03-fixed-effects.Rmd

# Sensitivity analysis using fixed effects {#fixed-effects}

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## Overview

__Purpose: __
In the primary manuscript, we compared estimates pooled across studies using random effects models, which are more conservative in the presence of heterogeneity across studies. Here, we present estimates pooled using fixed effects. Inferences about estimates from fixed effects models are restricted to only the included studies, while random effects estimates assume included studies are sampled from a distribution of hypothetical studies.[^1] 

__Interpretation: __

Fixed effect estimates had narrow confidence intervals, and therefore more risk factors had statistically significant PIEs. 

__Implications:__

The fixed effect estimates are weighted towards results from larger studies, so are more heavily influenced by the large Jivita-3, Probit, and ZVITAMBO trials. But in general, the key exposures identified from the random-effects estimates were also had the strongest associations when pooled using fixed-effect estimates.



```{r setup, include=FALSE}
library(knitr)
knitr::opts_chunk$set(echo = TRUE)
source(paste0(here::here(), "/0-config.R"))
```



## Primary manuscript figures recreated with estimates pooled using fixed effects

More estimates are significant when pooling using fixed effects due to the generally smaller confidence intervals.

```{r, echo = FALSE}
include_graphics(paste0(fig_dir, "/risk-factor/fig-sig-heatmap_FE.png"))
```
**Figure 1a.  Heatmap of significance and direction across exposure-outcome combinations of associations estimated using fixed effects. ** 

```{r, echo = FALSE}
include_graphics(paste0(fig_dir, "/manuscript-figure-composites/risk-factor/extended-data/fig-laz-PAR-strat-age_FE.png"))

```
**Extended Data Figure 3 | Age-stratified population attributable differences in length-for-age Z-scores estimated using fixed effects. ** 

```{r, echo = FALSE}
include_graphics(paste0(fig_dir, "/manuscript-figure-composites/risk-factor/extended-data/fig-wlz-PAR-strat-age_FE.png"))

```
**Extended Data Figure 4 | Age-stratified population attributable differences in weight-for-length Z-scores estimated using fixed effects. ** 



```{r, echo = FALSE}
include_graphics(paste0(fig_dir, "/manuscript-figure-composites/risk-factor/extended-data/fig-laz-PAR-strat-region_FE.png"))

```
**Extended Data Figure 7 | Region-stratified population attributable differences in length-for-age Z-scores estimated using fixed effects. ** 

```{r, echo = FALSE}
include_graphics(paste0(fig_dir, "/manuscript-figure-composites/risk-factor/extended-data/fig-wlz-PAR-strat-region_FE.png"))

```
**Extended Data Figure 8 | Region-stratified population attributable differences in weight-for-length Z-scores estimated using fixed effects. **