the birth weight paradox revisited - NCRMeprints.ncrm.ac.uk/3355/1/CIM2014_destavola.pdf · 2014-06-20 · This (selection) bias may explain the ÔÔparadox.ÕÕ We now provide a

Social disadvantage and infant mortality:the birth weight paradox revisited

Bianca De Stavolawith Rhian Daniel, Richard Silverwood, Rachel Stuchbury, Emily Grundy

UK Causal Inference Meeting · 28 − 29 April 2014

Bianca De Stavola/BW Paradox 1/25

Background Alternative Questions Preliminary results Conclusions

Infant mortality and disadvantage

Infant mortality (deaths <1 yr):- negatively related to birth weight (BW)- patterned by socio-economic conditions.





Complication:low BW babies in high-risk populations tend to have lowermortality rates than low BW babies in low-risk populations.





Complication:low BW babies in high-risk populations tend to have lowermortality rates than low BW babies in low-risk populations.

First observed by Yerushalmy (1964, 1971) and interpreted as BWmodifying the effect of many factors associated with infant mortality:

BW paradox



Example

Smoking known risk factor for low BW.

Low BW babies born to smokers lower mortality than those ofnon-smokers:

those networks (15, 16), as figure 3 shows. The diagramslink variables (nodes) by arrows (directed edges) that rep-resent direct causal effects (protective or causative) of onevariable on another. DAGs are acyclic because the arrowsnever point from a given variable to any other variable in itspast (i.e., causes precede their effects); thus, one can neverstart from one variable and, following the direction of thearrows, end up at the same variable. The absence of an arrowbetween two variables indicates that the investigator be-lieves there is no direct effect (i.e., a causal effect not me-diated through other variables in the DAG) of one variableon the other (15, 17). In this article, we build upon previouspublications in which investigators used DAGs to show howstandard adjustment (stratification or regression) for vari-ables affected by exposure may create bias by introducinga spurious (noncausal) association between the exposureand the outcome (9, 10, 14).

Figure 3.1 depicts the simplest scenario, in which smok-ing affects mortality solely through a reduction of birthweight. Under this scenario, the crude mortality rate ratiofor smoking would be greater than 1, whereas the adjustedrate ratio and, equivalently, the stratum-specific rate ratiosshould be 1. Therefore, the proposed DAG in figure 3.1 isnot consistent with our findings. Note that there might becommon causes of smoking and infant mortality (e.g., socio-economic factors) that would induce confounding. For sim-plicity, we assume that our analyses are conducted withinlevels of those common causes (i.e., there is complete con-trol for confounding) and thus omit them from the graphs.

Alternatively, smokingmight affect mortality solely throughpathways not mediated by birth weight (figure 3.2). In this

case, the crude and adjusted rate ratios would be the same.Again, this is not consistent with our findings.

Figure 3.3 combines the previous two diagrams: The ef-fect of smoking is only partly mediated by birth weight. Inthis case, the adjusted rate ratio would generally differ fromthe crude rate ratio and from 1 due to the direct (i.e., notmediated by birth weight) effect of smoking on mortality,which is consistent with our findings. Actually, figure 3.3would be consistent with any finding, because figure 3.3 isa complete DAG; that is, it does not impose any restrictionson the values of the stratum-specific rate ratios. As a conse-quence, figure 3.3 is the simplest graphical representationof the theory that there is a qualitative modification of thesmoking effect by birth weight. However, most expertswould agree that figure 3.3 is an overly simplistic represen-tation of nature. In a more realistic yet still naı̈ve causaldiagram (figure 3.4), there would be common causes ofLBW and mortality (e.g., birth defects, malnutrition). Thepresence of these risk factors (U), usually unmeasured bythe investigator, would generally induce a spurious associ-ation between smoking and mortality when the analysis wasstratified on birth weight (10, 14, 18). This (selection) biasmay explain the ‘‘paradox.’’

We now provide a heuristic explanation of why this typeof selection bias arises. To do so, we will use the simplifieddiagram shown in figure 3.5. This new diagram uses birthdefects as the unmeasured variable (U) and includes only thethree arrows that are necessary for the bias to occur: an ar-row from smoking (the exposure) to birth weight (the vari-able that the analysis is being stratified on), an arrow frombirth defects to birth weight, and an arrow from birth defects

1

10

100

1,000

1,000

2,000

3,000

4,000

1,250

2,250

3,250

4,250

1,500

2,500

3,500

4,500

1,750

2,750

3,750

4,750

Birth Weight (g)

Mor

talit

y pe

r 1,

000

Liv

ebir

ths

Nonsmokers Smokers

FIGURE 2. Birth-weight-specific infant mortality curves for infants born to smokers and nonsmokers, United States, 1991 (national linked birth/infant-death data, National Center for Health Statistics).

