Glossary
The vocabulary used across this site, defined once. Terms link here automatically from every primer, tutorial and software page that uses them.
Short definitions, not explanations. Where a term has a primer or a worked example behind it, the entry points at it — and where merlin implements it, the entry carries the syntax — R, Stata, or both.
A
accelerated failure timealso: AFT
A parameterisation where covariates scale time rather than the hazard: log T = mu + x beta + sigma epsilon.
The AFT families are "lognormal", "loglogistic" and "ggamma".stmerlin x, distribution(lognormal | loglogistic | ggamma)adaptive quadraturealso: AGHQ, adaptive
Gauss-Hermite quadrature with the points recentred and rescaled per cluster, so far fewer of them are needed for the same accuracy.
method = "aghq" (the default).intmethod(mvaghermite) (the default)analytic gradientalso: analytic gradients, analytic derivative
A hand-derived derivative of the likelihood rather than a numerical one. Faster and exact, and the thing most worth testing, since a subtly wrong gradient still converges — to the wrong place.
association structure
How the longitudinal submodel enters the survival submodel in a joint model — the current value, the slope, the area under the trajectory, or a combination.
B
baseline hazard
The hazard when every covariate is zero — the shape of risk over time before any covariate effect is applied.
C
cause-specific hazardalso: cause-specific
The hazard for one cause, treating the others as censored. Answers a question about rates, not about the probability of that cause occurring.
censoringalso: censored
When the event time is not observed exactly, only bounded — most often because follow-up ended before the event happened.
clock-resetalso: clock-forward
Whether the time axis for a transition restarts on entering the state (clock-reset) or keeps running from origin (clock-forward). The choice changes the estimand.
competing risks
More than one kind of event can end follow-up and only the first is seen. Because a death has one cause, the end states are mutually exclusive.
Cox model
Semi-parametric proportional-hazards regression: covariate effects are estimated while the baseline hazard is left entirely unspecified.
family = "cox" via the Stata wrappers; merlin for R models the baseline explicitly.stmerlin x, distribution(cox)cumulative hazard
The hazard accumulated up to time t. Survival is its negative exponential, which is why modelling on this scale is convenient.
cumulative incidencealso: cumulative incidence function, CIF
The probability of failing from a given cause by time t, accounting for the fact that the other causes remove people from risk.
cure modelalso: mixture cure, non-mixture, cure fraction
Allows a fraction of the population to be long-term event-free, rather than forcing survival to zero given enough time.
cure = "mixture".cure() on the survival modelcurrent value
The commonest association structure: the hazard depends on the biomarker's expected value at that instant.
D
data-generating mechanismalso: DGM
The known-truth model a simulation study samples from, against which an estimator's behaviour is judged.
E
extrapolation
Predicting beyond observed follow-up. The model's parametric form, not the data, drives the answer — which is why the choice of family matters most exactly where it is least checkable.
F
flexible parametricalso: Royston-Parmar, Royston–Parmar
Modelling the log cumulative hazard with restricted cubic splines in log time — a smooth baseline that can take almost any shape, unlike a one-parameter distribution.
family = "rp", with df = or knots =.stmerlin x, distribution(rp) df(3)frailtyalso: frailties
A random effect on the hazard scale. Because the hazard is not collapsible, the population-average hazard ratio is attenuated relative to the cluster-specific one.
G
Gauss-Hermitealso: GHQ, Gauss–Hermite
Quadrature with points and weights chosen for a Gaussian integrand — the standard choice for normally distributed random effects.
method = "ghq".intmethod(ghermite)generalised gammaalso: ggamma
A three-parameter family containing the Weibull, log-normal and gamma as special cases, which makes it useful for testing which of them a dataset prefers.
family = "ggamma".stmerlin x, distribution(ggamma)Gompertz
A distribution whose hazard rises or falls exponentially — the standard choice for adult human mortality.
family = "gompertz".stmerlin x, distribution(gompertz)H
hazard
The instantaneous rate of the event at time t among those still at risk. Not a probability: it has units of one over time and is not bounded above.
hazard ratioalso: hazard ratios
The ratio of two hazards. Constant over time only if proportional hazards holds; otherwise it is a weighted average of a changing effect.
Hessian
The matrix of second derivatives. Its inverse at the maximum gives the standard errors, so an inaccurate one produces confident nonsense.
I
immortal time bias
Time during which the outcome cannot occur by construction, assigned to the group that only membership after that period defines — which makes the exposure look protective.
interval-censoringalso: interval-censored
The event is known to have happened between two visits, but not when. Common wherever the outcome is only detectable at examination.
