Copy the shape, not the size

Ask how big a hospital should be and you will usually get an answer about a hospital somebody has seen. That is not laziness. A building that works is genuine evidence, and the instinct to reproduce it is sound about most of what it reproduces.

But size and shape are answers to different questions, and they transfer differently.

Shape is a response to a parcel, a climate and a technology. It is a solved problem in the sense that the number of good answers is small, the constraints that produce them recur, and a form that resolves a constrained urban site in one city is very likely to resolve one in another. Shape travels.

Size is a response to a population: how many people, how ill, how often, how long they stay, and, in this market, how many of them can pay. None of those is a property of the building. Size does not travel at all, and copying it is the most common way a hospital ends up wrong in a way nobody can fix afterwards.

So the method for this decision is to take the shape and the ratios from the comparator, where they are measurable and transferable, and to derive the size from the catchment, where it is not.

A single comparator is a trap, and which trap depends on which one you pick.

Take only the temperate urban hospital and you import an operating standard with a set of infrastructure assumptions welded to it, and you discover the assumptions at licensing. Take only the local tertiary hospital and you inherit a context as though it were a specification, and you have quietly accepted every constraint that the market imposes rather than deciding which of them you intend to beat.

So there are two, and they do different jobs. The first is the reference for how a hospital should work: what an operating standard looks like when it is met, how a constrained parcel is resolved into a plan, what area per bed buys. The second is the reference for what a hospital in this city is: the ground, the grid, the water, the workforce, the scale of demand that actually presents, and what it takes to run at that scale here.

The proposal sits between them, and that is a statement about kind before it is a statement about size. It is not a small private facility serving a thin slice of the market, and it is not a public tertiary centre absorbing everything that arrives. It is a hospital large enough to hold the specialties the outbound money is already buying elsewhere, and small enough to be run to a standard it can actually demonstrate.

Between them is also a wide space, and this page is not going to narrow it to a figure. The bed number is an output of the parcel, the catchment and the payer mix, and none of those three is settled. Fixing it now would produce a number with the appearance of a decision and none of the evidence, which is precisely the failure mode the rest of this study is about.

The standard comparator is a general hospital on a constrained urban London site, opened in 1993, with four hundred and thirty beds across five floors and a basement, arranged around courtyards with a central atrium. The form was a direct response to the parcel: planning limited the height, so the architects used the site to its edges and brought light into the middle rather than accepting a dark core.

The local comparator is the teaching hospital in the target city, which by its own account runs above nine hundred and fifty beds and began life at three hundred and thirty. It is the reference for scale, for what tertiary demand in this market actually looks like, and for what running at that size here requires of power, water and workforce.

That gives two documented answers to two different questions, and the table sets out what each comparison is good for. Read the last column. Most of the comparisons are useful and one is not, and the one that is not is the bed number, because of the row about who can use the building.

The chain is short enough to argue with, which is the reason to show it as a chain rather than as a bed number at the end of a report.

Take the population that can reach the site in a tolerable journey. Take the share of them who can actually pay, because in a market where most health spending comes straight out of the patient’s pocket, a person who cannot pay is not demand, however ill they are. Apply an admission rate, multiply by how long people stay, divide by the year, and divide again by the occupancy the hospital can run at.

The fourth term is the one that does not appear in any version of this calculation written in a country with a universal payer, and it is the term with the most leverage. Halve it and the hospital needs twice the catchment for the same number of beds, which means a larger radius, which means a longer drive, which means fewer people willing to make it. It is also the term with the weakest data behind it, and the honest response to that is to run the answer across a range rather than to pick a number and defend it.

It is worth saying plainly what that term also means, because it is uncomfortable. The people excluded from it are ill at the same rate as everybody else. They are absent from this arithmetic not because they do not need a hospital but because they cannot buy one, and the whole of the clinician supply argument elsewhere in this study exists because of what that does to the place.

One thing this worked example is not is the recommendation. It is the method run once, on stated assumptions, to show what each term does and how much it moves the answer. The bed number and the land area are both outputs of the same unsettled inputs, and both stay as ranges in the brief until the paying share has been measured. A figure written down before then acquires an authority it has not earned, and the rest of the programme then defends it.

