Abstract
Even if the value of the risk factor evolves continuously in the extended Cox model, the inference may be somewhat biased because it employs a discrete approximation method. As a result, if the risk factor’s value not only fluctuates constantly but also contains measurement error, a model that substitutes the average value rather than the measured value of the risk factor might be considered. Such a model is known as a joint model. After introducing the most widely used the present-value model among joint models, this model was extended to various types of data. In addition, several residuals for model diagnosis were introduced, methods for predicting the probability of event occurrence and the value of the longitudinal risk factor by application of the estimation model were introduced, and an index that can evaluate how well the longitudinal risk factors divide patients into high-risk and low-risk groups was introduced. Finally, all the statistical inference methods introduced in this study were implemented using the JM R package and the source codes were supplied.
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