Skip Navigation


American Journal of Epidemiology Advance Access originally published online on November 23, 2005
American Journal of Epidemiology 2006 163(1):84-96; doi:10.1093/aje/kwj003
This Article
Right arrow Abstract Freely available
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
163/1/84    most recent
kwj003v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (47)
Right arrowRequest Permissions
Right arrow Disclaimer
Google Scholar
Right arrow Articles by De Stavola, B. L.
Right arrow Articles by Leon, D. A.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by De Stavola, B. L.
Right arrow Articles by Leon, D. A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

American Journal of Epidemiology Copyright © 2005 by the Johns Hopkins Bloomberg School of Public Health All rights reserved; printed in U.S.A.

Practice of Epidemiology

Statistical Issues in Life Course Epidemiology

Bianca L. De Stavola1, Dorothea Nitsch1, Isabel dos Santos Silva1, Valerie McCormack1, Rebecca Hardy2, Vera Mann1, Tim J. Cole3, Susan Morton1 and David A. Leon1

1 Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
2 MRC National Survey of Health and Development, Department of Epidemiology, Royal Free and University College Medical School, London, United Kingdom
3 Centre for Paediatric Epidemiology and Biostatistics, Institute of Child Health, University College London, London, United Kingdom

Correspondence to Dr. Bianca L. De Stavola, Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom (e-mail: bianca.destavola{at}lshtm.ac.uk).

Received for publication September 9, 2004. Accepted for publication July 25, 2005.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MODELS FOR DISTAL OUTCOMES
 EXAMPLES AND DATA
 RESULTS
 DISCUSSION
 References
 
There is growing recognition that the risk of many diseases in later life, such as type 2 diabetes or breast cancer, is affected by adult as well as early-life variables, including those operating prior to conception and during the prenatal period. Most of these risk factors are correlated because of common biologic and/or social pathways, while some are intrinsically ordered over time. The study of how they jointly influence later ("distal") disease outcomes is referred to as life course epidemiology. This area of research raises several issues relevant to the current debate on causal inference in epidemiology. The authors give a brief overview of the main analytical and practical problems and consider a range of modeling approaches, their differences determined by the degree with which associations present (or presumed) among the correlated explanatory variables are explicitly acknowledged. Standard multiple regression (i.e., conditional) models are compared with joint models where more than one outcome is specified. Issues arising from measurement error and missing data are addressed. Examples from two cohorts in the United Kingdom are used to illustrate alternative modeling strategies. The authors conclude that more than one analytical approach should be adopted to gain more insight into the underlying mechanisms.

correlation; lifetime; path analysis; regression; structural equation model

Abbreviations: G0, grandparents; G1, study participants; G2, study participants' offspring


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MODELS FOR DISTAL OUTCOMES
 EXAMPLES AND DATA
 RESULTS
 DISCUSSION
 References
 
In the last decade, there has been a growing realization that prenatal and early-life biologic and social factors may play an important role in the etiology of many later-life conditions (1Go–9Go), in addition to—or in synergism with—those of well-established adult exposures. This field of inquiry is now referred to as life course epidemiology (10Go).

Studying complex interrelationships of biologic and social variables over time requires longitudinal information spanning broad periods of life. It also raises analytical problems because temporal, and possibly causal, hierarchies among the exposures need to be taken into account (11Go, 12Go). For example, risk factors for breast cancer operate at a number of stages in the life course (figure 1). They also may influence each other; for instance, childhood weight is inversely correlated with timing of puberty (13Go) and, directly or indirectly, later obesity (14Go). Age at puberty and adult obesity affect breast cancer risk (15Go) and thus may mediate the effect of childhood weight. If standard multiple regression models are used to study these variables, the effect of childhood weight would be estimated conditionally on all other exposures, thus missing the life course perspective, as we show below. Alternatively, if a joint modeling approach is used, where, for example, age at menarche, adult obesity, and breast cancer risk are all outcomes, their interrelationships would be explicitly estimated, albeit within an assumed multivariate structure.



View larger version (18K):
[in this window]
[in a new window]
  		FIGURE 1. A simplistic time-line representation of conceptual (ovals) and observable risk factors for breast cancer.

 
We discuss these problems by introducing a sequence of increasingly complex models to deal with the temporal and causal hierarchies among the exposure variables. We compare them in terms of interpretability as well as flexibility in dealing with missing data and measurement errors, both of which are common features in life course studies. We illustrate issues and models with two examples: the first studies intergenerational influences on size at birth by using data from a Scottish cohort of children recruited in 1962; the second examines childhood height and its impact on adult leg length with data from a United Kingdom birth cohort of women born in 1946. Our aim is to present a broad analytical framework for studies in life course epidemiology and to highlight its relevance to the current debate on causal modeling (16Go–18Go).


   MODELS FOR DISTAL OUTCOMES
TOP
 ABSTRACT
 INTRODUCTION
 MODELS FOR DISTAL OUTCOMES
EXAMPLES AND DATA
 RESULTS
 DISCUSSION
 References
 
When a structure among the exposure variables is known or presumed, a distinction can be made between variables that act at the inception ("background") or in the middle ("intermediate") of the process that leads to the main ("distal") outcome of interest (16Go). In the breast cancer example described above, childhood weight is a background variable, age at menarche and adult obesity intermediate variables, and breast cancer the distal outcome.

Statistical models can offer only simplified representations of reality (19Go). We classify those relevant in life course epidemiology according to the degree to which they explicitly acknowledge the relations among their components.

Conditional models for one outcome
Typically, standard multivariable regression models define the expectation of the outcome of interest Y, E(Y) (or a suitable transformation g(.)), as a function of several explanatory variables, X1, X2, ..., Xk,

(1)
where g(.) is the link function used in generalized linear models (20Go), and the coefficient ßj (j = 1, ..., k) represents the conditional effect attributed to a one-unit increase in Xj when all of the other variables are held constant. If g(.) is the identity function and Y is continuous, equation 1 represents a linear regression model.

A regression model such as equation 1 can be fitted with only background variables, thus avoiding the inclusion of exposures that may be on the causal pathway. This was the approach adopted in the early studies linking birth weight with coronary heart disease (21Go). Therefore, its estimated coefficients measure the effect of each background variable, controlled for that of the others. The longer the time gap between background variables and distal outcome, however, the greater the possibility of intervening modifying effects (see the debate surrounding the fetal programming hypothesis (1Go–3Go, 22Go–24Go)).

If all types of exposures (background and intermediate) are included in the same model for Y, the resulting regression coefficients measure mutually adjusted effects, that is, effects of background variables not mediated via the intermediate variables and effects of intermediate variables conditional on the background ones. More specifically, if the background variable X1 influences the intermediate variable Xk, ß1 would capture only the effect of X1 on Y not mediated by Xk.

