Table 1 Definitions

Bayesian credible interval (BCI)

An interval of a posterior distribution that defines the domain within which the value of a parameter lies with a specified probability (typically 0.95 or 95 %). The Bayesian analogy to the classical frequentist confidence interval.

Best linear unbiased prediction (BLUP)

A frequentist technique used in linear mixed models to estimate random effects terms, so-called empirical best linear unbiased predictors (EBLUPs).

Bootstrapping

A numerical resampling technique typically used to generate estimates of uncertainty associated with calculated statistical quantities.

Cure rate (CR)

Proportion of individual hosts positive for parasites who become parasitologically negative after treatment.

Intensity reduction rate (IRR)/egg reduction rate (ERR)

The intensity of infection after treatment expressed as a proportion of the intensity of infection before treatment. For schistosomiasis (and soil-transmitted helminthiases), this is typically expressed as an egg reduction rate; the egg count after treatment expressed as a proportion of the egg count before treatment.

Drug response

Dynamics of parasite (transmission) stages following anthelminthic treatment.

Fixed effect

The component of an effect exerted by a particular value or level of a covariate that is the same among all observations within a unit of a structured dataset

Generalized estimating equation (GEE)

A technique for estimating the parameters of a marginal model fitted to correlated repeated measures (observations). The GEE approach is semi-parametric because it relies on the first two moments of the observed data, but not on the full likelihood.

Generalized linear model (GLM)

An extension of the simple linear regression model that is compatible with error distributions from any of the exponential family of probability distributions, including the normal, Poisson, binomial, and gamma distributions. The simple linear regression model is a GLM with normally distributed errors.

Conditional (linear) mixed model (also called a generalized linear mixed model, GLMM)

An extended GLM that includes a linear predictor comprised of covariate coefficients that exert both fixed and random effects.

Hyperparameter

A parameter in a hieracrchical or multilevel statistical model that governs the distribution of lower-level random effects terms

Marginal model

An adaptation of a GLM for use with correlated repeated measures (observations). Marginal refers to the marginal mean of observations from individuals (units) sharing a set of covariates. A marginal model comprises three model components; a marginal mean, which depends on covariates; a marginal variance, which is typically a function of the marginal mean, and a correlation structure for the repeated measures.

Markov chain Monte Carlo (MCMC)

A stochastic algorithm central to Bayesian statistical inference which samples parameter values from the posterior probability distribution by combining information from the likelihood of the observed data and the prior probability distribution of the parameters.

Random effects

The component of an effect exerted by a particular value or level of a covariate that is different among observations within a unit of a structured dataset. The magnitude of the deviations from the fixed effect component is governed by (typically a normal) distribution defined by estimable hyperparameters.

Repeated measures

Measurements or observations made repeatedly on the same unit, for example, multiple schistosome egg counts measured from the same individual host.

Restricted maximum likelihood (REML) estimation

An alternative to maximum likelihood (ML) estimation for models that include random effects. In REML estimation, the dispersion of the random effects is estimated having averaged over some of the uncertainty in the fixed effects. By contrast, in ML estimation, the fixed effects estimates are treated as precisely correct.

Sandwich estimator

A standard error (SE) of an estimated quantity that is robust to misspecifications in the variance-covariance of the error distribution in a statistical model. Sandwich estimators are typically used with marginal models so that SEs (and confidence intervals) are invariant to inaccuracies in the specification of the repeated measures correlation structure. In this context, sandwich estimators are based on the empirically observed variation among unit-level statistics rather than on the model-derived variance-covariance matrix which depends on the assumed correlation structure.