American Journal of Epidemiology ª The Author 2011. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail:
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Vol. 174, No. 1 DOI: 10.1093/aje/kwr045 Advance Access publication: March 23, 2011
Practice of Epidemiology Placental Abruption and Perinatal Mortality With Preterm Delivery as a Mediator: Disentangling Direct and Indirect Effects
Cande V. Ananth* and Tyler J. VanderWeele * Correspondence to Dr. Cande V. Ananth, Division of Epidemiology and Biostatistics, Department of Obstetrics, Gynecology, and Reproductive Sciences, University of Medicine and Dentistry of New Jersey-Robert Wood Johnson Medical School, 125 Paterson Street, New Brunswick, NJ 08901-1977 (e-mail:
[email protected]).
Initially submitted November 22, 2010; accepted for publication January 31, 2011.
The authors use recent methodology in causal inference to disentangle the direct and indirect effects that operate through a mediator in an exposure-response association paradigm. They demonstrate how total effects can be partitioned into direct and indirect effects even when the exposure and mediator interact. The impact of bias due to unmeasured confounding on the exposure-response association is assessed through a series of sensitivity analyses. These methods are applied to a problem in perinatal epidemiology to examine the extent to which the effect of abruption on perinatal mortality is mediated through preterm delivery. Data on over 26 million US singleton births (1995–2002) were utilized. Risks of mortality among abruption and nonabruption births were 102.7 and 6.2 per 1,000 births, respectively. Risk ratios of the natural direct and indirect (preterm delivery-mediated) effects of abruption on mortality were 10.18 (95% confidence interval: 9.80, 10.58) and 1.35 (95% confidence interval: 1.33, 1.38), respectively. The proportion of increased mortality risk mediated through preterm delivery was 28.1%, with even higher proportions associated with deliveries at earlier gestational ages. Sensitivity analyses underscore that the qualitative conclusions of some mediated effects and substantial direct effects are reasonably robust to unmeasured confounding of a fairly considerable magnitude. abruptio placentae; bias (epidemiology); causal model; gestational age; perinatal mortality
Abbreviation: RR, risk ratio.
Recent developments in the causal inference literature (1–5) have proposed new methodological approaches to partition the total effect of an exposure on the risk of an outcome into 2 components: one that acts through a mediator (the mediated or indirect effect) and another that acts directly on the outcome through other pathways. This work builds on more conventional approaches to such ‘‘mediation analysis’’ but provides a more general framework. Specifically, approaches from causal inference permit the effects of the exposure and the mediator to interact when conducting mediation analysis. The causal inference literature has also clarified the no-unmeasured-confounding assumptions that are necessary to identify direct and indirect effects. Analyses that attempt to estimate the direct and indirect effects will be biased if there are unmeasured variables that confound the mediator-outcome relation (1, 2, 4, 6, 7). In such settings, sensitivity analysis techniques for direct and
indirect effects to evaluate the impact of such mediator-outcome confounding have been developed (4). In this paper, we show an application of these methods to observational studies in the context of perinatal epidemiology. CASE STUDY IN PERINATAL EPIDEMIOLOGY
In normal pregnancies, placental separation occurs immediately following the birth of the baby, while in pregnancies complicated by abruption, the placental detachment occurs prematurely (8). Placental abruption—often a catastrophic condition—complicates roughly 0.5%–1.5% of pregnancies (9–12) and is associated with increased risks of maternal and perinatal morbidity and mortality (13–16). Women diagnosed with abruption are at 4–6-fold increased risk of delivering at preterm gestations (13). It is believed that release of thrombin because of decidual-placental hemorrhage 99
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(17–19) and hemosiderin deposition (8, 20)—both commonly found in the setting of abruption—triggers labor leading to preterm delivery. Abruption is also associated with disproportionately high risk of perinatal death (14, 21, 22). In the United States, for instance, the perinatal mortality rate is 8 per 1,000 singleton births among nonabruption births, whereas in pregnancies complicated by abruption, the rate is at least 15-fold higher (i.e., 120 per 1,000 births) (14). We focus our exploration of mediating effects relating abruption (exposure) and perinatal mortality (outcome) and of the role preterm delivery (mediator) plays in this relation. We seek to address 2 important issues: 1) Is the increased risk of mortality in relation to abruption entirely dependent (i.e., mediated) on preterm delivery? and 2) If not, what proportion of the increased mortality risk is directly the consequence of abruption through pathways other than preterm delivery? We also illustrate, through a set of sensitivity analyses (4), the bias due to unmeasured confounding for these aforementioned relations. There is little doubt, if any, that preterm delivery is in the causal pathway between abruption and mortality. However, we demonstrate methodologically how one can assess the magnitude of the effect mediated and assess its sensitivity to unmeasured confounding.
