How to use

We consider 3 different phases for evaluation.

Under standard operation, the number of patients seeking treatment (after being diagnosed) is also the number of patients being treated monthly in order to keep the number of waiting patients constant.

Under restricted operation due to the COVID-19 outbreak or other event, the number of patients being treated becomes lower, so there is a damming, increasing the waiting time for treatment initiation. This event has certain duration.

After the event ends, the number of patients treated monthly must be preferentially higher than standard operation, as the waiting lines may grow substantially. To regain standard waiting times, this additional effort should be made until the number of waiting people returns to normal.

To perform a simulation, you must enter the information correctly:

• Usual time to treatment initiation (TTI; time from diagnosis to treatment initiation) under standard circumstances (before the outbreak) is the time from the diagnosis until the treatment initiation under standard operation of your service;
• Monthly treated under standard circumstances (before the outbreak) is the usual number of patients treated per month under standard of your service;
• Patients monthly treated during the COVID-19 outbreak is the number of patients that will be treated per month during the COVID-19 outbreak or similar event. This rate must be lower than the normal rate above.
• Expected monthly treated patients after the pandemic is the expected number of patients treated per month during the phase after the pandemic (mitigation period), where additional effort should be made to reduce the waiting time. This rate should be, therefore, higher than the normal rate above.
• Duration (in days) of restricted operation due to the outbreak is the real or expected duration in days of the limited operation phase due to the COVID-19 outbreak or similar event.

From this data it is possible to estimate needed time of effort to recovery after the COVID-19 pandemic, the peak and average waiting time to treatment during COVID-19 outbreak and mitigation period, the number of patients exposed to the risk of dying, the peak value of added risk due to increased time to treatment initiation (TTI) delay and also the baseline risk of dying due to prolonged TTI when the time exceeds 67 days (in this specific model).

A simulation is performed which estimates the waiting time (TTI) for each simulated individual. The arriving time of the individuals depend on the input rate and is linearly distributed through time. The exit time of an individual depends on the output rates experienced inside the simulation and the number of accumulated patients.

Based on a simplification of the model in the paper by Murphy et al. [2016], the hazard ratio is estimated as a function of the TTI. Hazard is considered 100% (normal) for waiting times lower than a threshold (TTI=67 as in the paper), and growing linearly with the TTI according to the expression: 100% + 100 (slope*TTI+intercept). The values for slope (0.003) and intercept (-0.2) are obtained from the graph of the model.

A Hazard of 120%, for example, means there is 20% additional chance of dying after treatment initiation above the standard expected risk due to the unnatural circumstances, in particular, longer waiting times to treatment.

• Hazard without the outbreak: if the usual waiting time is higher than the threshold, there is already added risk in the normal operation. The normal value is 100%.
• Max number of waiting patients: this represent the peak number of diagnosed people waiting for treatment during the event due to long wait lines.
• Average waiting time (TTI): this is the expected waiting time for patients whose waiting times are affected by the event, since before the beginning of the event, when still affected by the limited rate of treatment, until normality of operation is reached.
• Exposed patients: The number of individuals simulated. All the simulated individuals that have added waiting time until treatment are considered.
• Hazard: The overall hazard, being 100% equal to normal.

• Mitigation chart: This presents the number of patients waiting in line for each particular day. From the brown line, you can visualize how long each phase will endure and the evolution of the size of the waiting lines.
• Time to Initiate Treatment timeline: This is the timeline of TTI, showing how waiting times change for each arrival time. Peak TTI happens for the first patient that will be treated during mitigation. The center of mass of the brighter area represents the average TTI.
• Risk of dying timeline: This is the histogram of added hazard (beyond 100%), displaying how patients at different arrival times are expected to undergo different levels of risk exposition. The center of mass of the brighter area is the average overall added hazard.
• Mitigation effort and duration: This chart has two ordinate axes where the green curve represents the time needed for mitigation and the red one represents the associated risk given a chosen volume for mitigation (patients per month).

Click here to fill in with working example data. Example

Reference