The Pace Every Context Keeps

I.The First Known Thing — the verb that acquired a helper

historical syntax · the rise of the auxiliary do

English once asked its questions and made its denials with the main verb alone: went he, he went not. Between about 1400 and 1700 it came to do both with an auxiliary, did he go, he did not go, and for three centuries the old pattern and the new were in use side by side. Alvar Ellegård in 1953 counted them, in dated prose, period by period and kind of sentence by kind of sentence: negative statements, negative questions, affirmative questions of several sorts. At any one date the new form was much commoner in some of these than in others. Negative questions ran well ahead; negative statements and questions on the object lagged for a century and more before they caught up.

the natural reading, and its law

The natural reading of such a table is that the change began where it was most favoured and went fastest there, each kind of sentence having a history of its own. C.-J. N. Bailey in 1973 made it a principle of his wave model: what is quantitatively less is slower and later; what is more is earlier and faster. On that reading the lead of one context over another is a difference of speed, and a table of frequencies at one date is a ranking of how far each separate change has got.

the rate, properly measured

Anthony Kroch in 1989 fitted the logistic curve to each of Ellegård’s contexts separately, which turns each history into a line with two numbers, a slope that is its rate and an intercept that is its level. For the seven periods up to 1575 the five slopes were 3.74, 3.45, 3.62, 3.77 and 4.01. A single slope of 3.70 fitted all five, and the test of their difference gave a chi-square of 0.504, at which the hypothesis of one slope is nowhere near rejected. The intercepts ran from −5.57 to −9.26. The contexts differed greatly in level and not detectably in rate. Kroch stated the result as a hypothesis about change in general: when one grammatical option replaces another with which it is in competition across a set of linguistic contexts, the rate of replacement, properly measured, is the same in all of them. His reading was that speakers were not changing five constructions. One option in the grammar, on his analysis the movement of the main verb to the position that carries tense, was being lost, and the five contexts were places where that one loss showed. What set the contexts apart was a fixed advantage or handicap in use, constant across the whole period and without interaction with time.

what the constancy is used for, and where it stops

The constancy became an instrument. In Middle French the decline of the inversion of subject and verb and the rise of a quite different construction, left dislocation, were found to run at one rate, and were on that ground taken for two faces of one change; later hands found the same constancy in the structure of the clause in Yiddish and in Old English. Two limits are stated by the field itself. The first is in Kroch’s own data. After 1575 the contexts part company, the negatives falling back for a time, the affirmative statement with do rising to a peak and then declining, the questions going on more slowly, and he read the parting as the point at which the grammar had been reanalysed and the single competition was over. The second is methodological. Kauhanen and Walkden in 2018 observed that fitting a separate curve to each context can serve at most as a proxy for the effect, that it leaves the differences of level unexplained, and that identity of slope is not a sufficient condition for a single underlying change; they derived the constancy instead from a model in which biases of production, fixed and peculiar to each context, promote or hinder one change in progress.

II.The Second Known Thing — the mechanism that went into every tumour

drug discovery · portfolio direction, programme termination, and herding

In 2012 Topalian and colleagues reported the first large trial of an antibody against PD-1, a receptor through which tumours restrain the immune cells sent against them. Among 296 patients with several kinds of advanced cancer, tumours shrank in 26 of 94 with melanoma, in 14 of 76 with lung cancer of the non-small-cell kind and in 9 of 33 with cancer of the kidney, and in none of the 19 with colorectal cancer nor in those with cancer of the prostate. The first approvals followed in 2014, for melanoma. What the industry then did is the best-documented case there is of a whole field moving in one direction.

the count

The Cancer Research Institute has published the count at intervals. In 2017 there were 1,506 active trials of antibodies against PD-1 or its ligand PD-L1; two years later there were 2,975, of which 76 per cent tested combinations, with 295 other drug targets among the partners; by the report of 2022 there were 5,683, given as an increase of 278 per cent on 2017. The report of 2018 noted that almost all types of cancer, many rare ones among them, were under study. The same series recorded that recruitment had slowed, that planned enrolment in trials of the antibodies alone had fallen sevenfold since 2014, and, in 2022, that the supply of trials might exceed the patients available to enter them. The counts are tabulated by tumour type and discussed as crowding.