A special setting that involves the analysis of background and intermediate exposures arises when repeated measures of the same variable are taken over time. In this case, the first available measure acts as background for all the following ones. Consider the influence of childhood anthropometric variables on adult obesity (14Go). Results obtained after including all childhood measurements in the same regression model for the distal outcome (obesity) are difficult to interpret, especially if the measures are taken close to each other in time, because of their respective conditioning. With two repeated body size measures, say Z1 and Z2, taken at times t1 < t2, the model

(2)
could be rewritten as either

(3)
or

(4)
where the difference (Z2 – Z1) represents the change in the explanatory variable, for example, body size, occurring from time t1 to time t2.

Equations 2–4 are different parameterizations of the same model (22Go, 23Go). When Z2 is replaced by (Z2 – Z1), the conditional effect of Z1 on the transformed dependent variable, g(E(Y)), changes from ß1 to (ß1 + ß2) (equation 3). A similar switch is observed for the effect of Z2 when it is conditioned on (Z2 – Z1) (equation 4). The conditional effect of the difference (Z2 – Z1) is either ß2 or –ß1, depending on whether you condition on the first or second measure, respectively. So, different interpretations are possible depending on the conditioning variable, as originally discussed by Lucas et al. (22Go), Horta et al. (25Go), and Cole (26Go) and revisited by others (23Go, 24Go).

A model with several repeated measures, Z1, Z2, ..., ZK, taken at times t1 < t2 < ... < tK, can be reparameterized in terms of the first one, Z1, and all subsequent consecutive increments, (Zj – Zj–1), j = 1,...,K. Thus, equation 3 becomes

(5)
and similarly for equation 4. In equation 5, the coefficient for Z1 is the sum of all conditional effects associated with Z1, Z2, Z3, ..., ZK; it is the cumulative effect of increasing each Zj by one unit. Such increases would happen, for example, when a unit change at time t1 has irreversible effects on all following values of Z. For instance, one extra centimeter in height at age t1 has an impact on all future height values for a child, since his or her trajectory is shifted upward from then on, holding everything else constant, and therefore has a cumulative impact on the outcome. Similarly, the coefficient for each increment (Zj – Zj–1), (j = 2, ..., K), captures the effect of increasing Z during the jth interval, with that change shifting all subsequent Z values. An alternative parameterization, often used in life course epidemiology (13Go, 14Go), replaces the increments with the equivalent changes per unit of time ("velocities"), that is, (Zj – Zj–1)/(tj – tj–1). In this case, the coefficients for the jth period are (tj – tj–1) times the coefficients for (Zj – Zi–1) defined in equation 5.

When the model is not reparameterized but left as in equation 2, a graphical approach—the "life course plot"—may help in interpreting the conditional impact of each repeated measure (26Go). It involves plotting the regression coefficients against the times when measures were taken (after standardization to make these coefficients comparable). When the coefficients switch sign at some time tj, as in figure 2, there is evidence that changes during (tj–1, tj) affect the outcome of interest.



View larger version (8K):
[in this window]
[in a new window]
  		FIGURE 2. Hypothetical life course plot indicating that a change in the explanatory variable between ages 4 and 6 years has a positive effect on the outcome.

 
Joint models
Joint models deal with several outcomes simultaneously. In this context, they would explicitly define a presumed process underlying intermediate and distal outcomes. For example, variables may be arranged as shown in figure 3 (top), where Y is the distal outcome and X1, X2, and X3 the explanatory variables. In this diagram, X3 is assumed to be directly affected by X1 and X2 and thus is an intermediate variable, while X1 and X2 are background variables. Its algebraic equivalent is a system of simultaneous equations, with as many equations as there are intermediate and distal outcomes, which takes the name of path analysis (27Go):

(6)



View larger version (12K):
[in this window]
[in a new window]
  		FIGURE 3. Example of path diagrams. Top: path for one distal outcome (Y), one intermediate outcome (X3), and two background variables (X1, X2); bottom: path for one distal outcome (Y) and a latent variable (U) measured by three proxy variables (X1, X2, X3). Arrows depicting random variation for each variable are omitted for simplicity. Boxes, proxy variables; circle, latent variable.

 
Here, as before, E(.) stands for expectation, while gy(.) and g3(.) are link functions. When gy(Y) and g3(X3) are conditionally normally distributed, estimation can be carried out by maximum likelihood or, avoiding the normality assumptions, by three-stage least squares (28Go). The indirect effects of a background variable, say, X1, on the distal outcome can be computed by multiplying the standardized coefficients (e.g., the effects for a one-standard-deviation increase in X1) found along each of the paths leading from X1 to Y and then summing them (18Go, 29Go). In this figure, there is only one indirect path from X1 to Y, via X3. Thus, if X1 and X3 are standardized and the path model is correct (30Go), the indirect effect of X1 is {alpha}1 multiplied by ß3.

When Y and X3 are not normally distributed, penalized maximum likelihood (31Go, 32Go) or nonparametric maximum likelihood estimation is used, with the latter recently suggested to improve the estimation properties (33Go).

When some of the variables are proxies for factors that could not be (or were not) measured precisely, latent variables can be introduced within this framework. For example, several dietary variables may be available via a food frequency questionnaire aiming to measure "usual diet" (34Go). Thus, each of them is a proxy, or "manifestation," of an unmeasurable construct that nevertheless is of interest. Similarly, repeated height observations during childhood are manifestations of an underlying growth pattern.

In figure 3 (bottom), three variables, X1, X2, and X3, act as proxy (or "manifest") measures for the unmeasurable/unmeasured variable U (the convention is to use squares for observed variables and circles for latent variables). The effect of U on Y can be estimated by specifying how the three proxies are linearly related to U and also how U is related to Y:

(7)

Usually, the latent variable U and its proxy variables are assumed to be normally distributed and the parameters µ1, µ2, and µ3 are set to be zero. The link function for Y, gy(E(.)), could be of any form, however. Other observed variables could be influencing Y; in this case, the last expression in equation 7 would have an additional term ß4X4.

The first three expressions in equation 7 define the measurement part of the model because U is not observed but is proxied by X1, X2, and X3. The fourth expression in this equation defines the structural part, that is, in this case, the relation between the unmeasured variable U and the distal outcome Y (35Go). Together, the measurement and structural models form a structural equation model (29Go).

Because U is not directly observed and does not usually have a quantifiable metric, its influence on the manifest variables can be measured in terms of an arbitrary metric only. One convention is to use the first of the proxy variables as the reference and thus adopt its metric, for example, that of X1, so that the effect of the latent variable on Y becomes expressed in terms of X1 units. Alternatively, the variance of the latent construct is fixed to be 1 and its effect on Y estimated in terms of a one-standard-deviation change in the latent variable.

