Some flexible parametric distributions for modelling time-to-event data

Parametric distributions

Time-to-event data appears in many research areas such as medicine, engineering, biology, and finance, to name but a few. For instance, modelling and understanding the survival times of cancer patients has become an important aim of many countries. In statistical terms, times-to-event correspond to a sample of positive observations, possibly censored due to lost of follow-up or administrative censoring. These observations represent either the time at which the event of interest happens (e.g. death of a patient or failure of an electric device) or the last time of follow-up. There exist several approaches to model time to event data, such as nonparametric, semiparametric, and parametric methods. Parametric distributions represent a parsimonious approach to modelling time-to-event data since they are typically easier to implement and to interpret. There is a large catalogue of flexible parametric distributions that can be used to model this kind of data. This shiny app illustrates different features (Hazard, Cumulative Hazard, and Survival functions) of interest of some of the most popular parametric distributions used to model time-to-event data. By changing the values of the parameters of the corresponding distributions, using the bars on the left hand side, the user can visualise the effect on the shapes of the hazard, cumulative hazard, and survival functions.
References
1. The Gompertz distribution: https://en.wikipedia.org/wiki/Gompertz_distribution
2. The log-logistic distribution: https://en.wikipedia.org/wiki/Log-logistic_distribution
3. The log-normal distribution: https://en.wikipedia.org/wiki/Log-normal_distribution
4. The Exponential distribution: https://en.wikipedia.org/wiki/Exponential_distribution
5. The Weibull distribution: https://en.wikipedia.org/wiki/Weibull_distribution
6. The ExponentiatedWeibull distribution: https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution
7. The Generalized Gamma distribution: https://en.wikipedia.org/wiki/Generalized_gamma_distribution