The Birth Weight ‘‘Paradox’’ 1117

Am J Epidemiol 2006;164:1115–1120

by guest on Septem

ber 28, 2010aje.oxfordjournals.org

Dow

nloaded from

Figure: Birth-weight-specific infant mortality curves, US, 1991 (Hernandez-Diaz, AJE 2006)



Outline

1 Background

2 An alternative model

3 Questions and estimands

4 Preliminary results

5 Critique and Conclusions



The low birth weight paradox: collider bias?

BW is on the causal pathway from “Disadvantage” (E) to ”Infantdeath”, but there are unmeasured confounders U1.

Comparing infant mortality rates at given values of BW leads toopening up a spurious path from E to “Infant death” (Hernandez-Diaz et

al. , 2006).

Paradox explained if U1 and U2 act in opposite directions (Basso et

al. , 2006 & 2009).

BW

E Infant E death






al. , 2006).


al. , 2006 & 2009).

UBW

U1

E Infant E death






al. , 2006).


al. , 2006 & 2009).

UBW

U1

E Infant E death






al. , 2006).


al. , 2006 & 2009).

U+

UU

U2

+BW

U1BW

U1 ++

‐

E Infant E death



An alternative explanation

Low BW is a crude measure of the mechanism of the exposure E ,“Disadvantage”:

It is only a proxy of intrauterine growth rate and time,

neither intrauterine dimensions are usually available in largeobservational studies.

Other pathways may link exposure to the infant mortality (hence the

added arrows).

BW

EIntrauterine Infant EGrowth death








added arrows).

BW









added arrows).

BW









added arrows).

BW


But how can we proceed without information on intrauterine growth?



Wilcox Birth weight model

Wilcox (1983,2001) suggested that there are two sub-populations ofnewborns:

(a) predominant: mostly term babies,

(b) compromised: mostly pre-term babies andsmall-for-gestational-age.

0.1

.2.3

.4.5

0 2 4 6 8Birth weight

Compromised Predominant Mixture



Reformulated alternative model

The model can be reformulated in terms of these classes.

Assuming that the birth weight distribution for eachsub-population is normal,

and including predictors, we can estimateProb(class = compromised) using Latent Class Modelling.

BW








BW

E Infant Wilcox growthE deathgrowth classes







BW

E Infant Wilcox growthE deathgrowth classes







Year of birth, gender, birth order maternal agebirth order, maternal age

BW

EWilcox growth

Infant E growth classes death



Questions

With this more general theoretical framework, we reconsiderthe two main questions.Is BW:

1 an effect modifier of the effect of “Disadvantage” on Infantmortality?

2 a mediator for the effect of “Disadvantage” on Infantmortality?



Questions

With this more general theoretical framework, we reconsiderthe two main questions.Is BW:

1 an effect modifier of the effect of “Disadvantage” on Infantmortality?

2 a mediator for the effect of “Disadvantage” on Infantmortality?



The extended mediation model

BW: potential mediator (M); “Disadvantage”: exposure (E);Infant mortality: outcome (Y ); “Intrauterine growth”: intermediateconfounder (L).

Replacing L with L̂ = Pr (L = 1) ( 1: compromised, 0: predominant),

MM

E L YE L Y



The extended mediation model

BW: potential mediator (M); “Disadvantage”: exposure (E);Infant mortality: outcome (Y ); “Intrauterine growth”: intermediateconfounder (L).

Replacing L with L̂ = Pr (L = 1) ( 1: compromised, 0: predominant),

MM

Ê L YE L Y



Question 1: is BW an effect modifier?

We address the first question:

by comparing Controlled Direct Effect of E on Y holding M ateither 0 or 1.

If these effects are similar there is no support for effectmodification by M.

MM

Ê L YE L Y







00

Ê L YE L Y







11

Ê L YE L Y



Question 2: is BW a mediator?

We address the second question:

by estimating the Natural Direct and Indirect Effects of E on Y ,where:

the indirect effect is made of (a)and (b),and the direct effect is (c):

MM

Ê L YE L Y







MM

Ê L YE L Y







M(a) M

Ê L YE L Y







M (b)M (b)

Ê L YE L Y







MM

Ê L YE L Y

(c)(c)



Estimands and their estimation

Estimands (CDE(m) and PNDE, TNIE) are expressed as ORcontrasts.Assumptions:No interference, consistency, conditional exchangeability, and,because of L, either:

No E–M interaction:Model I (Robins and Greenland, 1992).