As for path analysis, estimation can be carried out by maximum, penalized maximum (31Go, 32Go), or nonparametric maximum likelihood (33Go), depending on the link functions. Generalizations to include more than one latent variable (and associations among them) are straightforward, although issues of identifiability constrain their numbers (29Go). Generalizations to discrete latent variables are also within the scope of these models. They involve the concept of latent classes, the probability of belonging to each of them being determined by a higher level latent continuous factor (36Go, 37Go), with estimation performed by maximum likelihood with the expectation-maximization algorithm (36Go, 38Go, 39Go). Joint models such as these can be fitted in Mplus (40Go) and Stata (33Go) software.

Data quality issues
A major difficulty that arises when analyzing life course studies derives from varying data quality. Because the focus is on different time periods, data from multiple sources (including routine data, e.g., cancer registries) are merged although their variables definition, as well as their completeness, may vary. The number of subjects for whom data are complete on any subset of the variables of interest can therefore be reduced to a small fraction of the total, while the precision of a variable may depend on when it was collected, for example, because of changes in units (as for birth weight, measured in pounds or kilograms). Thus, measurement errors and missing values affect life course studies to a greater extent than standard observational studies.

Several methods are available to deal with measurement errors (41Go). For example, when data on two or more proxy variables for an exposure of interest are collected, calibration methods can be used within a two-stage conditional approach (42Go, 43Go). Alternatively, as described above, joint models that include latent variables can be fitted (44Go). When the data are affected by missing values, analyses based on complete records (via conditional or joint models) are rarely appropriate because the incorrect assumption of a "missing completely at random" mechanism would lead to biased results (45Go). If missingness can be assumed to be "at random," either of two closely related (46Go) approaches can be used: 1) imputation methods, with conditional models (47Go); or 2) maximum likelihood plus the expectation-maximization algorithm (36Go) or Bayesian simulations (48Go), with joint models. When, instead, data are suspected to be systematically missing because of unmeasured factors (e.g., informative dropout), extensive sensitivity analyses should be performed, whatever the modeling approach (49Go–52Go).


   EXAMPLES AND DATA
TOP
 ABSTRACT
 INTRODUCTION
 MODELS FOR DISTAL OUTCOMES
 EXAMPLES AND DATA
RESULTS
 DISCUSSION
 References
 
Two examples arising in the analysis of two United Kingdom cohorts will be used for illustration. The first investigates how maternal and grandmaternal factors influence the size of an offspring at birth; the Children of the 1950s Study is used. This cohort includes all people who, in 1962, participated in a reading survey while attending primary school in Aberdeen, Scotland (53Go, 54Go). Data were collected from the participants' obstetric records and on characteristics of their parents and grandparents. In 1999–2000, 4,497 female study members (78 percent of the total) were anonymously linked to Scottish maternity records leading to birth data on their offspring. Thus, information on three generations (the grandparents, denoted G0; the study participants, G1; and their offspring, G2) can be studied.

The second example focuses on how adult leg length, which has been used in cancer and cardiovascular epidemiology as a marker of childhood environmental factors (55Go, 56Go), is determined by different periods of childhood growth. Leg length of participants in the Medical Research Council National Survey of Health and Development was measured by a trained nurse when participants were aged 43 years. The National Survey of Health and Development is a socially stratified birth cohort that includes 2,547 women and 2,815 men born during the week of March 3–9, 1946 (57Go–59Go) and followed prospectively, with childhood height measured at ages 2, 4, 6, 7, 11, and between ages 14 and 15 years by trained personnel.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MODELS FOR DISTAL OUTCOMES
 EXAMPLES AND DATA
 RESULTS
DISCUSSION
 References
 
Example 1: intergenerational influences on size at birth
We aimed to investigate how strongly intergenerational factors influence a baby's size at birth (defined as birth weight standardized for gestational age) by using data from the Children of the 1950s Study (figure 4; (54Go)). For illustration, we consider only biologic G1 and G0 factors (birth size of the mother, and height and parity of the mother and grandmother) and restrict the analyses to 1,724 first singleton baby girls.



View larger version (14K):
[in this window]
[in a new window]
  		FIGURE 4. Simplified path diagram of intergenerational influences on birth size. Arrows depicting random variation for each variable are omitted for simplicity. Double-lined boxes, dependent variables. G0, grandmothers; G1, mothers (index); G2, offspring.

 
Fitting a multiple linear regression model for G2 birth size on all potential explanatory variables shows that all conditional maternal factors have positive effects, unlike the grandmaternal ones (table 1, top). Thus, offspring (G2) size at birth is larger when the mother (G1) is taller, holding constant all other variables, but is reduced (although not significantly) when, again holding all other variables constant, her grandmother (G0) is taller or had more children. The negative G0 height effect should be interpreted in conjunction with the positive G1 effect, since these two variables are de facto repeated measures of the same variable. A clearer interpretation would focus on their difference and conclude that the taller a G1 woman is relative to her mother, the larger her offspring (estimated ß2 = 0.18 in equation 3).


View this table:
[in this window]
[in a new window]
  		TABLE 1. Mutually adjusted coefficients obtained from a conditional regression model for offspring birth size* and from a joint regression model for offspring birth size, maternal birth size, and maternal adult height in the Children of the 1950s Study, (N{dagger} = 1,692), Aberdeen, Scotland, 1962–2001{ddagger}

 
By instead fitting the path analysis model equivalent to figure 4, we can deal with these associations simultaneously (table 1, bottom). The estimated direct-effect coefficients corresponding to the arrows leading to the other two joint outcomes (in double boxes), likewise the distal outcome, G2 birth size, show that G1 adult height increases with G0 adult height and G1 birth size but decreases with increasing G0 parity (i.e., it was lower in larger families), while G1 birth size increases with increasing G0 parity and G0 adult height. By multiplying the standardized parameters along the relevant pathways, the indirect effects on G2 birth size of G0 parity, G0 adult height, and G1 birth size can be estimated (table 2). Doing so shows that, although G0 adult height has a negative direct effect (i.e., not mediated), its indirect effect via G1 birth size and G1 adult height is positive (0.13 = 0.49 x 0.18 (via G1 adult height) + 0.20 x 0.19 (via G1 birth size) + 0.20 x 0.19 x 0.18 (via G1 birth size and adult height); table 2), leading to a positive and significant total effect. So, although the conditional model provided an insight into intergenerational direct effects, the joint model led to a more comprehensive summary of their interrelationships.


View this table:
[in this window]
[in a new window]
  		TABLE 2. Direct, indirect, and total effects on offspring birth size estimated from the joint model for offspring birth size,* maternal birth size, and maternal adult height in the Children of the 1950s Study (N{dagger} = 1, 692), Aberdeen, Scotland, 1962–2001

 
Example 2: childhood growth and adult leg length
We used data on 2,349 female participants in the National Survey of Health and Development, for whom at least one childhood height or adult leg length measure was available, to investigate which childhood periods are most associated with adult leg length. A series of conditional regression models for adult leg length were fitted by adding each childhood height measure one at a time, starting from age 2 years. Because of missing values, these models are based on different numbers of observations (table 3, top).