what is known of how firms learn from one another

How firms respond to one another has been measured on the side of stopping. Krieger in 2021 followed 10,639 projects, each a drug in an indication, through phase II between 1997 and 2014, and asked what a competitor’s failure did to the chance that a project would be abandoned. Where the failed competitor shared both the indication and the mechanism, the chance more than doubled, an increase of 109 per cent. Where it shared the mechanism and not the indication, the increase was 17 per cent. Where it shared the indication and not the mechanism there was no significant effect. Stopping, on this evidence, is decided project by project, and news about the mechanism from another disease moves it little.

what the field has not asked of the entries

Starting has not been examined in this way. Evidence peculiar to an indication has not been wanting: the absence of any response in colorectal cancer in 2012; the demonstration by Le and colleagues in 2015 that within colorectal cancer the responses belong to tumours deficient in mismatch repair and are absent from the rest, which led in 2017 to an approval defined by that deficiency and not by the organ; and randomised trials that failed in one tumour while others succeeded elsewhere. Whether such results bent the course of entry into the indication they concerned, or whether every indication went on gaining at the rate of all the others from the level at which it began, is a question the counts could answer and have not been asked. A crowded indication is read as one the field has judged promising. That reading takes a difference of level for a verdict.

III.The Bridge

no paper on the rise of the English auxiliary cites a paper on the crowding of a drug target; both halls count a new option displacing an old one context by context, and only one of them has asked whether the contexts differ in rate

The halls do not meet. The constant rate belongs to historical syntax and is argued over corpora, parsed texts and the competition of grammars; the crowding of a target belongs to the economics of drug development and is argued over trial counts, recruitment and the incentives of sponsors. Neither cites the other and no review spans them. Three neighbours must be set aside before the proximity is worth anything. That a new thing spreads along an S-shaped curve is not the bridge; both halls have known it for decades, and it says nothing about contexts. That sponsors who follow one another may be resting on one piece of evidence counted many times is not the bridge either; that concerns the descent of grounds, where the matter here is the level at which a decision is taken, whatever grounds it rests on. And the finding that a failure travels by indication and mechanism together more than by either alone concerns stopping, and events; the matter here is starting, and rates. The bridge is a statement about what a difference of rate, and the absence of one, can show.

X: where one option is displacing another across contexts whose differences in favour are fixed, the contexts differ in level and never in rate; unequal rates are the signature of contexts changing separately, and equal rates at unequal levels the signature of one change showing in many places

Call it rate identity. Where one option is replacing another across a set of contexts, and what distinguishes the contexts is a fixed advantage or handicap that does not itself alter as the replacement proceeds, the share of the new option in each context, properly measured — on the logistic scale, where a fixed advantage is a fixed displacement — rises along parallel lines. The contexts differ in level and not in rate. The converse is the useful part. Were the contexts changing separately, each on what was learnt within it, nothing would hold their rates together, and the favoured would be expected to move faster, as Bailey supposed. So rates that differ are the signature of several changes, and rates that agree while levels differ are the signature of one, taken somewhere above the contexts and merely showing in them. Under one change the levels were fixed when it began, and nothing that has happened in any context since has moved them.

