A repeated time-to-event analysis of onset and offset times of sildenafil erectile response

Sildenafil has been commonly used for the treatment of erectile dysfunction [1]. A previous research explored sildenafil’s effectiveness based on qualitative indices [2], but there has been no report on the quantitative aspect of erectile response of sildenafil. Based on this background, using a repeated time-to-event (RTTE) model, this study aimed to assess onset and offset times of erectile response as the direct measure of drug effects in conjunction with sildenafil pharmacokinetics (PK).
Data were taken from 58 healthy Korean volunteers who received a sildenafil 100mg tablet. Plasma samples for PK analyses were obtained up to 24 hours after dosing, and onset and offset times of erectile response were recorded over 6 hours after dosing. The plasma concentration of sildenafil and primary metabolite, N-demethyl sildenafil, was sequentially modeled, testing various combinations of absorption and disposition models. BQL observations were handled in M3 method [3]. A RTTE model was developed by using an ordinary hazard function for the onset time and a secondary hazard function for the offset time, where the offset hazard function was modeled with its time shifted by the onset time on the assumption that its occurrence was conditioned on the onset event. The hazard functions were modeled under various distributional assumptions including exponential, Gompertz and Weibull distributions. The influence of drug effect was incorporated by scaling the baseline hazard by the exponential of the predicted drug effect. The final models were further tested for covariate effects and evaluated by VPC. PK and PD parameters were estimated using FOCEI and EM methods of NONMEM 7.3.
Parent and metabolite sildenafil concentrations were best described by a two-compartment model with Gamma-weibull absorption [4] and another two-compartment model with enterohepatic recirculation model. The model appropriateness was well confirmed by VPC. For a RTTE model, onset times were best described by Gompertz hazard with scale and shape parameters of 0.70/hr and -1.35/hr, respectively, and offset times by Weibull hazard with scale and shape parameters of 0.66/hr and 1.39/hr, respectively, yielding the estimated median onset and offset times of about 0.45hr and 0.40hr, respectively. Overall, the observed onset and offset times were well included within the 90% predicted intervals by VPC. When plasma concentrations included, the model performance improved. No significant relationship was found between covariates and hazard parameters.
This work has demonstrated the feasibility of applying a RTTE model to quantitatively understanding the drug response in general clinical situations, with an application to the erectile response of sildenafil.

1. Sildenafil Tablets – Pfizer [http://www.pfizer.com/files/products/uspi_viagra.pdf]
2. Gruenwald I, Leiba R, Vardi Y: Effect of sildenafil on middle-aged sexually active males with no erectile complaints: a randomized placebo-controlled double-blind study. Eur Urol 2009, 55(4):969-976.
3. Beal SL, Ways to fit a PK model with some data below the quantification limit. Journal of Pharmacokinetics and Pharmacodynamics, Vol. 28, No. 5, October 2001
4. Provost SB, The Gamma-weibull distribution, Pak. J. Statist. 2011 Vol. 27(2), 111-131