The case-time-control design is an extension of the case-crossover design capable of handling time trends in the exposure of the general population. Time-invariant confounders are controlled for by the design itself. The idea is to compare the exposure status of a person in one or several reference periods during which no event occurred with the exposure status of the same person in the index period where the event occurred. By comparing case-crossover results in cases to case-crossover results in controls, the exposure-outcome association can be estimated by conditional logistic regression. We review the mathematical assumptions underlying the case-time-control design and examine sensitivity to deviations from the assumed independence of within-individual exposure history. Results from simulating various scenarios suggest that the design is quite robust to deviations from this model assumption. In addition, we show that changes in exposure probability over time can be modeled in a flexible way using splines.