I've put this up as a joint presentation with my colleague from Birmingham, Robyn Fenner,
that's our department on the left and he did our work at the city hospital in Birmingham as well as other places.
I'll sit down if that's okay. You're happy with that? Nobody going to throw rotten eggs at me.
Good. Yeah, right. Well, that is a man called Philips Aurelius Theophrastus from Bastos von Hohenheim.
And to make life easy for all of us, he called himself Paracelsus, which makes life a lot easier.
You can see his dates there from the 16th century when he called himself Paracelsus because he was interested in this man who is Celsus,
a very famous Roman physician who was highly regarded and whose name is Celsus means high or noble or high minded.
So our friend decided to call himself Paracelsus, which is sort of noble ish or high ish or high minded ish, but it's also a pun on his surname.
Which is Hockenheim. And Hockenheim means the hi ho, literally a place near heaven.
Which Celsius is as well a high place.
So Paracelsus is a pun on Hohenheim and is in homage to his hero Celsius.
Hmm. And in 1564, Paracelsus wrote this book.
It's called Septem Defence Bonus, although its proper title is in German.
Surprisingly, for those times, you'd expect a medical text to have been written in Latin.
But he wrote in the vernacular Sieben Tag Diggings Raiden and the subtitle means Paracelsus is the reply.
If you like two criticisms from his opponents which have demeaned him in the eyes of his patrons,
he was rather arrogant man and his theories built not on the classical theories
of the day which were dependent on the Hippocratic Theory of the four humours.
So which I guess many people are familiar. Hot and cold, but dry and wet.
And the balance in the humours in the body, the choleric, the melancholic, the the sanguine in the splenetic humours.
The idea was that there was an imbalance in the humerus in the body causing disease.
If you could rebalance the body, the humerus would come into perfect harmony and you'd be cured of your disease.
And this was, as I say, a Hippocratic theory, which Galen had propounded from the seventh second century onwards and which
actually dominated medical thinking until even the middle of the 19th century.
Very powerful theory. But Paracelsus had a different theory.
He had a tripartite theory based on things that he used to treat based on the Trinity, the Holy Trinity, and so on.
So he wasn't very popular among his colleagues and was highly criticised.
So in 1564 was published after he died, of course he wrote it before his death, his seven defences.
And this is a page from the first defence.
As you can see, it's written in German in typical Gothic print of the time and I've blown up the top bit so you can see it a bit more clearly.
And I've highlighted the most famous sentence from this book, which is still quoted today,
and there it is for us is thus net gift est allerdings in gift and Nixon gift align the doses marked ascending kind gift ist.
It is written out. It means what is a poison?
Everything he says. Allerdings in gift. Gift is a poison nowadays felt with one ask.
Everything is a poison. And then he repeats.
It admits own gift, and nothing is not a poison.
He really wants to tell you this. Everything is and nothing is not only the dose determines that something is a poison.
And he's absolutely right. And this is a message that has been forgotten for 400, 500 years or more.
Not only does he tell you it twice in German, but he tells you it in Latin as well.
In the marginal note, nothing is without poisonous effect.
Except for the dose. That determines it.
So 1564 posthumously published.
We now move forward 300 years to 1864.
And these two gentlemen, Cato Goldberg. On the left, there's a Norwegian professor of chemistry and his colleague, if you can spot him there.
Pater Varga surprisingly had time for anything in the scientific world, was a mathematician.
And these two together discussed the question of chemical interactions.
And they gave a talk on the 11th of March 1864 to the Norwegian Academy of Science and Letters.
This is the first page of the published paper that came from that talk written in Norwegian.
They are the title, says Varga. On behalf of his friend or his colleague, Goldberg presents their joint work studies on affinity.
And for those of you whose Norwegian is not as good as mine and mine is nonexistent, there's a translation of the first paragraph.
And what they say is we're studying chemical forces.
There are lots of theories about them, but we doubt if anybody will ever understand the laws whereby chemical forces interact.
This is a little disingenuous, actually,
because in this paper they go on to say exactly how chemical forces interact and propound a law which is now known as the law of mass action.
They didn't actually use that term there so themselves.
But I'll show you in a minute. Well, not surprisingly, nobody read this paper.
It's in Norwegian. And at that time, maybe one and a half million people lived in Norway.
So three years later, Golberg and Varda republished their work now increased in volume in this French paper called H2,
Xfinity, XI MC, which was taken notice of.
Even so, it took a little time for the new ideas to take time to emerge.
And the idea of the law of Mass Action wasn't formally stated until about, what, 35 years later.
This is from 1879. This is an extract from the Oxford English Dictionary and it defines mass action.
You can see the law of mass action. You read it there.
The principle and this is important, the rate of a reaction, that equilibrium is proportional to the concentrations or activities of the reactants.
That is the law of mass action. It has nothing to do, incidentally, with Extinction Rebellion,
which is a type of mass action of a different sort, as this latter definition shows you.
But there it is quoted in 1879, the first time that the OED lists it.
