Staff shortages and staffing requirements in hospitals

Why the gap cannot be closed:

Staffing requirements continue to rise – and cannot be met with the wrong measures!

It is too ‘plain’ if the problem of staffing requirements is only superficially reduced to formal figures of: ‘filled positions – medical activity – patients’(1) (2) without checking the origin of the data and its statistical interpretation. Information must always be generated from raw data, especially when it comes to a basic economic problem. It has already taken on widespread, insolvency-threatening proportions and is generating …

In order to recognise the seriousness of the situation, the following probing questions should be asked, for example:

– What ‘intellectual aberrations’ make it possible to separate full-time staff (PZ) and patients (FZ) in planning, when they are inseparable in medical practice?
– How large must the number of staff be for the hospital to actually become insolvent?
– What facts must be overlooked for personnel costs to become unaffordable?

a. There are objective facts that describe the threatening situation.

b. There are (unfortunately) subjective issues of personnel overplanning (see ‘Tips’ from the Medical Association; ⁽¹⁾)

First, the reference level that forms the basis of these ‘calculations’ must be determined. It is extremely self-assured and highly subjective. It is claimed:

An average time and a mean time function were formally calculated, but both are meaningless. None of the actual times correspond to the formal time. The search for a fixed time value has led to a ‘time fiction’. This means that there is no ‘average value’ as a basis for calculating the operating time of the TuR-P. It is often common practice to calculate with the largest single value for safety reasons. The result: there are several values that can be calculated per year and per full load – an unclear situation.

These ‘time blocks’ are unrealistic and become rigid in their formalism.

No operating theatre has 2.5 doctors per operation. All doctors are employed ‘full-time’. A “half” doctor would not be able to make a living and would therefore be un-able to treat patients. Even if it seems unusual, staffing requirements must be calculated using whole numbers if they are to be realistic. Half-time positions were ‘invented’ in business administration because they mean halving the working hours. Medical work requires ‘full-time’ doctors.

Even when the „Millin“ method was the only surgical method available for prostate adenomectomy, it did not require 2.5 full-time employees, but a maximum of 2. Since the introduction of minimally invasive surgery, only 1 full-time employee is required. The fixed ‘surgical factor of 2.5’ was incorrect in the past and has become even more “incorrect” today. This is (only) one of the very practical forms of ‘inflated’ staffing requirements.

The confusion surrounding calculations means that many hospital managers completely forego calculations when planning their staffing requirements. They (often) use the most obvious ‘substitute’: they ask medical practitioners (CHA). Because…

Practitioners then use ‘empirical values,’ ‘rules of thumb’ and ‘benchmarks’ to arrive at their answers. However, since they have never learned how to convert raw time data into time information, this approach, even if it appears correct at first glance, does not lead to reliable values. These only arise when false premises are discarded, premises that ‘thoughtlessly’ assume that medical processes can be calculated in the same way as industrial ones. Arithmetic calculations cannot adequately represent individual medical activity times (a1≠a2) using uniform structures (a1=a2).

Real measured TuR-P times are typically characterised by their wide dispersion. Unlike the point in time, time dispersion is useless for conventional performance unit calculation. In-stead of dispersion (point cloud), the individual times would have to be available in the form of a Gaussian bell curve in order to use an average time. This is not the case.

Conclusion: The mathematics indicate ‘misuse’ due to their properties – but: Apodictic, medical self-reflection is very unsuitable for correcting misuse!

How temporal foundations for problem solving are created:

n the graph, the real time values of the TuR-P form an amorphous point cloud in which no arithmetic mean can be calculated. The values are not distributed symmetrically (in the form of a Gaussian bell curve). The mean, including its mean value function for the entire value range, which is also calculated, is not a real mathematical representation of the time structure. However, if (a1=a2) does not apply, the individual values have no group properties, meaning that no meaningful arithmetic operation can be performed. But this is precisely the implicit assumption made when calculating personnel requirements. Until now, this has been based on the theory of ‘work units’ with ‘uniform time constraints’.

The consequence of an unfulfilled premise is that personnel requirements cannot be calculated arithmetically. Solving the problem requires a qualitatively different kind of mathematics.

How can we find the number system that adequately represents the real-time data?

Since there is no direct relationship between empirical data (real-time operating theatre data) and theory (operating theatre scheduling), but theory is a reflection of empirical data, the structure of the theory must be ‘measured’ – i.e. adjusted and constructed in such a way that the calculated consequences of the theory correspond to the (known) real data.
An operationalisation is carried out for the (postulated) number system. It checks the number system for (a) correspondence and (b) coding.

