Theoretical disease model | Bayesian approach to estimating the model from data | Data required by the Bayesian model | ...Given estimates and denominators | Smoothly disaggregating data from age groups to years of age | Determining numerators and denominators from point and/or interval estimates | Bayesian modelling process | Alternative models / prior assumptions | Fitting Bayesian models with the Stan software via disbayes | Running disbayes: optimisation method | Running disbayes: MCMC method | IHD example: Results | Other options to disbayes | Advanced models | Hierarchical models | Hierarchical models with additive area and gender effects | Trends through time (non-hierarchical models only) | References

Introduction | Installing CmdStan | Compiling a model | Running MCMC | Posterior summary statistics | Summaries from the posterior package | CmdStan's stansummary utility | Posterior draws | Extracting draws | Plotting draws | Sampler diagnostics | Extracting diagnostic values for each iteration and chain | Sampler diagnostic warnings and summaries | CmdStan's diagnose utility | Running optimization and variational inference | Optimization | Laplace Approximation | Variational (ADVI) | Variational (Pathfinder) | Saving fitted model objects | Comparison with RStan | Additional resources

Introduction | Compilation | Immediate compilation | Delayed compilation | Pedantic check | Stan model variables | Executable location | Processing data | Named list of R objects | JSON file | R dump file | Writing CmdStan output to CSV | Default temporary files | Non-temporary files | Reading CmdStan output into R | Lazy CSV reading | read_cmdstan_csv() | as_cmdstan_fit() | Saving and accessing advanced algorithm info (latent dynamics) | Developing using CmdStanR | Pre-compiled Stan models in R packages | Troubleshooting and debugging

Introduction | Adding profiling statements to a Stan program | Accessing the profiling information from R | Comparing to a faster version of the model | Per-gradient timings, and memory usage | Accessing and saving the profile files | References

Examples | Simplest model: no external data | Note on model tuning | Note on computation settings | Divergent transitions | Restricted mean survival | Custom posterior summaries | Extrapolation using long term population data | Modelling differences between the trial and external data | Expert elicitation on the long term | Covariates | Covariate-specific outputs | Standardised outputs | Notes on computation of standardised outputs | Time-dependent standardised outputs | Non-proportional hazards model | Treatment effect waning models | Model comparison | Cure models | Additive hazards / relative survival models | Background hazard defined at all times | Stratified background hazards | Background hazard only defined at the event times | Comparison with other ways of supplying external data in survextrap

Summary statistics | Extracting posterior draws/samples | Structured draws similar to rstan::extract()

M-splines | Traditional M-spline basis | Smoothed M-spline basis | Using M-splines to represent particular hazard shapes | Why not other kinds of spline? | Bayesian model specification | Prior distribution for the hazard curve | Choice of knots when modelling data | Effect of covariates on the hazard | Proportional hazards model | Flexible, non-proportional hazards model | Cure models | Relative survival / additive hazards models | Combining relative survival and cure models | Treatment effect waning models | Principles | Waning model: details | Waning models: example | Waning models: distribution utilities

Converting prior judgements about survival to external data | Further notes on elicitation | Priors on spline parameters | Plotting plausible hazard trajectories | Constant hazard level | Hazard as a function of time | Ratio between high and low hazards over time | Hazard ratios for effects of covariates | SD of hazard ratios over time in non-proportional hazards models

Phase-type shape-scale distributions | Implementation in msmbayes | Specifying a basic semi-Markov model | Summarising shape parameters | Choice of priors | Comparing the Gamma and Weibull | Sojourn distribution | Specifying a semi-Markov model with covariates | Time acceleration factors | Outputs from fitted models by covariates | Semi-Markov models with competing risks | Summarising covariate effect parameters | Summarising outputs by covariates

Phase-type semi-Markov models | Fitting phase-type models in msmbayes | Example: data simulated from a standard Markov model | Example: data simulated from a phase-type model

Multi-state models with misclassification | Specifiying prior distributions for misclassification probabilities | Fixed misclassification probabilities

Motivation and design | General parametric survival model | Fitting standard parametric survival models | Custom survival distributions | Arbitrary-dimension models | Multi-state models | Potential extensions

Simple example model | Specifying model inputs | Specifying model outputs | Expected value of perfect information | Computation using random sampling | Using the voi package to calculate EVPI | Analytic computation | Expected value of partial perfect information | Invoking the evppi function. | Changing the default calculation method | Gaussian process regression | Multivariate adaptive regression splines | INLA method | Bayesian additive regression trees (BART) | Tuning the generalized additive model method | Single-parameter methods | Traditional Monte Carlo nested loop method | Model evaluation function | Parameter simulation function | Invoking evppi_mc | Accounting for parameter correlation | Expected value of sample information | Function to generate study data | Built-in study designs | Importance sampling method | Moment matching method | Moment matching method: example using a built-in study design | Moment matching method: example using a custom study design | Value of Information in models for estimation | EVPI and EVPPI for estimation | How regression-based EVPPI estimation works | EVSI for estimation | Expected net benefit of sampling

Option 1: Using RStan for all chunks | Option 2: Using CmdStanR for all chunks | Example | Option 3: Using both RStan and CmdStanR in the same R Markdown document | Caching chunks | Running interactively

Background | Standardized survival measures | Calculating marginal expected survival and hazard | Incorporation of background mortality into survival models | standsurv | A worked example: the pbc dataset | A stratified Weibull model | Using standsurv to calculate marginal survival | Other metrics: marginal hazards and marginal RMST | Calculating contrasts | Confidence intervals and standard errors | Adding age as a covariate | Calculating expected survival and hazard in standsurv | Incorporation of background mortality | Conclusions | References

Example EVSI dataset | EVSI curves | Expected net benefit of sampling | Optimal sample size | Smooth interpolation | Note about uncertainty | Curve of optimal sample size | Probability of a cost-effective trial

Overview | Multi-state modelling using cause-specific hazards | Multi-state modelling using mixtures | Comparison of frameworks for parametric multi-state modelling

Examples of custom distributions | Examples of custom model summaries | Spline models | Right truncation: retrospective ascertainment

a2bcovid: introduction | Times of symptom onset | Genome sequence alignment data | Patient location data | Staff location data | Example analysis | Using just the symptom onset times | Using symptom onset times and sequence data | Using symptom onset times, sequence data and patient location data | Using symptom onset times, sequence data, patient location and staff location data | Additional plotting options