are of more use. The risk ratio for the natural direct effect (RRNDE) is defined by PrðY1M0 ¼ 1j C ¼ cÞ ; RRNDE m ¼ PrðY0M0 ¼ 1j C ¼ cÞ that is, the effect of the exposure if the mediator were set to what it would have been without the exposure. The risk ratio for the natural indirect effect (RRNIE) can be defined as PrðY1M1 ¼ 1j C ¼ cÞ ; RRNIE m ¼ PrðY1M0 ¼ 1j C ¼ cÞ that is, the effect on the outcome when the exposure is present after setting the mediator value to what it would have been with versus without the exposure. In our application, the natural direct effect risk ratio, RRNDE, compares the mortality risk between those with versus without abruption if, in both cases, delivery were delayed to the preterm delivery status that would have occurred without abruption. The natural indirect effect risk ratio, RRNIE, provides an assessment, among abruption births, of the mortality risk if we were able versus unable to delay delivery to what it would have been without abruption.
COUNTERFACTUAL EFFECT DEFINITIONS
We let X, Y, M, and C denote the exposure, outcome, mediator, and a set of covariates, respectively. Within the counterfactual framework (23, 24), let Yx denote the counterfactual outcome Y if, possibly contrary to fact, X had been set to x (i.e., X ¼ x). The total effect of X on Y for an individual is given by (Y1 Y0). We define Yxm as the potential outcome Y if, possibly contrary to fact, X ¼ x and M ¼ m. Similarly, we define Mx as the potential outcome M if, possibly contrary to fact, X ¼ x. Direct and indirect effects in mediation analysis
Robins and Greenland (1) and Pearl (2) provided definitions for direct and indirect effects within the framework of counterfactuals. A controlled direct effect (CDE) on the risk ratio (RR) scale (4, 5) conditional on C ¼ c, comparing X ¼ 1 and X ¼ 0 for some fixed level of M ¼ m, can be defined as PrðY1m ¼ 1j C ¼ cÞ : RRCDE m ¼ PrðY0m ¼ 1j C ¼ cÞ Note that, for a binary mediator, there will be 2 controlled direct effects, one corresponding to when the mediator is set to 1 and the other to when the mediator is set to 0. Although controlled direct effects can be useful for examining whether there are any pathways for the exposure independent of the mediator, they are not useful for effect decomposition, except under very specific conditions when there is no interaction at the individual level between the effects of the exposure and mediator (25). In general, there is nothing that can be defined as a controlled indirect effect (25, 26); instead, for purposes of effect decomposition within the counterfactual framework, natural direct and indirect effects
MEDIATION ANALYSIS
The mediation analysis requires several no-unmeasuredconfounding assumptions. Specifically, we assume that the set of covariates for which adjustment is made suffices to control for confounding of the 1) exposure-outcome; 2) mediator-outcome; and 3) exposure-mediator relations. We further assume that there is no effect of exposure that confounds the mediator-outcome relation. We pursue a sensitivity analysis to assess the robustness of our conclusions to violations of these assumptions. We use methods for mediation analysis for a dichotomous outcome (5). These methods were developed for use within the framework of logistic regression and a rare outcome, but they are also applicable to common outcomes when using log-linear models (log-binomial regression models to directly estimate risk ratios (27)). The formulas given for a dichotomous outcome were for the setting of a continuous mediator (5) but can be adapted to include a dichotomous mediator; we report these formulas here. Derivations for the expressions for a dichotomous mediator are provided elsewhere (28). In our application, the natural direct and indirect effects of the abruption-mortality relation were estimated from fitting a model for mortality (Y), conditional on abruption (X), preterm delivery (M), an abruption-preterm delivery interaction (X 3 M), and a set of confounders (C): log Pr Y ¼ 1j X ¼ x; M ¼ m; C ¼ c ¼ h0 þ h1 X þh2 M þ h3 X 3 M þ h#4 C; and a model for preterm delivery (M), conditional on abruption (X) and a set of confounders (C): Am J Epidemiol. 2011;174(1):99–108
Abruption and Perinatal Mortality
log½PrðM ¼ 1j X ¼ x; C ¼ cÞ ¼ b0 þ b1 X þ b#2 C: From these combined models, we can estimate risk ratios of controlled direct effect, RRCDE, natural direct effects, RRNDE, and natural indirect effects, RRNIE, for a dichotomous exposure using the following expressions: RRCDE ðmÞ ¼ expðh1 þ h3 MÞ; expðh1 Þ½1 þ expðh2 þ h3 þ b0 þ b#2 CÞ ; RRNDE ¼ 1 þ expðh2 þ h3 þ b#2 CÞ # ½1 þ expðb0 þ b2 CÞ½1 þ expðh2 þ h3 þ b0 þ b1 þ b#2 CÞ RRNIE ¼ : ½1 þ expðb0 þ b1 þ b#2 CÞ½1 þ expðh2 þ h3 þ b0 þ b#2 CÞ