View this table:
[in this window]
[in a new window]
  		TABLE 3. Conditional linear regression models for leg length (cm) at age 43 years on childhood height measures using either absolute childhood height measures or absolute height at age 2 years plus height increments after that age, women in the Medical Research Council National Survey of Health and Development, United Kingdom, 1946–1999

 
At first glance, the results are difficult to interpret because of the changing size and, occasionally, sign of the parameters obtained for the same height measure in different models. The only systematic feature of these models is the consistently larger size and significance of the estimated conditional coefficient corresponding to the oldest age. Model 4 is the exception, however. Here, the oldest age, 11 years, reflects stage of sexual maturation as much as linear growth, and stage of maturation is a poor predictor of adult leg length. Thus, it is not surprising that height at this age has a weak effect on adult leg length when conditioned on earlier stature.

In the model including all available childhood measures (model 5), the conditional effects of height at ages 2 and 11 years are negative, showing that, conditionally on all other childhood measures, being shorter at these ages leads to longer adult leg length. This conclusion is also evident when plotting the equivalent standardized coefficients, as suggested by Cole ((26Go); figure 5). When heights are replaced by height increments (table 3, bottom), the coefficients in each newly fitted model are the sum of the coefficients in the original one (as shown in equation 5). For example, in model 5, the coefficient for height increments between ages 6 and 7 years is precisely 0.493 = 0.148 – 0.102 + 0.447; that is, it is the sum of the conditional height effects at ages 7, 11, and 15 years. Thus, the coefficients shown in the bottom part of table 3 capture the cumulative effect of a shift in height at one age as it affects a girl's height at all subsequent ages.



View larger version (13K):
[in this window]
[in a new window]
  		FIGURE 5. Life course plot of the conditional regression coefficients in the model of leg length on standardized height measures from age 2 to age 15 years, Medical Research Council National Survey of Health and Development, United Kingdom, 1946–1999 (N = 791).

 
Given the similarity of the conditional coefficients for the earliest height increments, the model can be simplified to include only the intervals 2–7 years, 7–11 years, and 11–15 years (table 4, middle). To obtain comparable measures of effect, the model with yearly height velocities is also reported (table 4, bottom). Here, the estimated conditional coefficients are multiples of those found when height increments are used; for example, the coefficient for height velocity between ages 2 and 7 years is five times that for the equivalent height difference, 0.55, and 0.55 = 0.19 – 0.10 + 0.45 is the sum of the corresponding conditional height effects (table 4, top).


View this table:
[in this window]
[in a new window]
  		TABLE 4. Conditional linear regression models for leg length (cm) at age 43 years on a selection of childhood height measures specified either as absolute measures or as absolute height at age 2 years plus height increments or absolute height at age 2 years plus height velocities,* women in the Medical Research Council National Survey of Health and Development, United Kingdom, 1946–1999

 
An equivalent joint analysis would assume that a girl's growth profile is determined by a latent process that influences her adult leg length. Thus, we parameterized the growth process in terms of "true" height at age 2 years and height velocities between the ages of 2 and 7, 7 and 11, and 11 and 15 years (figure 6). These are latent variables manifested by the observed heights at 2, 4, 6, 7, 11, and 15 years (the "measurement model") (figure 7), where the latent variables are equivalent to random coefficients in a generalized linear mixed model (60Go–62Go). The structural part of this joint model defines instead how the latent variables influence adult leg length (figure 7).



View larger version (12K):
[in this window]
[in a new window]
  		FIGURE 6. Hypothetical piecewise linear model for childhood growth. Velocity was defined as height increment divided by the difference between the ages.

 


View larger version (27K):
[in this window]
[in a new window]
  		FIGURE 7. Simplified path diagram of the relation between height measurements at ages 2, 4, 6, 7, 11, and 15 years and adult leg length. Arrows depicting random variation for each variable are omitted for simplicity. Boxes, proxy variables; circles, latent variables. Velocity was defined as height increment divided by the difference between the ages.

 
The measurement and structural models were jointly fitted, the first giving estimated mean growth parameters (table 5), which were consistent with both observed values (table 4, bottom) and standard growth charts (63Go, 64Go). The structural model gave estimates of the effects of the growth parameters on adult leg length, which were similar to those found by the conditional model (table 4, bottom). The mainly small numeric differences between conditional and joint results are to be attributed to two main factors. First, the joint model was fitted by using all height measures, not just those at ages 2, 7, 11, and 15 years, with the consequent impact on average height at age 2 years. Second, it dealt with the measurement error inherent in the calculated height velocities by specifying them as latent variables. Thus, the confidence intervals for the joint model parameters are wider, better reflecting the uncertainty about the underlying growth process.


View this table:
[in this window]
[in a new window]
  		TABLE 5. Joint estimation of the measurement and structural models described in figure 7 obtained by using only complete records or all records with at least one of the measures and obtained via EM*-ML* assuming MAR,* women in the Medical Research Council National Survey of Health and Development, United Kingdom, 1946–1999

 
For comparison, the parameters of the joint model were estimated by using the same subset of women contributing to the conditional model (N = 794). However, if it is assumed that the missing height and leg length values occurred at random (45Go), the joint model can be refitted by using data on the 2,349 women for whom at least one height or leg measure was available, via the expectation-maximization algorithm available in Mplus (table 5, right; (40Go)). The results are marginally different from those found earlier, reflecting the fact that the 794 women in the initial analyses were, on average, taller at younger ages, grew slower from ages 11 to 15 years, and had a shorter leg length than the rest of the women (table 6).


View this table:
[in this window]
[in a new window]
  		TABLE 6. Characteristics of women for whom records on childhood height and adult leg length were or were not complete, Medical Research Council National Survey of Health and Development, United Kingdom, 1946–1999

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MODELS FOR DISTAL OUTCOMES
 EXAMPLES AND DATA
 RESULTS
 DISCUSSION
References
 
In this paper, we have described the issues arising when explanatory variables are closely associated because of underlying temporal or biologic processes, a frequent feature of life course studies. Conditional and joint models have been compared by using examples drawn from our work in cardiovascular and cancer epidemiology. These models were chosen for their relative simplicity, the purpose of the analyses being illustrative, so that thorough epidemiologic investigations were restrained and technical details avoided. Other, more complex applications can be found in the life course literature (e.g., Naumova et al. (14Go), De Stavola et al. (65Go), and Nitsch et al. (66Go)). Related joint models can also be found in the survival analysis literature concerned with time-changing internal (i.e., intermediate) exposures, such as CD4 counts in patients with human immunodeficiency virus, as reviewed in Tsiatis and Davidian (67Go). Issues of measurement error, temporally correlated data, and, especially, informative missingness arise in that context as they do in life course epidemiology, with the proposed solutions partly mirroring those discussed here (68Go–72Go).

