Knot placement in the Distributed non-linear lag models (DNLM) framework

Abstract

BACKGROUND AND AIM: Distributed non-linear lag models (DNLM) provide flexible methods to model non-linear exposure-response relationships over time, with common applications in environmental epidemiology. When the lag functions of the cross-basis include a spline function, the number and placement of knots for the function are specified in the model although the preferred number and placement of knots may not be known a priori. Our goal is to develop a flexible algorithm to explore the impact of knot selection on the final model. METHODS: We use data describing weekly maternal exposure to nitrogen dioxide (NO2) and fetal growth trajectories during the first 12, 20 and 12-20 weeks of pregnancy for 2,021 women from the INfancia y Medio Ambiente (INMA) project (2003-2008) for the exploration of two knot selection methods. We generated multiple search grids containing potential knot placement for the lag dimension of the cross-basis; each search grid had a distinct level of resolution for knot placement. We compared the number and placement of knots from each grid as well as the inference from the resulting DLNM models utilizing knots selected from each search grid. RESULTS:Our results showed that models with 12 lags resulted in the same number and placement of knots regardless of search grid used. Similarly, the models with 20 lags (i.e., both the 20 week and 12–20-weekfetal growth trajectories), produced the same number of knots regardless of search grid used; however, the placement of the knots changed depending on the search grid utilized. CONCLUSIONS:Choosing an appropriate search grid for knot selection in the model may impact the knot vector selected in some contexts. A simulation study to investigate the model impact of different knot selection processes may reveal more detailed information about the overall importance of this step in the DLNM framework and model building. KEYWORDS: DLNM, knot selection, splines, DLM