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Scott Gilmore, MD

3 min read

Optimal Deployment of Automation in Healthcare

When we talk about implementing AI in healthcare, a lot of people envision using computers to offload part of the cognitive work related to direct patient care. Countless startups promise to reduce cost by automating, say, writing doctors notes in a more efficient way, or automatic physician messages to patients.

But a very large proportion of the cognitive work in health systems is not performed by providers, but the vast administrative staff who support them. But since clinicians are paid more for their time, that must be the highest value target for automation, right?

A First-Principles Approach
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Assume that there are ii roles, and the work to be performed requires nin_i individuals, the initial required headcount for the iith role. Assuming no change in the required work output, and assuming AI can perform α∈[0,1]\alpha \in [0,1] proportion of the iith role, then after AI implementation:

n~i=ni(1−αi) \begin{equation} \tilde{n}_i = n_i(1-\alpha_i) \end{equation}

Where n~i\tilde{n}_i is the modified headcount to maintain constant work output. Then the cost savings of this change is:

T=∑i=0mSi(ni−n~i)−niαiκ \begin{equation} T = \sum_{i=0}^{m} S_i(n_i - \tilde{n}_i) - n_i\alpha_i\kappa \end{equation}

Where each SiS_i is the salary of the iith role, and κ\kappa is a proportionality constant that assumes the cost of compute is proportional to the cognitive work performed. Substituting (1) into (2), we have:

T=∑i=0mniαi(Si−κ) T = \sum_{i=0}^{m} n_i \alpha_i(S_i - \kappa)

This captures the idea that the cost savings is proportional to the initial labor cost multiplied by the difference between the cost of human labor and the cost of automation. In the limit of negligible compute cost, we have:

lim⁡κ→0T=∑i=0mSiniαi \begin{equation} \lim_{\kappa \rightarrow 0} T = \sum_{i=0}^{m} S_i n_i \alpha_i \end{equation}

This suggests that in order to minimize the labor cost, one must consider the number of individuals in a role, the salary of that role, and the automation potential of that role in equal measure.

Low-Hanging Fruit
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Let’s work through a hypothetical example. Let’s say that an organization pays physicians, on average, about four times as much as administrative staff, but four administrators are needed for every physician. Let’s propose that the workload for a physician can be reduced by 10% with automation, whereas the administrator can enjoy a 50% reduction in the labor required. Which is the lower hanging fruit? Here we can write the proportion:

Spnpαp:Sanaαa {S_p n_p \alpha_p}:{S_a n_a \alpha_a}

Where the subscripts pp and aa refer to physician and administrator. Plugging in the numbers from the example, we have:

4×1×0.1:1×4×0.5 { 4 \times 1 \times 0.1 }:{1 \times 4 \times 0.5 }
1:5 1 : 5

So with these assumptions, it would be five times as economically valuable to automate the administrator role.

In real life, things are much more complex, but this reality check and (3) have made me more interested in learning more about all the roles that exist in a healthcare organization, their cost, and their automation potential, because you need to understand all three to decide where to focus attention.