Introduction The Cox proportional hazards model is frequently used to model survival or time-to-event data. In occupational settings it is common to have an occupational exposure as one of the explanatory variables in the model and the association between the outcome and this exposure is of interest. Interpretation of nonlinear exposure-response relationships is useful in epidemiological risk assessment and methods for modelling nonlinearities are needed in those situations when a linear exposure-response is not expected or when one desires to formally assess a nonlinear association.

Methods Truncated power basis expansions and penalised spline methods are demonstrated for estimating nonlinear exposure-response relationships. Interpretation of the nonlinear estimates are given. Methods are illustrated on a simulated data set under a known exposure-response relationship and in a data application examining the association between risk of carpal tunnel syndrome and job physical exposure as measured by the Strain Index in an occupational cohort.

Discussion Regression modelling often focuses on interpreting coefficient estimates. When exposure-response relationships are nonlinear and a nonparametric or smoothing method is used to estimate the relationship, the resulting regression coefficients are not individually interpretable. But, these methods do provide effect size estimates which are interpretable – estimates at specific exposures of interest. The methods can be coded directly in R, using readily available example R code as a guide.