No non-linearities in L:Model II (Petersen et al. , 2006).

Estimation:

via Monte Carlo G-computation (Daniel, et al, 2011),

accounting for the estimation of Pr(L = 1) and clustering ofchildren.







Estimation:









Estimation:





The ONS Longitudinal Study (ONS LS)

Record linkage study set up in 1974 (see http://celsius.lshtm.ac.uk/).

Comprises linked census and event (and thus infant mortality1)records for 1% of the population of England and Wales (about 500,000

people at any one census).

Includes BW of babies born to LS mothers (regularly since 1981, recorded at

registration).

Several indicator of social disadvantage: here we show resultsfor maternal education

Today: data restricted to births of white mothers (85%), withcomplete information on maternal education (loss of 3.8%).

(Data only available at a dedicated lab at the Office for NationalStatistics, all results vetted before release.)



The ONS Longitudinal Study (ONS LS)

Record linkage study set up in 1974 (see http://celsius.lshtm.ac.uk/).

Comprises linked census and event (and thus infant mortality1)records for 1% of the population of England and Wales (about 500,000

people at any one census).

Includes BW of babies born to LS mothers (regularly since 1981, recorded at

registration).

Several indicator of social disadvantage: here we show resultsfor maternal education

Today: data restricted to births of white mothers (85%), withcomplete information on maternal education (loss of 3.8%).

(Data only available at a dedicated lab at the Office for NationalStatistics, all results vetted before release.)



The study population

160,366 singleton live births in 1981-2011.

E : 38% of mother with fewer that 5 O-levels (“Low education”).

M: 5.3% with birth weight<2.5kg.

Y : 0.54% (862) infant deaths.

Mortality rates vary greatly by BW, moderately by sex, improvingwith calendar time:

































0

.05

<2.7

2.7-

2.8

2.9-

3.0 3.1

3.2-

3.3 3.4

3.5

3.6-

3.7

3.8-

3.9

4.0+

<2.7

2.7-

2.8

2.9-

3.0 3.1

3.2-

3.3 3.4

3.5

3.6-

3.7

3.8-

3.9

4.0+

M FInfant death rates Infant death rates

1980-89 1990-99 2000-09

Rat

es p

er 1

,000

Birth weight deciles

Graphs by Sex of baby



Natural direct and indirect effects of low maternal educationVERY PRELIMINARY RESULTS- SEs not yet corrected

Model I Model IIln OR (SE) ln OR (SE)

CDE(0) – – 0.205 (0.076)CDE(1) – – 0.206 (0.076)

PNDE 0.221 (0.082) 0.227 (0.077)TNIE 0.011 (0.007) -0.012 (0.005)

TCE 0.232 (0.082) 0.205 (0.076)Model I and II give similar results, despite the difference inassumptions.

CDE(0) and CDE(1) from Model II are very similar: no evidenceof effect modification.

There is little support for a mediating effect of BW (also supported by

sensitivity analyses).

However problems of stability of the results.



Natural direct and indirect effects of low maternal educationVERY PRELIMINARY RESULTS- SEs not yet corrected

Model I Model IIln OR (SE) ln OR (SE)

CDE(0) – – 0.205 (0.076)CDE(1) – – 0.206 (0.076)

PNDE 0.221 (0.082) 0.227 (0.077)TNIE 0.011 (0.007) -0.012 (0.005)

TCE 0.232 (0.082) 0.205 (0.076)Model I and II give similar results, despite the difference inassumptions.

CDE(0) and CDE(1) from Model II are very similar: no evidenceof effect modification.

There is little support for a mediating effect of BW (also supported by

sensitivity analyses).

However problems of stability of the results.



Critique

What about unmeasured confounders?Results would still be biased.

However, not if U1 and U2 influenced L directly.

U

U

U2

BWU1




Critique

What about unmeasured confounders?Results would still be biased.

However, not if U1 and U2 influenced L directly.

U

U

U2

BWU1




Conclusions

Approach may contribute to the debate about the BW paradoxby representing the underlying biological process via a latentvariable.

Results depends on strong and partly unverifiable assumptions,although similarity of results from alternative parametricspecifications are reassuring.

Estimation of mediation effects and their SEs raises severalproblems. There are issues with:

estimation of the class probability,correlations among the outcomes of siblings,instability due to small number of events.

These are being addressed by extending the Monte CarloG-formula algorithm.



