## 3 Results  
There were 560 patients generating a total of 1450 alerts during the time in which the VILIAIert system was observed for this study. Out of the 560 patients, 298 (53%) were male patients generating 691 of the 1450 alerts (47.7%). The chi-square test of independence  
Figure 2: A schematic overview of five analysed post alert time windows (APA) covering the period of 6 h post-alert generation. (**a**) An illustration of the tabular dataset in its raw form, where 0 and 1 symbolise defective (DB) and non-defective (NDB) blocks, respectively. (**b**) An illustration of the lengths of their follow-up times, where each length corresponds to the time to occurrence of the event of interest, i.e., 1 st DB block during APA. These lengths are used for the calculation of defect free and conditional defect free survival probabilities. (\(\chi^{2}\)) and [PERSON]'s V (\(V\)) effect size coefficient indicate the existence of a strong association between the gender and alert invocation (\(\chi^{2}_{1}=42.71;\ p=0;\ V=0.22\)). This suggests that even though there were a higher proportion of males in the study, the female patients are the ones who have a higher chance of triggering the alert upon starting mechanical ventilation. An overview of the patient demographics of those involved in our VILIAlert study is provided in our earlier work [6]. In general, survival times are highly skewed and therefore best represented using the median. The time to first DB follows this skewed nature, thus it is the median overall time which is used to report time to the first DB block appearing in the APA (i.e., the median of overall defect free survival time). This is 180 min. The corresponding KM estimates are provided in Figure 3. which illustrates the estimated DFS curve for the VILIAlert data for the time until the first DB for each patient. This is typical of the survival curve shape where it is highly skewed in nature with the majority of patients experiencing the event quickly, but some taking much longer to experience the event, hence featuring in the tails of the distribution. It can be seen from Figure 3. that the probability of APA remaining defect free, i.e., the probability that \(TV_{15}\) will remain above 8 mL/kg until the end of the 6 h follow-up period, decreased over time, from 0.67 at the 60 th minute to 0.37 at the 360 th minute upon triggering the alert. On the other hand, the probability of the APA continuing to be defect free, conditional on it already having existed defect free in a specific time period, gradually increases. That is to say, the estimated CDFS of APA being defect free at the end of the 6 h follow-up period was more than twice lower for alerts than that which were just triggered, compared to the alerts for which their APAs were defect free for 2 h (Table 1). For instance, if APA was defect free at 60 min, the probability of it remaining defect free at the end of the follow-up period is 0.56 whereas if APA was defect free at 300 min upon triggering the alert, the probability of remaining defect free at the end of the follow-up period, from generating the alert is 0.92. A detailed overview of estimated the \(CDFS\big{(}t_{y}\big{|}t_{x}\big{)}\) probabilities for the various combinations of \(t_{x}\) and \(t_{y}\) timestamps in minutes, is provided in Table 1.  
Figure 3: Kaplan–[PERSON] estimates of overall defect free survival probability. The median survival times for male and female patients were 105 and 300 min, respectively. Their corresponding KM estimated defect free survival curves, in Figure 4, illustrate the first DB blocks in the APAs of the males occurring much sooner during their length of stay in ICU than the female patients. The log-rank test is conducted to test whether there is a significant difference between survival times for males and females. This indicates a very highly significant difference between the male and female survival distributions (\(\chi_{1}^{2}=65.8,\;\;p<0.0001\)).