A scalable approach for continuous time Markov models with covariates.

Existing methods for fitting continuous time Markov models (CTMM) in the presence of covariates suffer from scalability issues due to high computational cost of matrix exponentials calculated for each observation. In this article, we propose an optimization technique for CTMM which uses a stochastic gradient descent algorithm combined with differentiation of the matrix exponential using a Padé approximation. This approach makes fitting large scale data feasible. We present two methods for computing standard errors, one novel approach using the Padé expansion and the other using power series expansion of the matrix exponential. Through simulations, we find improved performance relative to existing CTMM methods, and we demonstrate the method on the large-scale multiple sclerosis NO.MS data set.

Combining MCMC with 'sequential' PKPD modelling.

We introduce a method for preventing unwanted feedback in Bayesian PKPD link models. We illustrate the approach using a simple example on a single individual, and subsequently demonstrate the ease with which it can be applied to more general settings. In particular, we look at the three 'sequential' population PKPD models examined by Zhang et al. (J Pharmacokinet Pharmacodyn 30:387-404, 2003; J Pharmacokinet Pharmacodyn 30:405-416, 2003), and provide graphical representations of these models to elucidate their structure. An important feature of our approach is that it allows uncertainty regarding the PK parameters to propagate through to inferences on the PD parameters. This is in contrast to standard two-stage approaches whereby 'plug-in' point estimates for either the population or the individual-specific PK parameters are required.

Determination of an optimal dosage regimen using a Bayesian decision analysis of efficacy and adverse effect data.

One of the aims of Phase II clinical trials is to determine the dosage regimen(s) that will be investigated during a confirmatory Phase III clinical trial. During Phase II, pharmacodynamic data are collected that enables the efficacy and safety of the drug to be assessed. It is proposed in this paper to use Bayesian decision analysis to determine the optimal dosage regimen based on efficacy and toxicity of the drug oxybutynin used in the treatment of urinary urge incontinence. Such an approach results in a general framework allowing modeling, inference and decision making to be carried out. For oxybutynin, the repeated measurement efficacy and toxicity data were modeled using nonlinear hierarchical models and inferences were based on posterior probabilities. The optimal decision in this problem was to determine the dosage regimen that maximized the posterior expected utility given the prior information on the model parameters and the patient response data. The utility function was defined using clinical opinion on the satisfactory levels of efficacy and toxicity and then combined by weighting the relative importance of each pharmacodynamic response. Markov chain Monte Carlo (MCMC) methodology implemented in Win-BUGS 1.3 was used to obtain posterior estimates of the model parameters, probabilities and utilities.