We have used the classification of conditional and joint models to contrast two main analytical approaches. The first class of models is relatively easy to apply but also to misinterpret when the conditioning variables are overlooked. In contrast, joint models may seem ideally suited to deal with life course problems because they explicitly specify the presumed causal and temporal mechanisms for the distal outcome. Further missing data problems can be dealt with directly, if a missing-at-random assumption is appropriate, and measurement error problems by specifying latent variables within a structural equation model. However, several alternative model specifications ("structures") might be appropriate for a particular application. Thus, the choices may be too subjective, especially because formal comparisons are problematic (73Go).

Whatever approach is adopted, the main issue is how to deal with life course dependencies while at the same time considering the impact of unmeasured—or poorly measured—factors that influence the pathways of interest. This is not a new topic in epidemiology (74Go–76Go), although it has recently become the focus of renewed interest, as demonstrated by the current debates on causal modeling (18Go, 24Go, 77Go–84Go) and on the role of statistics in causal inference (85Go–88Go). Inspired by that debate, we have used the distinction between conditional and joint modeling in the context of life course studies, mirroring that between descriptive and causal modeling (74Go). Indeed, structural equation models could be viewed as algebraic representations of causal beliefs (18Go). It must be stressed, however, that either approach is prone to misspecifications and thus should not be singly relied upon for causal inference (16Go). To achieve robust conclusions, more than one analytical approach should be adopted, with the results compared and inconsistencies investigated, thus carrying out sensitivity analyses in the broader sense (89Go).


   ACKNOWLEDGMENTS
 
This work was conducted within the framework funded by the Medical Research Council Co-operative Group grant (G9819083) on "Life-course and trans-generational influences on disease risk."

The authors thank Professors Michael Wadsworth and Diana Kuh for access to the Medical Research Council National Survey of Health and Development data, and Michael Hills and Jonathan Sterne for invaluable comments on an earlier draft of the manuscript.

Conflict of interest: none declared.


