Summary Standard methods for inference about direct and indirect effects require stringent no‐unmeasured‐confounding assumptions which often fail to hold in practice, particularly in observational studies. The goal of the paper is to introduce a new form of indirect effect, the population intervention indirect effect, that can be non‐parametrically identified in the presence of an unmeasured common cause of exposure and outcome. This new type of indirect effect captures the extent to which the effect of exposure is mediated by an intermediate variable under an intervention that holds the component of exposure directly influencing the outcome at its observed value. The population intervention indirect effect is in fact the indirect component of the population intervention effect, introduced by Hubbard and Van der Laan. Interestingly, our identification criterion generalizes Judea Pearl's front door criterion as it does not require no direct effect of exposure not mediated by the intermediate variable. For inference, we develop both parametric and semiparametric methods, including a novel doubly robust semiparametric locally efficient estimator, that perform very well in simulation studies. Finally, the methods proposed are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health programme in Tanzania.

Background: Most maternal health programs in low-and middle-income countries estimate gestational age to provide appropriate antenatal care at the correct times throughout the pregnancy. Although various gestational dating methods have been validated in research studies, the performance of these methods has not been evaluated on a larger scale, such as within health systems. The objective of this research was to investigate the magnitude and impact of errors in estimated delivery dates on health facility delivery among women enrolled in a maternal health program in Zanzibar. Methods: This study included 4225 women who were enrolled in the Safer Deliveries program and delivered before May 31, 2017. The exposure of interest was error in estimated delivery date categorized as: severe overestimate, when estimated delivery date (EDD) was 36 days or more after the actual delivery date (ADD); moderate overestimate, when EDD was 15 to 35 days after ADD; accurate, when EDD was 6 days before to 14 days after ADD; and underestimate, when EDD was 7 days or more before ADD. We used Chi-squared tests to identify factors associated with errors in estimated delivery dates. We performed logistic regression to assess the impact of errors in estimated delivery dates on health facility delivery adjusting for age, district of residence, HIV status, and occurrence of past home delivery. Results: In our data, 28% of the estimated delivery dates were a severe overestimate, 23% moderate overestimate, 41% accurate, and 8% underestimate. Compared to women with an accurate delivery date, women with a moderate or severe overestimate were significantly less likely to deliver in a health facility (OR = 0.71, 95% CI: [0.59, 0.86]; OR = 0.74, 95% CI: [0.61, 0.91]). When adjusting for multiple confounders, women with moderate overestimates were significantly less likely to deliver in a health facility (AOR = 0.76, 95% CI: [0.61, 0.93]); the result moved slightly towards null for women with severe overestimates (AOR = 0.84, 95% CI: [0.69, 1.03]). Conclusions: The overestimation of women's EDDs reduces the likelihood of health facility delivery. To address this, maternal health programs should improve estimation of EDD or attempt to curb the effect of these errors within their programs.

No abstract