three consequences, not one said three times

Three things follow. The first is that to be ahead is not to be faster, and on the raw shares the two cannot be told apart. Suppose, for illustration only, that the new option stands at 27 per cent in one indication and at 5 per cent in another, and four years later at 73 and at 27. The gap has grown from 22 points to 46, and the first indication appears to be drawing away. On the logistic scale the two have gone from −1.0 and −3.0 to +1.0 and −1.0: each has gained exactly 2.0, and neither has gained on the other. A count by indication at one date, or a gap between counts that widens, is what a single rate makes of two starting levels, and holds nothing about the indications that was not in those levels at the start. The second is that the test is of an interaction and has a rival of the opposite sign. If entry were decided indication by indication, the indications with early responses should gain faster, and an indication that returns a failure of its own should fall away from its line. If it was decided once, neither should happen. The third is that the parallel has an end, and the linguist’s case shows where to expect it. After 1575 the contexts of do went their several ways, because the competition that had bound them was over. An indication in which the mechanism has been approved is in the same condition: the antibody is now the standard of care there, later trials must include it whatever their sponsors believe, and that indication has left the competition. The parallel is a property of the years before approval, indication by indication, and it is there that it must be looked for.

IV.The Question That Becomes Possible

neither discipline would ask this alone

The linguist has no reason to ask it. The contexts of a sentence do not return results; a negative question cannot fail a trial, and nothing learnt in one context is available to move it apart from the others, so that the single change is for him the expected case and the constancy its confirmation. The analyst of drug portfolios has no reason either. His unit is the project, his counts are of trials by tumour type, his models of herding concern who follows whom and on what information, and the rate at which a mechanism gains ground within one indication, set against its rate in another, is not an object his methods name. Held together, the halls pose a question that is neither’s: when a mechanism spreads across indications, do the indications differ in rate or only in level, and has any result obtained within an indication ever moved that indication from its line.

the single-decision hypothesis

Concretely. Take the public registry of trials, which records for each a start date, the conditions studied and the interventions. Fix in advance a list of tumour types, a list of the antibodies against PD-1 and PD-L1, and a window, say trials started from 2011 to 2019. For each tumour type and year compute the share of newly started interventional trials in that tumour that include one of the antibodies, and set aside, for each tumour type, the years from its first approval onward. Fit the shares on the logistic scale, once with a separate slope for every tumour type and once with a single slope and separate levels, as Kroch did. The claim has three parts. First, that the single slope is not rejected, in data with the power to have detected a faster rise in the tumours that responded first. Second, that the levels stand in the order of what was known at the outset, the responses of 2012 and the number of patients to be had, and keep that order. Third, that dated results belonging to one tumour type, an early cohort without responses or a failed randomised trial, are followed by no departure of that tumour type from its line. The first part is the linguist’s finding carried across. The third is the one that bears on direction.

why it would matter

Because the count of trials in an indication is used. Sponsors cite it as evidence that a setting is validated, investors as evidence that it is contested, and commentators as the measure of a herd. If the rates are one, the count is a starting level multiplied by a common clock, and nothing in it has been learnt in the indication since the clock began. It would also show an asymmetry worth knowing: an industry that, on Krieger’s evidence, stops its projects chiefly on news from the same indication, and that starts them, on this hypothesis, without regard to it. And for whoever sets the direction of the next mechanism the distinction is practical. Entry by a single decision is no error where the mechanism does not depend on the organ; but then the place to look for information about an indication is not how many have gone into it.

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 data. The registry is public, the dates of approval are public, and the landscape reports give totals against which a reconstruction can be checked.

the honest status

Note the narrowness. The claim concerns one mechanism, the starting of trials and not their outcome, and the years before approval in each tumour type. It does not say that the trials ought not to have been started; a mechanism that acts on the immune system and not on the tumour may warrant a decision taken once, and the hypothesis is about the level at which the decision was taken, not its merit. Equal rates would not show imitation, since many sponsors reasoning alike from one result would produce them as surely as many sponsors following one another. Unequal rates would not show that the learning was sound. That entry has not been examined in this way is the finding of a search and not of a review, and stands until someone produces the paper. The illustrative shares above are invented to show the arithmetic and carry no evidential weight. The constant rate is itself a qualified finding in its own hall, where the fitting of each context separately is now treated as a proxy for the effect and not a model of it. And where a mechanism was tried in one indication only, the proposal has nothing to say, which is how it ought to behave.