Early methodological approaches Sample Clauses

Early methodological approaches. The first attempt of modelling neural networks for censored data was made by Xxxxxx and Xxxxx in 1992 [14]. The authors use a simple 3-layer FFANN and code time as an additional prognostic variable. Input features are replicated for several time intervals [1, · · · , Tmax] with equal event rates, where Tmax is the maximum follow- up time (in years). A patient who experienced the event of interest, is replicated exactly Tmax times, while a censored patient is replicated only until the time of censoring. The output layer contains a single output unit representing the survival status and is set to 0 for all time intervals where the subject is alive, and to 1 for the time interval where the event of interest occurred (and the following intervals up to Tmax). The hyperbolic tangent activation function is used for the units in the hidden and output layers. To correct for the bias introduced by the data transformation in a long format (as the number of deaths is over-represented in the late intervals), a selective sampling approach is performed, such that the proportion of deaths matches the information of the Xxxxxx-Xxxxx [8] estimate. Selective sampling, however, is not an exact procedure and weighting cases would be a preferable approach [9]. The output layer provides death probabilities and can be seen as a prognostic index. An advantage of the methodology proposed by Xxxxxx and Xxxxx is that time-varying covariates can be included, as subject entries are duplicated across multiple time periods. In 1994, Xx Xxxxxxxxxx and Xxxxxx proposed two alternative FFANNs [15]. The first is very similar to Ravdin and Xxxxx’x approach, and also specifies the time interval as an additional input variable. In this model, the distinct time intervals are selected such that each interval reflects a constant increase in event probability. Again, no data is present for censored cases after the last interval on study. Bias is controlled in a similar fashion, by obtaining the same frequency of censoring and events. The second FFANN proposed by Xx Xxxxxxxxxx and Xxxxxx is a multiple time point model. This network does not require any modification of the wide data format and can accommodate only baseline characteristics and no time-varying covariates. The output layer is a vector with multiple output units (nodes) of Ik non-overlapping ordered intervals, and estimates event (death) probabilities. In the training data censored cases can be imputed at given times of follow-up (e.g., b...