson's paradox in biological data at a molecular level through the compositional analysis of chemical structures. "

[Show abstract] [Hide abstract]**ABSTRACT:**Compositional analyses of nucleic acids and proteins have shed light on possible origins of living cells. In this work, rigorous compositional analyses of ∼5000 plasma membrane lipid-constituents of 273 species in the three life domains (archaea, eubacteria and eukaryotes) revealed a remarkable statistical paradox, indicating symbiotic origins of eukaryotic cells involving eubacteria. For lipids common to plasma membranes of the three domains, number of carbon atoms in eubacteria was found to be similar to those in eukaryotes. However, mutually exclusive subsets of same data show exactly the opposite - number of carbon atoms in lipids of eukaryotes was higher than eubacteria. This statistical paradox, called Simpson's paradox, was absent for lipids in archaea and for lipids not common to plasma membranes of the three domains. This indicates presence of interaction(s) and/or association(s) in lipids forming plasma membranes of eubacteria and eukaryotes, but not for those in archaea. Further inspection of membrane lipid structures, affecting physico-chemical properties of plasma membranes, provides the first evidence (to our knowledge) on symbiotic origins of eukaryotic cells based on the "third front" (i.e. lipids) in addition to the growing compositional data from nucleic acids and proteins. © 2015 by The American Society for Cell Biology.

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

This publication is classified Romeo Yellow.

Learn more