A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations

There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from the Bayesian estimation perspective. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated, an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.

A practical guide to pre-trial simulations for Bayesian adaptive trials using SAS and BUGS

It is often unclear what specific adaptive trial design features lead to an efficient design which is also feasible to implement. Before deciding on a particular design, it is generally advisable to carry out a simulation study to characterise the properties of candidate designs under a range of plausible assumptions. The implementation of such pre‐trial simulation studies presents many challenges and requires considerable statistical programming effort and time. Despite the scale and complexity, there is little existing literature to guide the implementation of such projects using commonly available software. This Teacher's Corner article provides a practical step‐by‐step guide to implementing such simulation studies including how to specify and fit a Bayesian model in WinBUGS or OpenBUGS using SAS, and how results from the Bayesian analysis may be pulled back into SAS and used for adaptation of allocation probabilities before simulating subsequent stages of the trial. The interface between the two software platforms is described in detail along with useful tips and tricks. A key strength of our approach is that the entire exercise can be defined and controlled from within a single SAS program.

Bayesian population pharmacokinetic modeling of florfenicol in pigs after intravenous and intramuscular administration

Bayesian population pharmacokinetic models of florfenicol in healthy pigs were developed based on retrospective data in pigs either via intravenous (i.v.) or intramuscular (i.m.) administration. Following i.v. administration, the disposition of florfenicol was best described by a two-compartment open model with the typical values of half-life at α phase (t_1/2α ), half-life at β phase (t_1/2β ), total body clearance (Cl), and volume of distribution (V_d ) were 0.132 ± 0.0289, 2.78 ± 0.166 hr, 0.215 ± 0.0102, and 0.841 ± 0.0289 L kg^-1 , respectively. The disposition of florfenicol after i.m. administration was best described by a one-compartment open model. The typical values of maximum concentration of drug in serum (C_max ), elimination half-life (t_1/2Kel ), Cl, and Volume (V) were 5.52 ± 0.605 μg/ml, 9.96 ± 1.12 hr, 0.228 ± 0.0154 L hr^-1  kg^-1 , and 3.28 ± 0.402 L/kg, respectively. The between-subject variabilities of all the parameters after i.m. administration were between 25.1%-92.1%. Florfenicol was well absorbed (94.1%) after i.m. administration. According to Monte Carlo simulation, 8.5 and 6 mg/kg were adequate to exert 90% bactericidal effect against Actinobacillus pleuropneumoniae after i.v. and i.m. administration.

Local site differences in survival and parasitism of periwinkles (Littorina sitkana Philippi, 1846)

The periwinkle, Littorina sitkana, is found throughout the intertidal zone, often in isolated subpopulations. The majority of trematode parasites use snails as intermediate hosts, and decreased survivorship is often observed in snails infected with trematodes. Sampling L. sitkana from four sites in Barkley Sound, British Columbia, Canada, we test the effects of parasitic infection on snail survival using maximum likelihood and Bayesian approaches using the software MARK and WinBUGS. We found that survival of periwinkles and trematode community composition differed among sites, but survival and trematode prevalence were uncorrelated. WinBUGS performed better than MARK in two ways: (1) by allowing the use of information on known mortality, thus preventing survival overestimation; and (2) by giving more stable estimates while testing the effect of body size on snail survival. Our results suggest that snail survival depends heavily on local environmental factors that may vary greatly within a small geographical region. These findings are important because the majority of experimental studies on survival are done on snails from a single location.

The pharmacokinetics of dexmedetomidine during long-term infusion in critically ill pediatric patients. A Bayesian approach with informative priors

The purpose of this study was to assess the pharmacokinetics of dexmedetomidine in the ICU settings during the prolonged infusion and to compare it with the existing literature data using the Bayesian population modeling with literature-based informative priors. Thirty-eight patients were included in the analysis with concentration measurements obtained at two occasions: first from 0 to 24 h after infusion initiation and second from 0 to 8 h after infusion end. Data analysis was conducted using WinBUGS software. The prior information on dexmedetomidine pharmacokinetics was elicited from the literature study pooling results from a relatively large group of 95 children. A two compartment PK model, with allometrically scaled parameters, maturation of clearance and t-student residual distribution on a log-scale was used to describe the data. The incorporation of time-dependent (different between two occasions) PK parameters improved the model. It was observed that volume of distribution is 1.5-fold higher during the second occasion. There was also an evidence of increased (1.3-fold) clearance for the second occasion with posterior probability equal to 62 %. This work demonstrated the usefulness of Bayesian modeling with informative priors in analyzing pharmacokinetic data and comparing it with existing literature knowledge.

Exploring the Specifications of Spatial Adjacencies and Weights in Bayesian Spatial Modeling with Intrinsic Conditional Autoregressive Priors in a Small-area Study of Fall Injuries

Intrinsic conditional autoregressive modeling in a Bayeisan hierarchical framework has been increasingly applied in small-area ecological studies. This study explores the specifications of spatial structure in this Bayesian framework in two aspects: adjacency, i.e., the set of neighbor(s) for each area; and (spatial) weight for each pair of neighbors. Our analysis was based on a small-area study of falling injuries among people age 65 and older in Ontario, Canada, that was aimed to estimate risks and identify risk factors of such falls. In the case study, we observed incorrect adjacencies information caused by deficiencies in the digital map itself. Further, when equal weights was replaced by weights based on a variable of expected count, the range of estimated risks increased, the number of areas with probability of estimated risk greater than one at different probability thresholds increased, and model fit improved. More importantly, significance of a risk factor diminished. Further research to thoroughly investigate different methods of variable weights; quantify the influence of specifications of spatial weights; and develop strategies for better defining spatial structure of a map in small-area analysis in Bayesian hierarchical spatial modeling is recommended.

Survival extrapolation using the poly-Weibull model

Recent studies of (cost-) effectiveness in cardiothoracic transplantation have required estimation of mean survival over the lifetime of the recipients. In order to calculate mean survival, the complete survivor curve is required but is often not fully observed, so that survival extrapolation is necessary. After transplantation, the hazard function is bathtub-shaped, reflecting latent competing risks which operate additively in overlapping time periods. The poly-Weibull distribution is a flexible parametric model that may be used to extrapolate survival and has a natural competing risks interpretation. In addition, treatment effects and subgroups can be modelled separately for each component of risk. We describe the model and develop inference procedures using freely available software. The methods are applied to two problems from cardiothoracic transplantation.

A Bayesian network meta-analysis for binary outcome: how to do it

This study presents an overview of conceptual and practical issues of a network meta-analysis (NMA), particularly focusing on its application to randomised controlled trials with a binary outcome of interest. We start from general considerations on NMA to specifically appraise how to collect study data, structure the analytical network and specify the requirements for different models and parameter interpretations, with the ultimate goal of providing physicians and clinician-investigators a practical tool to understand pros and cons of NMA. Specifically, we outline the key steps, from the literature search to sensitivity analysis, necessary to perform a valid NMA of binomial data, exploiting Markov Chain Monte Carlo approaches. We also apply this analytical approach to a case study on the beneficial effects of volatile agents compared to total intravenous anaesthetics for surgery to further clarify the statistical details of the models, diagnostics and computations. Finally, datasets and models for the freeware WinBUGS package are presented for the anaesthetic agent example.