The occupancy term in that chain is not a policy choice. It is a property of size, and the relationship is strong enough to decide the answer on its own.

Demand does not arrive at its average. If a unit has thirty beds, the day everybody turns up is a far larger proportion of thirty than the equivalent day is of three hundred, so a small unit has to hold much more spare capacity to offer the same chance of a bed being free. The table solves that directly: for each size, the occupancy at which there is a one in fifty chance that an arriving patient finds every bed full.

Read the third column, which is the same fact in money. A thirty bed unit needs about forty per cent more beds per unit of demand than a large one does, permanently, for no clinical benefit whatsoever. That is the arithmetic reason small hospitals are expensive, and it has nothing to do with management.

It compounds with everything that is indivisible. A twenty four hour consultant rota needs roughly the same number of consultants whether the unit has thirty beds or two hundred. A theatre, a scanner, a blood bank, a generator and an oxygen plant are all lumps. Spread across thirty beds they are ruinous; across two hundred they are ordinary.

All of which argues for going bigger, right up until the fourth column.

A hospital feeds on a catchment, and a catchment is an area. Double the beds and you need double the people, but people live on a surface, so the radius grows with the square root and the drive grows with the radius.

Follow the last column of the table and the trade looks obvious. Going from thirty beds to a hundred and twenty buys sixteen points of occupancy and costs about eighteen minutes of journey. Going from two hundred to four hundred and thirty buys four points and costs another twenty two minutes. The gain is running out while the cost is not.

That is the standard argument and it needs a correction that this study got wrong first time round. It assumes every patient is deterred by distance in the same way, and they are not. The unplanned stream is deterred absolutely, because minutes are clinical. The returning stream is deterred severely, because a journey made three times a week for years is a different thing from a journey made once. The planned stream is barely deterred at all, and in this market that is not a hypothesis: those patients are currently flying to other continents.

So the geographic penalty applies in full to emergency and cyclical work and only faintly to elective work. A hospital whose demand is mostly elective can be considerably larger, and considerably further out, than the isochrone argument suggests, because most of its patients are not measuring the isochrone.

What remains true is the rest of it. Internal walking distance rises with size, and this study has put a number on what ten metres costs. Adjacency gets harder, because a bigger hot floor is a bigger plate and eventually it will not fit the parcel. Those are properties of the building rather than of the catchment, and they do not care what kind of demand fills it.

The two calculations on this page were arrived at independently and they are worth putting side by side, because a single model agreeing with itself is not evidence.

The chain starts from a catchment and a paying share and produces about a hundred and fifty beds. The scale table starts from queueing and geography, knows nothing about the catchment size, and puts the efficient range at roughly a hundred and twenty to two hundred. They agree, and they agree for unrelated reasons: one is about how much demand exists, the other about where the trade between pooling and distance turns over.

So the working position is a hospital in the low hundreds of beds, with the structure, services and land to grow well beyond it without rebuilding. Not a figure, and deliberately not the four hundred and thirty of the standard comparator nor the nine hundred and fifty of the local one. Those two bracket the question rather than answering it.

The convergence is also the warning. Both calculations share the paying share, the admission rate and the length of stay. If those are wrong, both move together and the agreement proves nothing, which is exactly why the shortfalls below name them rather than the arithmetic.

There is a conflict on this page and it should be stated rather than smoothed over.

The chain earlier produces a hospital in the low hundreds of beds from a catchment, a paying share, an admission rate and a length of stay. The comparators bracket something considerably larger. Both cannot be right, and the disagreement is not vague: it localises onto exactly one term.

Hold the admission rate and the length of stay, which are reasonably well understood and would have to be wrong by a factor nobody would defend. Hold the drive time, because the geography is the geography. What is left is the paying share, and a hospital several times larger than the chain produces requires a paying population several times larger than the chain assumes.

That is not a refutation of either. It is a statement that the two views differ on the single term this page has already called the weakest and the most decisive, and it converts an argument about ambition into a measurement.