   References
TOP
 ABSTRACT
 INTRODUCTION
 MODELS FOR DISTAL OUTCOMES
 EXAMPLES AND DATA
 RESULTS
 DISCUSSION
 References
 

  1. Barker DJP. Mothers, babies and health in later life. Edinburgh, United Kingdom: Churchill Livingstone, 1998.
  2. Leon DA, Lithell HO, Vågerö D, et al. Reduced fetal growth rate and increased risk of ischaemic heart disease mortality in 15 thousand Swedish men and women born 1915–29. BMJ 1998;317:241–5.[Abstract/Free Full Text]
  3. McCormack VA, dos Santos Silva I, De Stavola BL, et al. Fetal growth and subsequent risk of breast cancer: results from long term follow up of Swedish cohort. BMJ 2003;326:248–53.[Abstract/Free Full Text]
  4. Lithell HO, McKeigue PM, Berlung L, et al. Relationship of size at birth to non-insulin-dependent diabetes and insulin levels in men aged 50 to 60 years. BMJ 1996;312:406–10.[Abstract/Free Full Text]
  5. Moore SE, Cole TJ, Collinson AC, et al. Prenatal or early postnatal events predict infectious deaths in young adulthood in rural Africa. Int J Epidemiol 1999;28:1088–95.[Abstract/Free Full Text]
  6. Hall AJ, Yee LJ, Thomas SL. Life course epidemiology and infectious diseases. Int J Epidemiol 2002;31:300–1.[Free Full Text]
  7. Krieger N. Themes in social epidemiology in the 21st century: an ecosocial perspective. Int J Epidemiol 2001;30:668–77.[Free Full Text]
  8. Nagin DS, Tremblay RE. Parental and early childhood predictors of persistent physical aggression in boys from kindergarten to high school. Arch Gen Psychiatry 2001;58:389–94.[Abstract/Free Full Text]
  9. Beebe-Dimmer J, Lynch JW, Turrell G, et al. Childhood and adult socioeconomic conditions and 31-year mortality risk in women. Am J Epidemiol 2004;159:481–90.[Abstract/Free Full Text]
  10. Ben-Shlomo Y, Kuh D. A life course approach to chronic disease epidemiology: conceptual models, empirical challenges and interdisciplinary perspectives. (Editorial). Int J Epidemiol 31:285–93.[CrossRef][Web of Science]
  11. Hallqvist J, Lynch J, Bartley M, et al. Can we disentangle life course processes of accumulation, critical period and social mobility? An analysis of disadvantaged socio-economic positions and myocardial infarction in the Stockholm Heart Epidemiology Program. Soc Sci Med 2004;58:1555–62.[CrossRef][Web of Science][Medline]
  12. Goldberg GR, Prentice AM. Maternal and fetal determinants of adult diseases. Nutr Rev 1994;52:191–200.[Web of Science][Medline]
  13. dos Santos Silva I, De Stavola BL, Mann V, et al. Prenatal factors, childhood growth trajectories and age at menarche. Int J Epidemiol 2002;31:405–12.[Abstract/Free Full Text]
  14. Naumova EN, Must A, Laird NM. Tutorial in biostatistics: evaluating the impact of ‘critical periods’ in longitudinal studies of growth using piecewise mixed effects models. Int J Epidemiol 2001;30:1332–41.[Abstract/Free Full Text]
  15. Kuller LH. The etiology of breast cancer—from epidemiology to prevention. Public Health Rev 1995;23:157–213.[Medline]
  16. Cox DR, Wermuth N. Causality: a statistical view. Int Stat Rev 2004;72:285–305.
  17. Pearl J. Direct and indirect effects. In: Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence. San Francisco, CA: Morgan Kaufmann, 2001:411–20.
  18. Greenland S, Brumback B. An overview of relations among causal modelling methods. Int J Epidemiol 2002;31:1030–7.[Abstract/Free Full Text]
  19. Cox DR. Role of models in statistical analysis. Stat Sci 1990;5:169–74.[CrossRef]
  20. McCullagh P, Nelder J. Generalized linear models. London, United Kingdom: Chapman and Hall, 1980.[CrossRef][Web of Science]
  21. Barker DJP, Osmond C, Winter PD, et al. Weight in infancy and death from ischaemic heart disease. Lancet 1989;2:577–80.[Web of Science][Medline]
  22. Lucas A, Fewtrell MS, Cole TJ. Fetal origins of adult disease—the hypothesis revisited. BMJ 1999;319:245–9.[Free Full Text]
  23. Tu YK, West R, Ellison GTH, et al. 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. Am J Epidemiol 2005;161:27–32.[Abstract/Free Full Text]
  24. Weinberg CR. Invited commentary: Barker meets Simpson. Am J Epidemiol 2005;161:33–5.[Free Full Text]
  25. Horta BL, Barros FC, Victora CG, et al. Early and late growth and blood pressure in adolescence. J Epidemiol Community Health 2003;57:226–30.[Abstract/Free Full Text]
  26. Cole TJ. Modeling postnatal exposures and their interactions with birth size. J Nutr 2004;134:201–4.[Abstract/Free Full Text]
  27. Wright S. On the method of path coefficients. Ann Math Stat 1934;5:161–215.
  28. Zellner A, Theil H. Three stage least squares: simultaneous estimate of simultaneous equations. Econometrica 1962;29:63–8.
  29. Bollen KA. Structural equations with latent variables. New York, NY: John Wiley & Sons, 1989.
  30. Cole SR, Hernán MA. Fallibility in estimating direct effects. Int J Epidemiol 2002;31:163–5.[Abstract/Free Full Text]
  31. Breslow NE, Clayton DG. Approximate inference in generalised linear mixed models. J Am Stat Assoc 1993;88:9–25.
  32. Muthén BO. A general structural equation model with dichotomous, ordered categorical and continuous latent indicators. Psychometrika 1984;49:115–32.
  33. Rabe-Hesketh S, Skrondal A, Pickles A. Reliable estimation of generalised linear mixed models using adaptive quadrature. Stata J 2002;2:1–21.[CrossRef][Web of Science]
  34. Willett WC. Nutritional epidemiology. 2nd ed. New York, NY: Oxford University Press, 1998.
  35. Clayton DG. Models for the analysis of cohort and case-control studies with inaccurately measured exposures. In: Dwyer HD, Feileib M, Lippert P, et al, eds. Statistical models for longitudinal studies on health. Oxford, United Kingdom: Oxford University Press, 1992.
  36. Muthen B, Shedden K. Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 1999;55:463–9.[CrossRef][Web of Science][Medline]
  37. Bollen KA. Structural equation models. In: Armitage P, Colton T, eds. Encyclopaedia of biostatistics. Chichester, United Kingdom: J Wiley, 1998:4263–72.[CrossRef][Web of Science]
  38. Dempster AP, Laird NM, Rubin DB. Maximum likelihood for incomplete data via the EM algorithm (with discussion). J R Stat Soc (B) 1977;39:1–38.
  39. Muthén BO. Latent variable mixture modeling. In: Marcoulides GA, Schumacker RE, eds. New developments and techniques in structural equation modeling. Mahwah, NJ: Lawrence Erlbaum Associates, 2001:1–33.[CrossRef][Web of Science]
  40. Muthén LK, Muthén BO. Mplus. Statistical analysis with latent variables. Version 3. User's guide. Los Angeles, CA: Muthén & Muthén, 2004.[CrossRef][Web of Science]
  41. Carroll RJ. Measurement error in epidemiological studies. In: Gail MH, Benichou J, eds. Encyclopedia of epidemiologic methods. Chichester, United Kingdom: John Wiley & Sons, Inc, 2000.[CrossRef][Web of Science]
  42. Carroll RJ, Stefanski LA. Approximate quasi-likelihood estimation in models with surrogate predictors. J Am Stat Assoc 1990;85:652–63.
  43. White I, Frost C, Tokunaga S. Correcting for measurement error and continuous variables using replicates. Stat Med 2001;20:3441–57.[CrossRef][Web of Science][Medline]
  44. Rabe-Hesketh S, Skrondal A, Pickles A. Maximum likelihood estimation of generalised linear models with covariate measurement error. Stata J 2003;3:385–410.
  45. Little RJ, Rubin DB. Statistical analysis with missing data. New York, NY: John Wiley & Sons, 1987.[CrossRef][Web of Science]
  46. Little RJ. Missing data. In: Gail MH, Benichou J, eds. Encyclopaedia of epidemiologic methods. New York, NY: John Wiley & Sons, Inc, 2000.
  47. Shafer JL. Analysis of incomplete multivariate data. London, United Kingdom: Chapman and Hall, 1997.[CrossRef][Web of Science]
  48. Gilks WR, Richardson S, Spiegelhalter DJ, eds. Markov chain Monte Carlo in practice. London, United Kingdom: Chapman and Hall, 1996.[CrossRef][Web of Science]
  49. Molenberghs G, Kenward MG, Goetghebeur E. Sensitivity analyses for incomplete contingency tables: the Slovenian plebiscite case. Appl Stat 2001;50:15–29.
  50. Kenward MG. Selection models for repeated measurements with non-random drop-out: an illustration of sensitivity. Stat Med 1998;17:2723–32.[CrossRef][Web of Science][Medline]
  51. Manski C. Anatomy of the selection problem. J Human Resources 1989;24:343–60.
  52. Verzilli CJ, Carpenter JR. Assessing uncertainty about parameter estimates with incomplete repeated ordinal data. Stat Modelling 2002;2:203–15.[CrossRef]
  53. Batty GD, Morton SMB, Campbell D, et al. The Aberdeen Children of the 1950s cohort study: background, methods, and follow-up information on a new resource for the study of life-course and intergenerational effects on health. Paedriatr Perinat Epidemiol 2004;18:221–39.
  54. Morton S. Intergenerational determinants of size at birth. PhD thesis. University of London, London, United Kingdom, 2002.[CrossRef][Web of Science]
  55. Gunnell D, Okasha M, Davey Smith G, et al. Height, leg length, and cancer risk: a systematic review. Epidemiol Rev 2001;23:313–42.[Free Full Text]
  56. Langenberg C, Hardy R, Kuh D, et al. Influence of height, leg and trunk length on pulse pressure, systolic and diastolic blood pressure. J Hypertens 2003;21:537–43.[CrossRef][Web of Science][Medline]
  57. Wadsworth ME, Mann SL, Rodgers B, et al. Loss and representativeness in a 43 year follow up of a national birth cohort. J Epidemiol Community Health 1992;46:300–4.[Abstract/Free Full Text]
  58. Wadsworth MEJ, Butterworth SL, Hardy RJ, et al. The life course prospective design: an example of benefits and problems associated with study longevity. Soc Sci Med 2003;57:2193–205.[CrossRef][Web of Science][Medline]
  59. Wadsworth MEJ, Butterworth SL, Montgomery SM, et al. Health. In: Ferri E, Bynner J, Wadsworth MEJ, eds. Changing Britain, changing lives. London, United Kingdom: Institute of Education Press, 2003:207–36.[CrossRef][Web of Science]
  60. Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics 1982;38:963–74.[CrossRef][Web of Science][Medline]
  61. Goldstein H. Multilevel statistical models. London, United Kingdom: Edward Arnold, 1995.
  62. Muthén BO, Khoo ST. Longitudinal studies of achievement growth using latent variable modeling. Learning Individual Differences 1998;10:73–101.[CrossRef][Web of Science]
  63. Tanner JM. Foetus into man. Physical growth from conception to maturity. 2nd ed. Ware, England: Castlemead Publications, 1989.
  64. National Center for Health Statistics. 2000 CDC growth charts: United States. (www.cdc.gov/growthcharts); accessed September 2004.
  65. De Stavola BL, dos Santos Silva I, McCormack V, et al. Childhood growth and breast cancer. Am J Epidemiol 2004;159:671–82.[Abstract/Free Full Text]
  66. Nitsch D, De Stavola BL, Morton S, et al. Linkage bias in estimating the association between childhood exposure and propensity to become a mother: an example of simple sensitivity analyses. J R Stat Soc (A) (in press).[CrossRef][Web of Science]
  67. Tsiatis AA, Davidian M. Joint modelling of longitudinal and time-to-event data: an overview. Statistica Sinica 2004;14:809–34.
  68. De Gruttola V, Tu XM. Modelling progression of CD-4 lymphocyte count and its relationship to survival time. Biometrics 1994;50:1003–14.[CrossRef][Web of Science][Medline]
  69. Tsiatis AA, De Gruttola V, Wulfsohn MS. Modelling the relationship of survival to longitudinal data measured with error: application to survival and CD4 counts in patients with AIDS. J Am Stat Assoc 1995;90:27–37.
  70. Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics 1997;53:330–9.[CrossRef][Web of Science][Medline]
  71. Xu J, Zeger SL. Joint analysis of longitudinal data comprising repeated measures and times to events. Appl Stat 2001;50:375–87.
  72. Lin H, Turnbull BW, McCullogh CE, et al. Latent class models for joint analysis of longitudinal biomarkers and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. J Am Stat Assoc 2003;97: 53–65.
  73. Jöreskog KG. Testing structural equation models. In: Bollen KA, Scott Long J, eds. Testing structural equation models. Newbury Park, London, United Kingdom: Sage Publications, 1993. (Sage focus editions, vol 154).
  74. Robins JM, Greenland S. The role of model selection in causal inference from nonexperimental data. Am J Epidemiol 1986;123:392–402.[Free Full Text]
  75. Phillips AN, Davey Smith G. How independent are "independent" effects? Relative risk estimation when correlated exposures are measured imprecisely. J Clin Epidemiol 1991;44:1223–31.[CrossRef][Web of Science][Medline]
  76. Victora CG, Huttly SR, Fuchs SC, et al. The role of conceptual frameworks in epidemiological analysis: a hierarchical approach. Int J Epidemiol 1997;26:224–7.[Abstract/Free Full Text]
  77. Pearl J. Causal diagrams for empirical research. Biometrika 1995;82:669–710.[Abstract/Free Full Text]
  78. Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology 1999;10:37–48.[CrossRef][Web of Science][Medline]
  79. Robins J, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology 2000;11:550–60.[CrossRef][Web of Science][Medline]
  80. Robins JM. Data, design, and background knowledge in etiologic inference. Epidemiology 2001;11:313–20.
  81. Hernán MA, Hernández-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.[Abstract/Free Full Text]
  82. Maldonado G, Greenland S. Estimating causal effects. Int J Epidemiol 2002;31:422–9.[Free Full Text]
  83. Vansteelandt S, Goethebeur E. Causal inference with generalised structural mean models. J R Stat Soc (B) 2003;65:817–35.[CrossRef]
  84. Frangalis CE, Rubin DB. Principal stratification in causal inference. Biometrics 2002;58:21–9.[CrossRef][Web of Science][Medline]
  85. Cox DR, Wermuth N. Multivariate dependencies. London, United Kingdom: Chapman and Hall, 1996.
  86. Wermuth N, Cox DR. Statistical dependence and independence. In: Gail MH, Benichou J, eds. Encyclopedia of epidemiologic methods. Chichester, United Kingdom: John Wiley & Sons, Inc, 2000.
  87. Clayton D. Some remarks on interpretation of models and their parameters in epidemiology. Presented at the XXIst International Biometrics Conference, Freiberg, Germany, July 21–26, 2002.
  88. Hogan JW, Lancaster T. Instrumental variables and inverse probability weighting for causal inference from longitudinal observational studies. Stat Methods Med Res 2004;13:17–48.[Abstract/Free Full Text]
  89. Last JM, ed. A dictionary of epidemiology. 4th ed. New York, NY: Oxford University Press, 2001.

