Topic

Model inputs and parameters

Every model depends on numerical inputs drawn from published studies, routine data or expert judgement. The concepts here cover probabilities and their conversion to and from rates, transition probabilities, correlated parameters, and Bayesian methods such as Markov chain Monte Carlo for estimating parameters from data.

Concepts in this topic

• Anchoring Bias in ElicitationAnchoring bias in elicitation is an expert's insufficient adjustment from a starting value, giving shifted, too-narrow distributions for model inputs.
• Competing RisksA situation where a person is at risk of more than one type of event, so one event's occurrence prevents another from ever happening.
• Conditional ProbabilityConditional probability is the probability of an event within the restricted set of outcomes in which a specified conditioning event has occurred.
• Contact RateContact rate is the expected number of defined, potentially transmission-relevant encounters an individual has per unit time in an infectious-disease model.
• Correlation MatrixA correlation matrix is a square table containing the pairwise correlation coefficients among a set of variables.
• Distribution FittingDistribution fitting selects a probability distribution and estimates its parameters from data to represent the frequency of possible values under stated assumptions.
• Event ProbabilityAn event probability is the chance that a specified event occurs in a defined population or risk set over a stated time interval.
• Expected UtilityExpected utility is the probability-weighted average of the utilities assigned to an uncertain option's possible outcomes, used to rank choices under risk when preferences satisfy the required axioms.
• Force of InfectionThe rate at which susceptible individuals become infected, determined jointly by disease prevalence and the rate and probability of transmission per contact.
• Gibbs SamplingA Markov chain Monte Carlo algorithm generating samples from a complex joint distribution by iteratively sampling each variable from its conditional distribution.
• Hazard-to-Probability ConversionThe mathematical transformation converting an instantaneous hazard rate into the probability of an event occurring over a specific discrete time interval.
• InterpolationInterpolation estimates a value between observed or modelled data points using an assumed relationship across the interval.
• Interval EstimateA range of values, such as a confidence interval, calculated to convey the uncertainty surrounding a point estimate of a parameter.
• Joint ProbabilityThe probability that two or more events all occur together, calculated as one event's probability multiplied by the others' conditional probability.
• Kalman FilterA recursive estimator that predicts an evolving latent state and updates that estimate and its uncertainty when a new noisy measurement arrives.
• Life TableA structured table that follows a hypothetical population through age or time intervals to summarize deaths, survivors, person-years, and expected remaining life.
• Markov Chain Monte CarloMarkov chain Monte Carlo is a class of simulation methods that constructs a Markov chain with a chosen target distribution as its stationary distribution and uses dependent draws from the chain to approximate expectations and uncertainty under that distribution.
• Metropolis-HastingsA Markov chain Monte Carlo algorithm generating samples by proposing candidate values and accepting or rejecting them by a rule ensuring convergence.
• Parameter EstimationParameter estimation is the process of using evidence and a specified model or estimating rule to infer the values of quantities needed to describe a population, relationship, or decision model.
• Parameter InputA parameter input (model parameter) is a value or distribution entered into a health economic model for a quantity such as a probability, cost or utility.
• Particle FilterA sequential Monte Carlo algorithm that approximates the evolving probability distribution of a hidden state with weighted simulated particles, updating their weights as observations arrive.
• Point EstimateA point estimate is a single numerical value calculated from observed data or a fitted model to represent a specified unknown quantity on a stated scale.
• Posterior ProbabilityThe updated probability of a hypothesis after accounting for observed evidence, combining a prior probability with the likelihood of that evidence.
• Prior ProbabilityThe probability assigned to a hypothesis before accounting for new evidence, representing existing belief later updated through Bayesian analysis.
• ProbabilityProbability is a number between zero and one assigned to the likelihood of a precisely defined event under stated conditions.
• Probability-to-Rate ConversionThe mathematical transformation converting a probability of an event over a discrete time interval into its corresponding continuous-time hazard rate.
• Rate-to-Probability ConversionThe mathematical transformation converting a continuous-time hazard rate into the probability of an event occurring within a discrete time interval.
• Sequential Monte CarloA class of algorithms, including particle filtering, estimating a sequence of unknown quantities over time by updating weighted samples as new data arrive.
• Subgroup AnalysisAn analysis that estimates and compares an association or intervention effect across defined categories of participants, with treatment-effect differences assessed through an interaction on a specified scale.
• Transition ProbabilityA transition probability is the chance of moving from one health state to another, or staying, during one cycle of a Markov or state-transition model.
• Transmission ProbabilityThe likelihood that an infectious disease passes from an infected to a susceptible individual during a single contact between them.
• Treatment Effect HeterogeneityVariation in the size or direction of a treatment's effect across different patients, so a trial's average effect may not fit any one person.
• Variance-Covariance MatrixA symmetric array of variances and pairwise covariances that describes the scale and joint movement of a set of random quantities or estimates.