Efficient parameter estimation for models of healthcare-associated pathogen transmission in discrete and continuous time

We describe two novel Markov chain Monte Carlo approaches to computing estimates of parameters concerned with healthcare-associated infections. The first approach frames the discrete time, patient level, hospital transmission model as a Bayesian network, and exploits this framework to improve greatly on the computational efficiency of estimation compared with existing programs. The second approach is in continuous time and shares the same computational advantages. Both methods have been implemented in programs that are available from the authors. We use these programs to show that time discretization can lead to statistical bias in the underestimation of the rate of transmission of pathogens. We show that the continuous implementation has similar running time to the discrete implementation, has better Markov chain mixing properties, and eliminates the potential statistical bias. We, therefore, recommend its use when continuous-time data are available.