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Am J EpidemiolHome page
K. Raikkonen, T. Forsen, M. Henriksson, E. Kajantie, K. Heinonen, A.-K. Pesonen, J. T. Leskinen, I. Laaksonen, C. Osmond, D. J. P. Barker, et al.
Growth Trajectories and Intellectual Abilities in Young Adulthood: The Helsinki Birth Cohort Study
Am. J. Epidemiol., August 15, 2009; 170(4): 447 - 455.
[Abstract] [Full Text] [PDF]

Home page
 Am J EpidemiolHome page
M. Gamborg, P. K. Andersen, J. L. Baker, E. Budtz-Jorgensen, T. Jorgensen, G. Jensen, and T. I. A. Sorensen
Life Course Path Analysis of Birth Weight, Childhood Growth, and Adult Systolic Blood Pressure
Am. J. Epidemiol., May 15, 2009; 169(10): 1167 - 1178.
[Abstract] [Full Text] [PDF]

Home page
 ChestHome page
R. Kohansal, J. B. Soriano, and A. Agusti
Investigating the Natural History of Lung Function: Facts, Pitfalls, and Opportunities
Chest, May 1, 2009; 135(5): 1330 - 1341.
[Abstract] [Full Text] [PDF]

Home page
 Diabetes CareHome page
T. Dwyer, C. G. Magnussen, M. D. Schmidt, O. C. Ukoumunne, A.-L. Ponsonby, O. T. Raitakari, P. Z. Zimmet, S. N. Blair, R. Thomson, V. J. Cleland, et al.
Decline in Physical Fitness From Childhood to Adulthood Associated With Increased Obesity and Insulin Resistance in Adults
Diabetes Care, April 1, 2009; 32(4): 683 - 687.
[Abstract] [Full Text] [PDF]

Home page
 Int J EpidemiolHome page
G. Mishra, D. Nitsch, S. Black, B. De Stavola, D. Kuh, and R. Hardy
A structured approach to modelling the effects of binary exposure variables over the life course
Int. J. Epidemiol., April 1, 2009; 38(2): 528 - 537.
[Abstract] [Full Text] [PDF]

Home page
 Int J EpidemiolHome page
D L Dahly, L. Adair, and K. Bollen
A structural equation model of the developmental origins of blood pressure
Int. J. Epidemiol., April 1, 2009; 38(2): 538 - 548.
[Abstract] [Full Text] [PDF]

