# How can I use polynomial distributed lag models for longitudinal categorical exposure?

I have SHS data from 13 time points and i want to describe the relationship between this cumulative exposure and health outcome after the 13th time point. It seems the dlnm package in R can model this if I partition the time points into equally spaced time periods, but I am not sure how I can specify lags from these time periods while at the same time being able to say something about the importance of timing of the exposure. The exposure is a binary variable (yes/no), so some subjects will have 0s in all time periods. The literature that has used PDL models in epidemiology are mainly on continuous exposures and I am quite unsure on how to incorporate categorical exposures in the models

• sorry, SHS is Secondhand smoke – Edith Apr 22 at 21:05

Spline-based distributed lag models are discussed in the book "Longitudinal Data Analysis" by Diggle, Heagerty, Liang, and Zeger.

The idea is including one or more lagged covariates in a model to estimate the relation between a cumulative exposure and a possible outcome. The point is that the functional form that relates the lags to the outcome is not known. Are the most heavily weighted exposures at the earliest periods of observation or the latest?

The authors propose a two-step approach to estimating the functional form of the PDL.

1. Fit a multivariate regression model simultaneously adjusting for all possible lagged effects.

2. Using the model estimates and their standard errors, input these to a weighted regression model using the lagged interval as the "X" variable and the regression model output as the "Y" variable. Control for the lag / time with a flexible polynomial spline.

The method of doing this doesn't matter whether the exposure is categorical or continuous. The spline/polynomial trendline describes the relation between the DL effect and the actual lag (which is continuous or pseudocontinuous in time).

• thank you for highlighting that the type of variable does not matter, this way I can proceed following examples that used continous exposures and see how I can interpret the results – Edith Apr 22 at 21:40