The correspondence checks whether the facts generated in theory (calculations in operating theatre scheduling) occur in practice or not. A theoretical construct could be a calculation, such as arithmetic division by ‘2’, resulting in “half” operating time. If the theory adequately reflects the times, this ‘half’ operating time should be found in the point cloud. It is immediately apparent from all operating times that none of them can have a ‘half’ operating time. These would lie (to the left) of the point cloud. This is a realistic result, as no surgeon can shorten an operation at will.

Conclusion: Point clouds of medical activity times are not arithmetic.

In order to calculate with quantities, their quantities are converted into numbers. The coding checks whether the real structures converted into numbers (quantities and their relationships) are identical to the numerical structures of the theory.

Application to the example:
In the operating theatre, a doctor’s TuR-P takes 60 minutes. For the second operation, she only operates for 30 minutes. Assuming that the real numerical structure could be represented using arithmetic, the theoretical staffing requirement for the 30-minute operation would only be ‘half’ as large. When the ‘theoretical size’ is applied to the reality of surgery, this results in a staff shortage. Unfortunately, because the coding was never done, this is common practice.

The coding of the example leads to the actual structure of the numbers. Like her other colleagues, the doctor works as a ‘whole’ full-time employee (FTE) in all operations, and all patients who undergo surgery never appear “half” but as a ‘whole’ for the operation. This means that medical activities must be calculated as integers, i.e. not arithmetically. Whole numbers are natural, cardinal and ordinal numbers.

Consequence for the associated times: The times for medical activities are also whole numbers.

On which characteristics of medical activities are your times based?

Evidence-based activities are performed from start to finish in a ‘medically logical’ sequence of qualitatively different sub-activities (including branches). For example, a TuR-P has the following sequence: insert laparoscope, remove gland, rinse gland parts, stop bleeding, insert catheter. These are qualitatively different sub-activities, each of which has its own activity time and which determine the total time of the TuR-P. Mathematically, the sequence can be ‘numbered’ with 1, … 5. It is finite and self-contained (complete) because it is medically complete. The times associated with the sub-activities therefore also form a ‘medically logical’ sequence of sub-times that determine the total activity time – they do not cause it causally.

Partial activity times have a special feature: they and the total activity time are generated by an incomparable full-time employee for an incomparable patient. Both generate indivi-dual times that are only valid for this activity and therefore have specific characteristics:

• Unique: there are no multiple times. Individual times cannot be multiplied.
• Unplannable: Individual patients shape the time with their physical characteristics.
• Indivisible: A medical activity cannot be terminated at will.
• Ordinal: Since there is no standard size for a ‘surgical unit’, there are no measur-able time intervals.
  Important: All of these sub-activities (including the overall activity) can be physically measured. They therefore have completely new properties. These are:
• Manipulation-free (no surgical nurse needs to ask the surgeon what operating time to enter in the operating theatre log).
• Real-time. The times can be processed by the AI without delay.

Since the multitude of identical medical subtasks merely repeats their order of priority, but each of their individual times is unique, a conditional relationship to the total activity time arises (which is arithmetically unpredictable), but no causal relationship.
If the same full-time employee repeats many of these medical activities, an individually typ-ical time dispersion for their activity arises with a more or less dense time centre that builds up over a time interval. For ordinal variables, the dispersion therefore determines the time centre. This reverses the arithmetic relationship and is an advantage for process control.

Applied to the point cloud, individual, ordinal time distributions for the five full-time employees become visible.

The graph shows that individual full-time staff have very individual patterns of activity (experience, operational routine, etc.) when dealing with individual patients. Their times differ by a factor of four. The average (46.3) is not only incorrect. In the monthly overview (45 operations), it inflates the ratio of actual times to ‘calculated’ times by one-third (18:27).
Realistic time profiles are provided by ordinally structured frequency distributions.

The specific properties of time can be calculated very accurately using ordinal mathematics, ordinal numbers (rankings), and cardinal numbers (extent). The algoritms are based on time variables, part-time quotas, event fields, time-dependent activity densities, permutations, rankings, etc.
These calculations lead to better results than arithmetic ones – they are just unfamiliar.
TuR-P served only as an example – but —

– Having your own digital operating theatre scheduling tested is best for you.