Home page
 J Am Coll CardiolHome page
C. G. Magnussen, A. Venn, R. Thomson, M. Juonala, S. R. Srinivasan, J. S.A. Viikari, G. S. Berenson, T. Dwyer, and O. T. Raitakari
The association of pediatric low- and high-density lipoprotein cholesterol dyslipidemia classifications and change in dyslipidemia status with carotid intima-media thickness in adulthood evidence from the cardiovascular risk in Young Finns study, the Bogalusa Heart study, and the CDAH (Childhood Determinants of Adult Health) study.
J. Am. Coll. Cardiol., March 10, 2009; 53(10): 860 - 869.
[Abstract] [Full Text] [PDF]

Home page
 Am J EpidemiolHome page
A. J. Sharma, M. E. Cogswell, and R. Li
Dose-Response Associations Between Maternal Smoking During Pregnancy and Subsequent Childhood Obesity: Effect Modification by Maternal Race/Ethnicity in a Low-Income US Cohort
Am. J. Epidemiol., November 1, 2008; 168(9): 995 - 1007.
[Abstract] [Full Text] [PDF]

Home page
 Am J EpidemiolHome page
M. A. Klebanoff and S. R. Cole
Use of Multiple Imputation in the Epidemiologic Literature
Am. J. Epidemiol., August 15, 2008; 168(4): 355 - 357.
[Abstract] [Full Text] [PDF]

Home page
 Int J EpidemiolHome page
F. Mardones, L. Villarroel, L. Karzulovic, S. Barja, P. Arnaiz, M. Taibo, and F. Mardones-Restat
Association of perinatal factors and obesity in 6- to 8-year-old Chilean children
Int. J. Epidemiol., August 1, 2008; 37(4): 902 - 910.
[Abstract] [Full Text] [PDF]

Home page
 Int J EpidemiolHome page
E. Kajantie, D. J P Barker, C. Osmond, T. Forsen, and J. G Eriksson
Growth before 2 years of age and serum lipids 60 years later: The Helsinki Birth Cohort Study
Int. J. Epidemiol., April 1, 2008; 37(2): 280 - 289.
[Abstract] [Full Text] [PDF]

Home page
 Stat Methods Med ResHome page
S. Rabe-Hesketh and A. Skrondal
Classical latent variable models for medical research
Statistical Methods in Medical Research, February 1, 2008; 17(1): 5 - 32.
[Abstract] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
A. L. Gunther, T. Remer, A. Kroke, and A. E Buyken
Early protein intake and later obesity risk: which protein sources at which time points throughout infancy and childhood are important for body mass index and body fat percentage at 7 y of age?
Am. J. Clinical Nutrition, December 1, 2007; 86(6): 1765 - 1772.
[Abstract] [Full Text] [PDF]

Home page
 Am J EpidemiolHome page
S. E. Gilman
Invited Commentary: The Life Course Epidemiology of Depression
Am. J. Epidemiol., November 15, 2007; 166(10): 1134 - 1137.
[Abstract] [Full Text] [PDF]

Home page
 Am J EpidemiolHome page
M. W. Gillman and K. Kleinman
Invited Commentary: Antecedents of Obesity--Analysis, Interpretation, and Use of Longitudinal Data
Am. J. Epidemiol., July 1, 2007; 166(1): 14 - 16.
[Abstract] [Full Text] [PDF]

Home page
 Int J EpidemiolHome page
G. D. Smith
Lifecourse epidemiology of disease: a tractable problem?
Int. J. Epidemiol., June 1, 2007; 36(3): 479 - 480.
[Full Text] [PDF]

Home page
 Int J EpidemiolHome page
Y. Ben-Shlomo
Rising to the challenges and opportunities of life course epidemiology
Int. J. Epidemiol., June 1, 2007; 36(3): 481 - 483.
[Full Text] [PDF]

Home page
 Int J EpidemiolHome page
N. Stettler
Commentary: Growing up optimally in societies undergoing the nutritional transition, public health and research challenges
Int. J. Epidemiol., June 1, 2007; 36(3): 558 - 559.
[Full Text] [PDF]

Home page
 Am J EpidemiolHome page
A. M. B. Menezes, P. C. Hallal, B. L. Horta, C. L. P. Araujo, M. de Fatima Vieira, M. Neutzling, F. C. Barros, and C. G. Victora
Size at Birth and Blood Pressure in Early Adolescence: A Prospective Birth Cohort Study
Am. J. Epidemiol., March 15, 2007; 165(6): 611 - 616.
[Abstract] [Full Text] [PDF]

Home page
 J. Epidemiol. Community HealthHome page
P. M L Skidmore, R. J Hardy, D. J Kuh, C. Langenberg, and M. E J Wadsworth
Life course body size and lipid levels at 53 years in a British birth cohort
J Epidemiol Community Health, March 1, 2007; 61(3): 215 - 220.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
A. Schienkiewitz, M. B Schulze, K. Hoffmann, A. Kroke, and H. Boeing
Body mass index history and risk of type 2 diabetes: results from the European Prospective Investigation into Cancer and Nutrition (EPIC)-Potsdam Study.
Am. J. Clinical Nutrition, August 1, 2006; 84(2): 427 - 433.
[Abstract] [Full Text] [PDF]

Home page
 Am J EpidemiolHome page
R. Hardy, Y. Ben-Shlomo, and D. Kuh
Hardy et al. Respond to "Beyond Frequencies and Coefficients"
Am. J. Epidemiol., July 15, 2006; 164(2): 126 - 127.
[Full Text] [PDF]

Home page
 Am J EpidemiolHome page
D. Kuh, R. Hardy, S. Butterworth, L. Okell, M. Richards, M. Wadsworth, C. Cooper, and A. A. Sayer
Developmental Origins of Midlife Physical Performance: Evidence from a British Birth Cohort
Am. J. Epidemiol., July 15, 2006; 164(2): 110 - 121.
[Abstract] [Full Text] [PDF]

Home page
 Eur J Public HealthHome page
M. Osler
The life course perspective: a challenge for public health research and prevention
Eur J Public Health, June 1, 2006; 16(3): 230 - 230.
[Full Text] [PDF]

Home page
 Int J EpidemiolHome page
C. E Kuehni and M. Zwahlen
Commentary: Numerous, heterogeneous, and often poor--the studies on childhood leukaemia and socioeconomic status
Int. J. Epidemiol., April 1, 2006; 35(2): 384 - 385.
[Full Text] [PDF]

Home page
 Int J EpidemiolHome page
R. Hardy and D. Kuh
Commentary: BMI and mortality in the elderly--a life course perspective
Int. J. Epidemiol., February 1, 2006; 35(1): 179 - 180.
[Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
163/1/84    most recent
kwj003v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (47)
Right arrowRequest Permissions
Right arrow Disclaimer
Google Scholar
Right arrow Articles by De Stavola, B. L.
Right arrow Articles by Leon, D. A.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by De Stavola, B. L.
Right arrow Articles by Leon, D. A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?