One of the key purposes of the Cox event history technique is to explain the causes behind the differences or similarities between the events encountered by subjects. For instance, Cox regression may be used to evaluate why certain individuals are at a higher risk of encountering some diseases than others. It can thus be effectively applied to studying acute or chronic diseases, hence the interest in medical science. The Cox event history model mainly focuses on the hazard function, which produces the probabilities of an event occurring randomly at any time or at a specific period or instance in time.
The basic Cox event history model can be summarized by the following function:
h(t) = h0(t)e(b1X1 + b2X2 + K + bnXn)
Where; h(t) = rate of hazard
h0(t) = baseline hazard function
bX’s = coefficients and covariates.
Cox event history mainly can be categorized under three models- nonparametric, semi-parametric and parametric.
Non-parametric: The non-parametric model does not make any assumptions about the hazard function or the variables affecting it. Hence, only a limited number of variable types can be handled with the help of a non-parametric model. This type of model involves the analysis of empirical data showing changes over a period of time and cannot not handle continuous variables.
Semi-parametric: Just like the non-parametric model, the semi-parametric model also does not make any assumptions about the shape of the hazard function or the variables affecting it. What makes this model different is that it assumes that the rate of the hazard is proportional over a period of time. The estimates for the hazard function shape can be derived empirically as well. Multivariate analyses are supported by semi-parametric models and are often considered a more reliable fitting method for choice in Cox event history analysis.
Parametric: In this model, the shape of the hazard function and the variables affecting it are determined in advance. Multivariate analyses of discrete and continuous explanatory variables is supported by the parametric model. However, if the hazard function shape is incorrectly estimated, then there are chances that the results could be biased. Parametric models are frequently used to analyze the nature of time dependency. It is also particularly useful for predictive modeling because the shape of the baseline hazard function can be determined correctly by the parametric model.
Cox event history analysis involves the use of certain assumptions. Like with every other statistical method or technique, if an assumption is violated, it will often lead to the results not being statistically reliable. The major assumption is that in using Cox event history, with the passage of time, independent variables do not interact with each other. In other words, the independent variables should have a constant hazard rate over time.
In addition, Hazard rates are rarely smooth in reality. Frequently they need to be smoothened in order for them to be useful for Cox Event History analysis.
Applications of Cox Event History
Cox event history can be applied in many fields although initially it was used primarily in medical and other biological sciences. Today it’s an excellent tool for other applications, frequently used as a statistical method where the dependent variables are categorical, especially in socio-economic analyses. For instance, in the field of economics, Cox event history is used extensively to relate macro or micro economic indicators in terms of a time series. For instance, figuring out the relationship between unemployment or employment with time. In addition, in commercial applications, Cox event history can be applied to estimate the lifespan of a certain machine and break down points based on historical data.