Three things could make the larger number right, and each is a different business. The paying population could simply be larger than assumed, which a survey settles. Insurance and corporate cover could carry patients the out of pocket figure misses, which is a payer mix question rather than a wealth question. Or the hospital could serve beyond the self paying market deliberately, through subsidised or contracted tiers, which is a different proposition from the one the demand case currently describes and would need its own argument.

Until one of those is established, the honest output is a range with the reasoning attached, and a note that the range narrows the moment somebody measures the paying share in the catchment. That measurement now settles the bed number, the parcel size, the city comparison and the capital, which makes it the highest value piece of work available anywhere in this study.

Everything above sizes a hospital for a catchment. It assumes the catchment, and the assumption deserves the same treatment as everything else, because a question raised about ground conditions turned into a question about the city and the arithmetic does not settle comfortably.

A catchment is not a population. It is the area a road network puts inside a tolerable journey, multiplied by the density of people in that area, multiplied by the share of them who can pay. Lagos is enormous and dense and its roads are slow. Abuja is far smaller and far less dense and its roads move. Those two effects work against each other and the result is not obvious until it is computed.

Inside forty five minutes the slower city reaches a tenth of the area the faster one does, and its density more than makes up for it on raw population. On payers it does not, because the third term is where the two cities differ most and the direction of that difference runs against Lagos. A capital city of civil service, diplomatic and corporate employment has a materially higher proportion of people who can buy private care than a city of twenty million with a very large informal economy.

The honest statement of the result is a condition rather than a conclusion. On these assumptions Lagos reaches more payers within forty five minutes only if its paying share is above about seventy per cent of the capital’s. The figures used here put it at forty. If that holds, the reach argument favours Abuja, and it favours it on the criterion carrying the second largest weight in the brief.

One correction belongs here and it weakens the challenge without removing it. The table counts payers inside a forty five minute drive, and for elective work that is the wrong measure, because the elective payer is the one already boarding an aeroplane. On the demand this project is actually built to capture, neither city is constrained by its isochrone, and the comparison reverts to where the paying population is in total and which city a patient would rather travel to. Lagos is larger on the first and the second is a question about reputation rather than geography.

Two things stop this overturning the recommendation today, and neither is comfortable. The paying shares are assumptions, clearly marked, and they are the weakest numbers on this site. And the reach table measures only one criterion: it says nothing about the outbound flow, which is concentrated in Lagos and is the observed demand the whole proposition rests on, nor about the depth of the teaching hospital ecosystem the academy partnership depends on, both of which the scoring already credits to Lagos.

What it does do is remove the comfort. The recommendation was already described as resting on a four to eleven point margin and on one deliberately heavy weight. It now also rests on an assumption about relative paying shares that nobody has measured and that this table says is decisive. Measuring it is a survey, it is cheap against the decision, and it belongs in the option period.

A paying population materially larger or smaller than assumed. This is the dominant term and it moves the answer proportionally. A measured figure from the catchment, rather than a national estimate, would be the single most valuable piece of work anybody could do before the massing gate.

A road network that converts distance into time differently. Every travel figure here assumes an average speed and a detour factor. A site on a route that moves, or a dedicated ambulance approach, changes the fourth column and therefore the knee.

An insurance market that grows. If third party cover expands materially, the paying share rises without the population changing, the catchment tightens and the same building serves a shorter radius. That would argue for building the structure for more beds now even while opening fewer.

A service mix that is mostly day case. The four specialties this project targets are not evenly weighted in bed demand, and a configuration that leans further into day surgery and ambulatory work needs fewer beds and more theatres and recovery bays for the same revenue. That is a different building, not a smaller one.

Four, and the first applies to every number in the scale table.

The occupancy column is a ceiling rather than a target. Queueing theory assumes arrivals are independent and random and that a bed is a server working at a constant rate, and this study has already spent a chapter explaining that the second of those is false. Real occupancy at any given standard sits below what the table says, the gap is largest when the hospital is busiest, and an organisation that reads the column as a target will discover that by filling a corridor.