The Edge Every Latecomer Has

I.The First Known Thing — the best so far

probability · the theory of records

A record is an observation larger than every one before it. The theory of records, opened by K. N. Chandler in 1952, begins from a fact that needs no calculation. If a sequence of observations is drawn from one unchanging source, each of the first n is equally likely to be the largest of them, so the chance that the nth is a record is one in n. Nothing about the source enters: not its mean, its spread, or the shape of its tails. The expected number of records in n observations is therefore the harmonic sum, which grows as the logarithm — about five in a hundred observations, and between seven and eight in a thousand.

two results that offend intuition

Two further results are standard, and both run against expectation. The first, due to Rényi, is that the events are independent: whether the fifth observation is a record tells nothing about whether the sixth will be. The second, in Chandler's paper, is that although another record is certain to come, the expected wait for it is infinite. Records from a fixed source are not merely infrequent. They thin on a fixed schedule, and a long run without one is the ordinary condition and not a sign that anything has stopped.

the count as an instrument

Because the schedule is known without knowing the source, a count of records is a measuring instrument. Foster and Stuart proposed in 1954 a test for trend built from nothing but the number of upper records and the number of lower ones, which an unchanging source supplies equally often; an excess of the first over the second is evidence that the source is moving, and the evidence owes nothing to any assumption about its distribution. The method is used on temperature series and on athletic performances, and the question is the same in both: are new bests arriving more often than a fixed source would send them?

three ways to have more records

The theory also says what can produce an excess, and it keeps the causes apart. A source that drifts upward gives records at a rate that settles to a constant instead of falling away, as Ballerini and Resnick showed for a linear trend. A source that does not move at all gives the same appearance if each entry is the best of a growing number of draws: in Yang's model of 1975, written for Olympic records and a growing population of athletes, the chance of a record at the nth entry is the share of all draws so far that were made at that entry, and geometric growth holds it constant. The third is a matter of logic and needs no theorem: a sequence from which the entries falling short of the standing best were removed before anyone read it will show records at whatever rate the removal was thorough enough to produce. An excess therefore has three sources — drift, more draws, and filtering — and only the first is improvement.

more than one coordinate

The last result concerns observations with several coordinates. An observation is admissible, or undominated, if no earlier one exceeds it on every coordinate at once. Barndorff-Nielsen and Sobel showed in 1966 that for coordinates varying independently the expected number of undominated observations among n is again free of the distribution, and that it grows as a power of the logarithm one less than the number of coordinates. The consequence is steep. The fifth observation in a sequence is the best so far on a single coordinate with probability 0.20. It is undominated on two coordinates with probability 0.46, on three with 0.67, and on four with 0.81. Add coordinates and nearly every arrival is beaten outright by nothing that came before it, while nothing whatever has improved.

II.The Second Known Thing — the class that keeps filling

drug discovery · portfolio direction, programme termination and herding

A mechanism shown to work attracts company. Many approved drugs belong to classes with several members, and whether to be the third, fifth or eighth sponsor into a class is among the commonest questions a portfolio committee decides and among the commonest grounds on which a programme is continued or stopped. DiMasi and Faden, examining entrants to new drug classes over five decades, found the pattern better described as a race than as imitation, with later entrants increasingly in clinical testing before the first was approved. A later analysis from the same centre found that, of the classes first approved between 2005 and 2011, roughly three-quarters already had a competitor in phase III on the day of that first approval.

how the field frames later entry

The framing is commercial, and it is carefully measured. The standing question is whether it is better to be first in class or best in class. Schulze and Ringel answered it in 2013 by scoring each product's therapeutic advantage and setting that against its share of the class's sales, and an update in 2023 repeated the exercise on 104 products in 29 classes opened since 2010. A study of 492 launches in 131 classes put the first entrant's advantage at about six points of market share and found a later entrant leading in more than half the classes. An analysis of 189 late entrants launched between 2012 and 2023 found that 22 beat the share their position predicted, chiefly by clinical differentiation. In each case the quantity explained is revenue, and position in the order of entry is the variable that explains it.

the word that carries the case

Inside a company the case for a later entrant rests on one word. The programme must be differentiated. Its target product profile lists the attributes on which it will be compared with what is already available — efficacy, safety, tolerability, dosing interval, route, interactions, the populations it may be used in — and the programme proceeds if it can claim an advantage on at least one of them without a deficit grave enough to cancel it. Regulators do not ask for superiority over the class; a new member is approved against placebo or on non-inferiority. The bodies that assess added benefit afterwards are harder to satisfy. Of 216 new drugs assessed in Germany between 2011 and 2017, more than half were found to have no proven added benefit over the existing standard, and analysts at the United States regulator sort new molecular entities into first in class, advance in class and addition to class.

what is missing

What the field does not have is a baseline. No analysis states how often a later entrant would be the best of its class, or would hold some advantage over every predecessor, if the entrants were nothing more than further draws from whatever the mechanism allows. Without that number a class in which the fourth and seventh entrants were improvements cannot be told from a class that is learning, a claim of differentiation cannot be weighed, and the decision to continue an eighth programme is taken against an order-of-entry curve that describes what later entrants have earned and is silent on how good they were.

