Estimating dose equivalence for new routes of drug administration

For patient's convenience, dose administration of insulin via oral inhalation is often considered as an alternative to subcutaneous administration. An important statistical problem is to estimate dose equivalence, which is the amount of drug needed to be delivered by inhalation to generate an equivalent pharmacokinetic (PK) response produced by a therapeutic dose of subcutaneous insulin. Because of high intersubject variability, a crossover design clinical trial is typically used where data from both routes of administration are obtained from the same subject. A linear mixed effects model is proposed to describe the relationship between AK response and insulin dose for the two routes of administration. Estimation of dose equivalence in this setting has not been discussed in the statistical literature. Several competing methods for estimating dose equivalence are proposed and contrasted. A formula for calculating an approximate sample size necessary to estimate dose equivalence with a desired precision for the new route of administration is also provided.