## 4 Discussion  
In this paper we presented a novel approach for analysing the performance of smart alerting real-time Healthcare 4.0 systems for scenarios in which there is no prior information that could indicate authenticity of the generated alert. The introduced technique is not a summary statistic, like for example AUC, Precision/Recall or RMSE are, where the quality of alerting algorithm is reported as a single number. Instead, the proposed approach enables researchers to dynamically estimate the probabilities that will describe for how long the patient physiological parameters exceed a certain threshold during the APA, and suggests that longer survival times indicate a better algorithm performance. In particular, in the VILIAIert use case scenario, we hypothesised that if the alert was generated when the metric \(TV_{15}>8\) mL/kg for four consecutive 15 min intervals, then this metric should continue to be above this threshold until the end of the 6 h long APA follow-up period. Hence the motivation for the research presented in this paper, is to model the time until the \(TV_{15}\) signal drops below 8 mL/kg (which we associate the clinical activity that results in stabilisation of the patient's health) using survival analysis methods. The technique presented in this paper is an enhancement of our previous work [19] in which we used the KM method in collaboration with the shared-frailty time to event methods (SF) to model this phenomenon. The best resulting model was the lognormal shared-frailty model, which had patients' height as a covariate. This showed that shorter patients are under increased risk of receiving poorer ventilation treatments, as the overall defect free probability of survival was reduced by a factor of 0.058 for each centimetre of increment in height. The motivation for an improvement from this previous work lies in the fact that both of these techniques (KM and SF) estimate the probability that \(TV_{15}\) is going to stay at a value above 8 mL/kg threshold until at least the time \(t\) in APA (i.e., defect free survival probability) using the time of generating the alert as a baseline reference. Hence, previously, it was unable to dynamically predict the changing defect free survival likelihood with increasing duration of follow-up after triggering the alert. In this paper we address this issue by complementing the KM approach with the conditional survival function, which is able to estimate the probability that APA will continue to be defect free (i.e., probability that \(TV_{15}>8\) mL/kg) until at least the time of interest \(t_{y}\) given that it was previously defect free until the time \(t_{x}\), where \(t_{x}<t_{y}\). Using this technique, we compared the quality of the alerts generated by the system for the two genders, and discovered that the alerting algorithm had better performance in the female patients compared to the male patients. This is according to the higher defect free and conditional defect free survival probabilities. However, it is important to put this into the survival time context. The median survival times for females is almost three times longer than that for male patients, which would actually suggest that the female patients receive poorer ventilation treatment than male patients due to them being exposed to the higher risk of injuriously high TVs (>8 mL/kg) for a much longer period of time, thus having a higher risk of developing VILL The longer that patients remain on the ventilator event free, the more potential there is for damage, which could be construed as the lesser quality of care. In addition to our earlier findings [19], the results presented in this paper have confirmed that they are consistent with discoveries from the literature, which suggests that the female patients, as well as those patients who in general are a shorter height, receive poorer quality of mechanical ventilation treatments.