Valeri and VanderWeele (28) provide more general expressions. Because RRNIE compares a change of delivery (timing of delivery with abruption vs. timing of delivery without abruption) among those with abruption, the baseline mortality risk will be quite high and, thus, small rate ratios may indicate large changes in absolute risk. Standard errors for these expressions can be obtained by either bootstrapping or using the delta method. Expressions for standard errors using the delta method are provided in the Web Appendix, which is posted on the Journal’s Web site (http://aje.oxfordjournals.org/), and derivations for these expressions are provided elsewhere (28). The proportion of the increased abruption-mortality association that is mediated through preterm delivery was computed, on the risk difference scale, as (5) RRNDE ðRRNIE 1Þ ¼ 3 100: Mortality% GA RRNDE 3 RRNIE 1 This measure provides a relative assessment of the extent to which the increased mortality risk following abruption is mediated through preterm delivery relative to the overall effect of placental abruption.
SENSITIVITY ANALYSIS FOR MEDIATION EFFECTS
In order to test the impact of potential unmeasured confounders on the direct and indirect effects of the abruption-mortality relation, we performed a series of sensitivity analyses (4). It is especially likely that the assumption of ‘‘no unmeasured confounding’’ for the mediator-outcome relation is violated; that is, there are common causes of preterm delivery and mortality for which we have not adjusted. Our sensitivity analysis is thus focused on this form of unmeasured confounding. We note that it is also possible that there are unmeasured confounders that affect both the exposure and the mediator. Despite control for a number of confounders, there is the possibility that a different set of factors (e.g., chorioamnionitis) may be associated with an increased risk of abruption (29, 30) and might also cause preterm delivery. In this case study, we focus our attention on the mediator-outcome unmeasured confounding scenario only. We consider a binary unmeasured confounding variable U indicating a common cause of preterm delivery (e.g., Am J Epidemiol. 2011;174(1):99–108
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preeclampsia or intrauterine infection (31, 32)) and mortality. The group of pregnancies with preterm delivery but without abruption is likely to have a higher prevalence of U because some factor other than abruption will be responsible for such preterm deliveries. The sensitivity analysis was performed with the following general assumptions: that the prevalence of U among term pregnancies was 5% with and without abruption and that the prevalence of U was 10% among preterm deliveries with abruption but 50% among preterm deliveries without abruption. On the basis of these assumptions, we estimated the impact of unmeasured confounding under 2 distinct scenarios: 1) moderate confounding, where we consider how the results would change if U increased the likelihood of mortality by a factor of 1.5 (i.e., RRU ¼ 1.5); and 2) substantial confounding, where we consider how the results would change if U increased the likelihood of mortality by a factor of 6 (i.e., RRU ¼ 6.0). MATERIALS AND METHODS
We utilized data on fetal deaths and linked livebirthsinfant death data files between 1995 and 2002 in the United States (33). We used the clinical estimate of gestational age for all analyses (34), which is deemed more reliable and superior to the menstrual estimate (35, 36). Placental abruption and perinatal mortality
A recording of placental abruption for both livebirths and stillbirths was made by using a check-box format by the physician/attendant at delivery (33). We defined preterm delivery as gestational age between 22 and 36 completed weeks. We examined risks of stillbirth and early (0–6 days) and late (7–27 days) neonatal mortality in relation to abruption. Further, because abruption is largely a condition that occurs (or is diagnosed) during labor, timely obstetric interventions may prevent the fetus from dying in utero, but such babies may die soon after birth. Thus, we also examined perinatal mortality defined as stillbirths plus early neonatal deaths. Confounders
The confounders considered for adjustment in the analyses included maternal age (
