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A time-varying covariate (also called time-dependent covariate) is a term used in statistics, particularly in survival analysis. [1] It reflects the phenomenon that a covariate is not necessarily constant through the whole study Time-varying covariates are included to represent time-dependent within-individual variation to predict individual responses. [2]
More generally, survival analysis involves the modelling of time to event data; in this context, death or failure is considered an "event" in the survival analysis literature – traditionally only a single event occurs for each subject, after which the organism or mechanism is dead or broken.
Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate .
Most survival analysis methods assume that time can take any positive value, and f T is the PDF. If the time between observed AC failures is approximated using the exponential function, then the exponential curve gives the probability density function, f T, for AC failure times.
In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
Recurrent event analysis is a branch of survival analysis that analyzes the time until recurrences occur, such as recurrences of traits or diseases. Recurrent events are often analyzed in social sciences and medical studies, for example recurring infections, depressions or cancer recurrences.
The lapse of time until that critical event occurs is usually interpreted generically as a ‘survival time’. In some applications, the threshold is a set of multiple states so one considers competing first hitting times for reaching the first threshold in the set, as is the case when considering competing causes of failure in equipment or ...
In survival analysis, hazard rate models are widely used to model duration data in a wide range of disciplines, from bio-statistics to economics. [1] Grouped duration data are widespread in many applications.