# Cox Event History

Quantitative Results
Statistical Analysis

Cox event history is a branch of statistics that deals mainly with the death of biological organisms and the failure of mechanical systems. It is also sometimes referred to as a statistical method for analyzing survival data. Cox event history is also known as various other names, such as survival analysis, duration analysis, or transition analysis. Generally speaking, this technique involves the modeling of data structured in a time-to-event format. The goal of this analysis is to understand the probability of the occurrence of an event. Cox event history was primarily developed for use in medical and biological sciences. However, this technique is now frequently used in engineering as well as in statistical and data analysis.

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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 contracting some diseases. Thus, it can be effectively applied to studying acute or chronic diseases, hence the interest in Cox regression by the medical science field. The Cox event history model mainly focuses on the hazard function, which produces the probability of an event occurring randomly at random times 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 can be categorized mainly 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. Consequently, 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 handle continuous variables.

Semi-parametric: Similar to 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 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 use in a 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 are supported by the parametric model. However, if the hazard function shape is incorrectly estimated, then there is a chance 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. As with every other statistical method or technique, if an assumption is violated, it will often lead to the results being statistically unreliable. 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 of rate over time.

In addition, hazard rates are rarely smooth in reality. Frequently, these rates need to be smoothed over 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 is 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, one could determine the relationship between unemployment or employment over 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.