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Background Intake of macronutrients and its components are associated with mortality and morbidity. Isocaloric substitution analysis is a tool to examine how changing the source of energy intake (e.g. from saturated to monounsaturated fat) is associated with health. However, conventional methods assume linearity, which may be untrue in many cases. This paper presents a nonlinear alternative, using UK Biobank data as an example data set. Methods Nonlinear isocaloric substitution analysis was conducted using penalised cubic splines in Cox proportional hazard models. In the UK Biobank, 195,658 participants completed at least one dietary questionnaire and were included in the analyses. Diet was assessed using the Oxford WebQ, a web-based 24-hour recall questionnaire. Prospective all-cause mortality was derived from on linked death records. Results More than half of the associations between macronutrient intake and all-cause mortality were nonlinear. Nonlinear isocaloric substitution analysis provides effect sizes conditional on the current intake, while conventional analysis provides an average over the whole range of intake. For example, conventional isocaloric substitution estimated no effect of replacing sugar with starch. However, the nonlinear method revealed that replacing sugar with starch was associated with a higher risk when the current starch intake was greater than 30% of total energy, and with a lower risk when current intake was less than 25%. Conclusions Nonlinear isocaloric substitution provides an alternative to conventional isocaloric substitution analysis when the underlying association is nonlinear. Key messages Nonlinear associations are common in nutritional epidemiology. In such cases, nonlinear isocaloric substitution analyses should be used.

194Nonlinear isocaloric substitution analysis in nutritional epidemiology: An example using the UK Biobank data