Methodological notes about the study: ‘Rainfall variability and adverse birth outcomes in Amazonia’

Exposure measurement

To evaluate the impacts of climatic variability on human health, it is relevant to properly define and measure exposure. In our case, rainfall variability exposure during pregnancy should consider location, period, metric, and summarised metrics.

• Location: Climatic conditions are spatially-varying, for this reason, it is fundamental to consider the area of exposure for the mother. We defined this as the municipality of residence because an extreme event does not necessarily have direct impacts on her health, but could affect the economic and health system of the mother’s Municipality, and consequently mother’s nutrition.
• Period: We did not consider only the pregnancy period, but also the pre-pregnancy period because of the importance of the mother’s health status at conception date.
• Metric: For a specific time and location, a classical approach would consider using the absolute rainfall level. However, we believe that this is not an adequate metric to evaluate the effects of rainfall because people used to high rainfall levels are likely to learn to cope with it. For this reason, we use a model-based standardised index (MBSI), applied to rainfall, that captures extremeness with respect to the long-term seasonal pattern. A 0-value would mean that the rainfall level is the same as the seasonal pattern, while a positive (negative) value would indicate intense (deficient) rainfall concerning the seasonal pattern. See Chacón-Montalván et al. (2019) for more details about the MBSI.
• Summarised metric: For a specific mother, we obtain a time series of the exposure metric. We need to apply a function to this MBSI time-series to obtain a summarised metric because we only have outcomes (e.g. birth weight) at the end of the pregnancy. This function should help us to identify different types of exposure. Using the mean function would be useless because deficit and intense events would be countered. It is more adequate to use bivariate functions (\(h_1\), \(h_2\)) that summarise only intense (\(h_1\)) and only deficient (\(h_2\)) events. We used this approach to define three types of exposure capturing (i) deviation from seasonality, (ii) non-extreme events (> 1 s.d., but < 1.96 s.d.), and (iii) extreme events (\(\geq\) 1.96 s.d.).

Statistical modelling

Specific details of our models can be found in the methods section of our paper. Here, I will answer four questions that were relevant to decide the type and structure of these models.

• Should we model only the mean parameter?: This question is only related to our BW models given that the assumed distributions have mean and scale parameters. We have seen heteroscedasticity of birth-weight with respect to Municipality, age, and other covariates, highlighting the importance of modelling the scale parameter. In general, we observed better fitting when modelling both parameters (mean and scale). It was straightforward to do using Bayesian additive models for location, scale, and shape implemented by Umlauf, Klein, and Zeileis (2018) in the bamlss package.
• What variables should we control for?: It depends on the effects that are desired to disentangle. For example, if you control for gestational age (GA) in a BW model, you obtain estimates of the effects of rainfall events on BW due to restricted foetus growth; while if you do not control for GA, you obtain estimates of the full effects due to either restricted foetus growth or gestational age. Similarly, we should not control for mosquito-borne diseases in case we want to obtain estimates of the full effects. Although we did not use causal models, we used directed acyclic graphs (DAG) to understand when we should control for certain covariates or not. More details about DAGs in causal inference can be found at Pearl, Glymour, and Jewell (2016). DAGitty is a great tool to explore the adjustments required.
• What type of relationships to use?: In real-world applications, linear relationships are not common, and birth weight analysis is not an exception. We observed that age, for instance, has a non-linear relationship with a peak around 35 years. Other complex relationships have been observed with respect to other covariates. For this reason, we preferred to use additive non-linear effects which are implemented in packages like mgcv and bamlss.
• How to include the summarised metrics of exposure?: As mentioned in the previous section we used three types of bivariate metrics of exposure where the first and second elements are related to deficient and intense rainfall events respectively. As expected, both elements are correlated and precaution should be taken when including them in the models. In case, we include the two elements independently, the associated estimated effects would not be interpretable due to their correlation. It is more appropriate to include the effects jointly to be able to estimate the effects according to different combinations for indices. We achieved this by using bivariate non-linear effects.

Future research

• Causal mechanisms: While it is clear that rainfall variability can have adverse impacts on newborns’ health; we still need to learn about the reason and causal mechanisms that are supported with empirical data. This will require the use of causal models for observational data to be able to disentangle the effects through different pathways (e.g. crop yields and quality; vector-borne diseases; and shock-related stress, anxiety, or mental health). We encourage researchers to focus on this approach to get better insights into the mechanisms of how rainfall variability impacts newborns’ health.
• Varying exposure susceptibility during pregnancy: An implicit assumption of our approach is that exposure to climatic variability has the same importance at any time of pregnancy; however, there are likely periods (e.g. first trimester) in which mothers are more susceptible. We can use a summarised metric that can capture this pattern by using smooth weighting functions. Parameters of these functions can be estimated from the data, but it can be possible to compare sensible hypothetical curves.
• Evaluate the exposure of other environmental and climatic conditions: Our approach can be applied to similar problems in which the goal is to assess the impacts of climatic or environmental events on human health (e.g. birth-weight, mortality, respiratory diseases). We can for example evaluate the impacts of exposure to extreme temperature, poor air quality, and so on.