**internship/residency crisis**facing New South Wales.

But what actually is the crisis? And where did it originate?

And is it

*really*a crisis?

I argue it's not that big of a deal in the long term

The problem can be simply characterised by looking at key policy changes in the late 20th century in combination with supply-and-demand.

## Policy overview

- 2009 - Universities start increasing the number of medical students
- 2012 - Official government policy to deregulate medical student admissions
- 81% increase in domestic graduates from Aussie med schools, from 1348 in 2005 to 2442 in 2012.
- No real provision of increased training resources at the other end of the spectrum.

Charts from MJA (reference below):

## Economic model

Let's define a "block" as a segment of a training pathway between two selection bottlenecks (e.g. block #1 = between HSC and internship, block#2 = between internship and registrar year 1, etc).

An simplified might be something like

*#trainees in block = ∑_i X_i*

*:= T*

where:

a block is years ranging from j to k

∑_i is the sum over all i (j≤i≤k)

X_i is the intake in year i

A step-wise policy update in year P1 that isn't replaced until year P2 changes the X_i for P1≤i≤P2. It will take k-j years for P1 to entirely affect T.

Of course if the policy at P1 is a time-dependent function the previous statement makes no sense. Which is basically the current situation: policy_P1 = f(t) = Ae^kt (some exponential).

The number reaching the next selection bottleneck B (outgoing cohort) is clearly X_k, with those "missing out" being X_k - B.

The potential size of

**X_k - B**is the source of fear: what happens to these 'lost commodities', who will be left to compete with the overflowing X_(k-1) the following year?
If B is fixed, we end up with a logjam in the system over Y years of

*Logjam = ∑[X_(k-y) - B]*

*= ∑[X_(k-y)] - BY*

where ∑ is from y=0 to y=Y

We could also subtract some attrition constant for the people who give up each year, but you get the point.

When a policy directive causes the term

*∑[X_(k-y)]*to be exponential rather than linear, this incites fear due to concern that the constant B is limited by consultants available to train new people.**However the assumption that B is constant is flawed.**B is also a function of time. Each newly trained consultant is available to train the next person.

Assuming 1<-->1 training:

With training time M,

**we get an additional boss pool of size B_[k-1-M]***B_k = B_[k-1] + B_[k-1-M]*

*= B_[k-2] +*

*B_[k-2-M] +*B_[k-1-M] by recursion

*=*

*B_[k-3] +*

*B_[k-3-M] +*

*B*

*_[k-2-M] +*

*B_[k-1-M]*

*etc.*

*= ∑B_[k-l-M]*

where the sum is on

*l*for 0*≤l≤k*
Peoples' concern is when

Logjam formula becomes:

Logjam =

*∑_y [X_(k-y)] -**∑_y*****∑_l B_[k-l-M]*
But if we wait l=k years (k usually no more than 6 years in reality), we find that the inner

*∑l*sum is stuck at B_[-M] (ie M years before the selection date), and we have that the right hand term reduces to:
Logjam =

*∑_y [X_(k-y)] - ∑_y**B_[-M] + ∑_y * constant**=*

*∑_y [*

*X_(k-y)] -*

*B_(-M) + constant ]*

So over time y, we look at the logjam and eventually, once y=k, the only variable term

*∑_y**X_(k-y) also becomes a sum of a constant.*
So we have

Logjam =

*∑_y[some other constant]*
Then ∑_y = Y/2*(Y+1) by adding the ends of the sum together.

I.e. independent of changes in intake at X_k, after k years you always just get a logjam proportional to a quadratic in Y (the total years you let the model progress). This quadratic can be multiplied by zero by balancing the constants:

- bosses available at time zero
- intake at time zero

## Summary (or TLDR)

- The training system is adaptive
- Things balance out in the long run.
- Things will balance out more quickly the higher the trainee:trainer ratio
- [Edit] Government funding is essential to allow this adaptation, but this cannot be judged until the current system has been running for k years (allowing the intake to block 1 to move to block 2). It is a matter of personal opinion as to whether it is at this 'judgement' stage yet or not. I think it is not.

## References

- https://www.theguardian.com/higher-education-network/2014/aug/07/lifting-the-cap-on-student-numbers-five-lessons-learned-from-australia
- https://www.mja.com.au/journal/2007/186/6/riding-wave-current-and-emerging-trends-graduates-australian-university-medical

## Your thoughts

Please leave your thoughts in the comments. I wrote this article to provide a (hopefully) refreshing counterpoint to the typical "doom and gloom" story espoused by media outlets.

## Error somewhere?

Entirely possible, comment below.

The issue here is that the number of training posts is dependent on funding and certification, not on the number of 'bosses' available to train up-and-comings. The criticism/fear expressed by those concerned is entirely that government funding for new postgraduate training posts is not keeping pace with the increase in graduate numbers.

ReplyDeleteGood point!

DeleteAssuming the mja source is correct, we are only about 7-8 years after the practice began. k=6 for medical schools usually, so can we really judge this yet?

I included an edit above in response, thanks for the comment!

Delete