Conclusions








Conclusions








Conclusions








Acknowledgements

This work is supported by the ESRC Pathways Node (AwardES/1025561/2) of the National Centre for ResearchMethodology.

The permission of the Office for National Statistics to usethe Longitudinal Study is gratefully acknowledged, as is thehelp provided by staff of CeLSIUS.CeLSIUS is supported by the ESRC Census of PopulationProgramme (Award Ref: ES/K000365/1).The authors alone are responsible for the interpretation ofthe data.Census output is Crown copyright and is reproduced withthe permission of the Controller of HMSO and the Queen’sPrinter for Scotland.



References

Basso O, Wilcox AJ, Weimberg CR. Birth Weight and Mortality: Causality or Confounding? AJE2006;164:303-311.

Basso O, Wilcox AJ. Intersecting Birth Weight-specific Mortality Curves: Solving the Riddle. AJE2009;169:787-797

Daniel RM, De Stavola BL, Cousens SN. gformula: Estimating causal effects in the presence oftime-varying confounding or mediation using the g-computation formula. Stata J. 2011;11(4):479-517.

Hernandez-Diaz S, Schisterman EF, Hernan MA. The birth weight ”paradox” uncovered? AJE2006;164(11):1115-2.

Kramer MS, Zhang X, Platt RW. Analysing risks in adverse pregnancy outcomes. AJE 2014;179(3):361-367.

Petersen ML, Sinisi SE, van der Laan MJ. Estimation of direct causal effects. Epidemiology.2006;17(3):276-284.

Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect effects. Epidemiology.1992;3(2):143-155.

Yerushalmy, J. Mother’s cigarette smoking and survival of infant. AJOG 1964;88:505-518.

Wilcox AJ, Russell I.Birthweight and perinatal mortality standardizing for birthweight is biased. AJE 1983;118 (6):857-864.

Wilcox AJ. On the importance - and the unimportance - of birth weight. International Journal ofEpidemiology. 2001 Dec;30(6):1233-41.

Yerushalmy, J. The relationship of parents cigarette smoking to outcome of pregnancy. Implications as toproblem of infering causation from observed associations. AJE 1971;93(6):443-456.



Additional slides



Estimands of interest(ignoring the confounders in these definitions; Vansteelandt, 2012)

The total causal effect (TCE):

TCEOR =E [Y (1)]/{1− E [Y (1)]}E [Y (0)]/{1− E [Y (0)]}

The natural direct effect (NDE):

NDEOR =E [Y (1,M(0))]/{1− E [Y (1,M(0))]}E [Y (0,M(0))]/{1− E [Y (0,M(0))]}

The natural indirect effect (NIE):

NIEOR =E [Y (1,M(1))]/{1− E [Y (1,M(1))]}

E [Y (1,M(0))]/{[1− E [Y (1,M(0))]]}

where Y (x) is the potential value of Y that would have occurred had X been set to x and Y (x, m) the potential

value of Y that would have occurred had X been set to x and M to m



Maternal education and infant mortality

Birth weight ≥ 2.5 kg Birth weight < 2.5 kgMat Education Low High Low High

Births 92,704 59,141 4,393 4,128Deaths 220 222 225 195

Rates (x 1,000) 2.4 3.8 51.24 47.2

Sex-adjusted OR 1.58 (1.31, 1.91) 0.92 (0.76, 1.12)

heterog test (p) (0.031)

Adjusted2 OR 1.23 (1.01, 1.49) 0.92 (0.76, 1.12)

heterog test (p) (0.036)



The Wilcox model

Variable Class 1 Class 2For µ

Intercept 3.51 3.65sex - -

year birth - +mat age + +

birth order - +

For σIntercept 0.90 0.45

For πsex -

Mat educ +

About 10% of births predicted to be “compromised”.



Further Critique

There is another source of bias: conditioning on live birth.

Still births are a form of competing event, reducing thedenominator of possible infant deaths.

Consider the composite outcome of Infant death or Still birth(Kramer et al. , 2014):

Only Infant deaths Only Infant deaths & Still birthsModel I Model II

ln OR (SE) ln OR (SE)

PNDE 0.221 (0.082) 0.174 (0.067)TNIE 0.011 (0.007) 0.018 (0.008)

TCE 0.232 (0.082) 0.192 (0.066)


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the birth weight paradox revisited - NCRMeprints.ncrm.ac.uk/3355/1/CIM2014_destavola.pdf · 2014-06-20 · This (selection) bias may explain the ÔÔparadox.ÕÕ We now provide a