III.The Bridge

no paper on records cites a paper on order of entry; each hall counts firsts and bests, and neither has seen the other's count

The halls do not meet. The theory of records is a corner of probability whose applications run to weather and sport; the literature on order of entry is pharmaceutical economics and strategy. Neither cites the other and no review spans them. Three neighbours must be set aside. This is not the question of first in class against best in class, which asks what a position earns and takes each product's merit as given; what follows concerns how often merit of a given rank should appear at all. It is not the difficulty, known in computational compound design, that a ranking by dominance stops discriminating between candidate molecules once many objectives are scored; that is a remark about a selection method inside one programme, and it has not been turned on the claims sponsors make across a class or tied to a position in the order of entry. And it is not regression to the mean or the winner's curse, which concern the error in a single estimate; the schedule of records holds when every entrant is measured exactly. The race that DiMasi and Faden describe matters here for a reason they did not need. Entrants developed side by side cannot have learnt from one another's clinical results, which makes further draws from one source the natural description of a class and not a pessimistic one.

X: the best arrives on a schedule the science does not set, and the edge arrives almost regardless

Call it the record rate. Where the successive entrants to a class are draws from one source, the chance that the kth is the best so far on any one measure is one in k, whatever the source and whatever came before. Three things follow. The count of new bests is a meter of whether the class is learning, and it needs no model of the pharmacology: at the harmonic rate nothing has been learnt however many improvements can be pointed to, and the improvements a fixed source supplies fall among the first few entries, which are exactly the ones a class's history remembers. An excess over that rate has three possible origins, which the same arithmetic keeps apart — a source that has moved, sponsors each choosing their entrant from more candidates than the last, and the quiet termination of candidates that fell short of the incumbent — and only the first is progress in what the mechanism can do. And when merit is counted on several attributes the chance that an entrant is beaten on all of them by some predecessor falls towards nothing, so that differentiation is supplied by the number of attributes in the comparison and withheld by nothing. A class can fill for as long as sponsors care to enter it, each entrant truthfully differentiated and none of them better.

IV.The Question That Becomes Possible

neither discipline would ask this alone

The probabilist has no reason to ask it. Records are studied where the sequence is long and the measure is single and agreed — a temperature, a time over a distance — and a sequence of eight entries scored on half a dozen attributes by parties with an interest in the scoring is not a case the theory was built for. The strategist has no reason to ask it either, because the working variables are share and timing, each entrant's merit is an input assessed product by product, and the idea that the frequency of best-in-class products has a value fixed before any chemistry is done does not arise. Held together they produce a question that the approved record of the last forty years can answer.

the record rate hypothesis

In drug classes that share a mechanism and a quantitative primary measure, is the frequency with which the kth entrant sets a new best on that measure distinguishable from one in k, and are new bests any more frequent than new worsts; is the frequency with which an entrant is undominated by its predecessors, on the attributes its label can claim, the one that the arithmetic of admissible points gives for that many attributes; and where a class does run ahead of the harmonic schedule, is the excess accounted for by the number of candidates each sponsor chose its entrant from and by the termination of candidates that fell short of the incumbent, with nothing left over for a change in what the mechanism can deliver?

why it would matter

Because it would give a best-in-class programme its prior odds before a compound is made: one in k at the kth position, to be raised only by naming which of the three sources of excess the programme relies on and showing that it is at work in that class. Because it would strike differentiation from the reasons to continue unless the attributes are fixed and counted beforehand, since with four in play the claim is open to four entrants in five and distinguishes nothing. And because it would give a class a measurable it does not now have — its count of new bests against the harmonic expectation — which says whether the crowding into that class bought improvement or only repetition, and which is computable for every established class from trials already published.

V.How It Could Be Proven — or Broken

a candidate must be breakable, or it is merely poetry

An intercognix candidate earns nothing until it names its own test. This one needs no new experiment. The entrants, their order and their trials are public, and the prediction is a number that can be written down for each class before its comparisons are assembled.

the honest status

Note the narrowness. The claim is confined to classes whose members share a mechanism and a primary measure and number at least four. It says nothing about the first entrant, about classes too young to have a sequence, or about the long succession of mechanisms within a disease, where the source plainly does move. It says nothing about what a later entrant earns, which the existing literature measures well, and nothing against later entrants as such: a drug that sets no record still brings price competition, a second source of supply, and an alternative for the patients who cannot take the others. It asserts no particular count for any particular class. The whole of the claim is that the count has an expected value the field has never written down, that differentiation has one too, and that both belong on the table before the eighth programme is funded.