Code the failure indicator 2 and pass the interval endpoint.merlin (t x, family(rp, df(3) failure(d) linterval(t_upper)))J
joint modelalso: joint models, joint modelling
Fits a longitudinal outcome and a survival outcome together, linked through shared random effects, so the biomarker path informs the hazard.
K
Kaplan-Meieralso: Kaplan–Meier
The non-parametric estimate of the survival function: a step function that drops at each event and is unaffected by censoring except through the risk set.
L
Laplace approximationalso: Laplace
Approximates the integral by a Gaussian at its mode. The single-point limit of adaptive quadrature: fastest, and least accurate when the integrand is skewed.
method = "laplace".left-truncationalso: left-truncated, delayed entry
Individuals enter observation some time after the origin, so anyone who had the event before entry never appears. Not the same as censoring, and it biases naive analyses.
ltruncated() on the model, or stset ..., enter()length of stay
Expected time spent in a state over a horizon. In health economics it is what carries the cost and the utility.
life tablealso: life tables
Population mortality rates by age, sex and calendar time, used as the expected-mortality reference in relative survival.
likelihoodalso: log-likelihood
The probability of the observed data under the model, read as a function of the parameters. Fitting maximises it, usually on the log scale.
M
multilevelalso: hierarchical
More than one level of clustering — patients within hospitals within trials — with a random effect at each.
stmixed, or nested M1[trial]@1 M2[trial>id]@1 in merlinmulti-statealso: multistate, multi-state model
A model with more than two states and defined transitions between them — illness-death, recurrence-then-death, and so on. Competing risks is the special case with one start state and no return.
N
net survival
Survival that would be seen if the disease were the only possible cause of death. The quantity a relative-survival model estimates.
P
partial likelihood
What the Cox model maximises: it conditions on the observed event times so the baseline hazard drops out and never has to be estimated.
probabilistic sensitivity analysisalso: PSA
Propagating parameter uncertainty through a health-economic model by resampling the fitted parameters, rather than varying them one at a time.
proportional hazardsalso: non-proportional, non-proportional hazards
The assumption that the ratio of hazards between groups does not change with time. On the log-hazard scale the groups run parallel.
Q
quadraturealso: numerical integration
Approximating an integral by a weighted sum at chosen points. Needed whenever random effects have to be integrated out.
nodes = sets how many points.intpoints(#)R
random effectalso: random effects
A parameter that varies by cluster and is drawn from a distribution, rather than estimated separately for every cluster.
lme4-style: (1 | id).M1[id]@1 in the linear predictorrandom intercept
A per-cluster shift in the linear predictor: some hospitals, trials or patients are simply higher-risk than others.
Written (1 | id).M1[id]@1random slope
A per-cluster covariate effect — the treatment works better in some centres than others.
Written (1 + trt | id).time#M2[id]@1 alongside M1[id]@1relative survivalalso: excess hazard
Mortality in a diseased population over and above what a matched general population would experience, estimated by adding an expected rate to the model rather than subtracting it afterwards.
Pass the expected rate as bhazard =.stmerlin x, distribution(rp) df(3) bhazard(rate)restricted cubic splinealso: restricted cubic splines, spline, splines
A piecewise cubic that is forced linear beyond the outer knots, so it stays well behaved where the data thin out — which is exactly where extrapolation happens.
rcs(t, df(3)) inside a merlin linear predictorrestricted mean survival timealso: RMST, restricted mean
Average survival up to a chosen horizon — the area under the survival curve. Well defined without proportional hazards, which a hazard ratio is not.
right-censoringalso: right-censored
The commonest kind: the participant was still event-free when observation stopped, so the true event time is known only to be later than that.
S
simulation study
Generating data from a known truth to check that a method recovers it — bias, coverage and precision, none of which are observable on real data.
standardised survivalalso: marginal survival, standardised
Averaging predicted survival over the observed covariate distribution, giving a population-level curve rather than one for a covariate pattern nobody has.
subdistribution hazardalso: subdistribution
Keeps those who failed from other causes in the risk set, so its regression coefficients map directly onto the cumulative incidence.
survival function
The probability of surviving beyond time t. Starts at one and never increases.
T
time-dependent effectalso: time-dependent effects
A covariate effect that changes with follow-up time — the direct way to model non-proportional hazards rather than averaging over it.
tvc(x) dftvc(2), or fp(t, powers(0)) in a merlin predictortransition matrix
The square matrix declaring which transitions are possible: a number where a move is allowed, missing where it is not.
transition probabilityalso: transition probabilities
The probability of being in a given state at a given time, having started somewhere specified. What a multi-state model is usually fitted to produce.
W
Weibull
A two-parameter distribution with a monotonic hazard. The one case where proportional hazards and accelerated failure time coincide.
family = "weibull".stmerlin x, distribution(weibull)No term matches that.