And you can see that they these authors of the Journal of Chemical Society refer to Goldberg and Vargas French paper.
And in case you're wondering why it's called mass action and not concentration action, because it's concentration is not mass.
It's because in those days, the term active mass which go back and forth they used in their French version, mass active meant smaller concentrations.
And again, there you are in 1879, this times in the London, Edinburgh and Dublin Philosophical Magazine,
another reference to go back and Varga in relation to active mass.
So a hugely important and influential paper demonstrating the relationship at
equilibrium between the concentrations of substances and the rates at which they react.
Actually in passing. It doesn't matter if you've got as many intermediates in the reaction as you like.
The rate at which the two,
let's say two compounds are converted into one at the end depends on the concentrations of those reactions those two reactants.
It doesn't matter how complicated the reaction is. So let's have a look and see what's actually going on here.
If we imagine two substances, A and B, which I imaginatively call them.
They react and they produce a compound.
Abby. That is. And that's the law of mass action.
The rate of reaction depends in this case on the chance of collision.
What does the chance of collision depend on? Well, it depends on the amount of molecules there are.
The more molecules, the more chances there are for collision. And so the probability of a collision in the first case on the left is one, one chance.
In the middle case, it's three chances, and here it's four chances.
So it's both substances that matter.
Concentrations of both increase the risk of the chance of a collision and therefore the chance of a reaction.
Now, if we look at what Goldberg and Vega published that say, yes,
this is their French edition referring to, incidentally, these slides come from Robin.
They are looking at reversible reactions.
And what they say is that if A plus B gives a B, there will be a forward rate constant and a backward rate constant.
Denoted by k forward rate constant kb u backward rate constant.
And the velocity of the reaction can be described as the product of these things.
So the velocity, the rate at which this reaction goes forwards is the product of the forward rate constant.
And the two concentrations of the substances, the square brackets indicate concentrations.
The backward velocity, similarly is the product of the backward rate constant and the concentration of the product.
For those who are interested in these kinds of things, this is a second order.
Reaction depends on two concentrations.
And this is a first order reaction to the solution of the differential equations are different but at equilibrium these two.
These two velocities are equal. So the rate at which the two compounds are combining is the same as the rate at the speed.
I should say the rate. The speed is the same as the speed with which the single compound is dissociated into the other two.
So there's complete equilibrium. And so these two equations, these two things become equal.
We can equate those two things. And if we say that that equals that and then rearrange it,
we get that the ratio of that to the product of the two compounds is the ratio of the two rate constants.
And we can now replace that constant by a single constant, which I've called K.
And this, in effect, is the law of mass action.
The rate of the reaction is proportional to the concentrations.
Now that's chemistry. In pharmacology, we deal with receptors, primarily other things, tube receptors and the receptacle.
This is a paper by my colleague Humphry Rang,
who started life in the Department of Pharmacology in Oxford with Bill Patten and then moved to become Professor of college at UCL.
And in this paper, Humphry writes about the history of the receptor concept.
And the idea is that you have a drug which reacts with proteins usually in the body, and the protein is that receptor for the drug.
And that protein then causes so-called second messengers to act producing effects in tissues.
So the interaction of a drug with its receptor is an important concept.
And it followed Erlich's idea of a magic bullet by this idea from a man called Jan Langley.
Who was a professor of physiology in Cambridge and who published this seminal paper in the Journal of Physiology in 1905.
And he was studying the effects that nicotine and curare had on skeletal muscle, striated muscle.
What he discovered was that there were substances in the muscle that recognised these drugs, nicotine and curare, and caused the muscle to contract.
And so he proposed. That this was an accessory substance in the muscle.
Recipient of stimuli transferred the contraction to the muscle.
And he talked about it as a receptive substance. And you'll see he puts that in the running head.
Although he didn't include the term receptive substance in the title of the paper.
Only in the running head and in the body of the paper. This idea is now what we call receptors.
The receptors are generally proteins, usually in the plasma membrane of a cell,
sometimes intracellular on which drugs act to produce effects via second messengers.
This is a hugely important principle in pharmacology.
And the more drug you have. The faster the reaction occurs and the bigger the effect.
And that is the principle of the dose response curve.
So let's look at the mathematics of the receptors, which is very similar to what we've just been talking about here,
the chemicals, A-plus, b, reacting to produce a B for a receptor.
We just replace the letters with different letters.
We have a receptor plus a drug gives a drug receptor complex, and that's a reversible reaction.
The drug can dissociate from the receptor. If it didn't, the receptor would be destroyed and you'd have to start making new receptors.
There are, of course, some reactions that are irreversible, but very few.
So let's have some definitions. We call our D, which is on the right side there the number of receptors that the drug is occupying.
Drug will not necessarily occupy all the receptors available.
It may or may not, depending on how much drug there is and what kind of drug it is.
We'll call our F the number of free receptors, the receptors that are not bound by the drug.
And so the total number, our T is our D plus our L.
Now we can write our equations. So we know that by the law of mass action, it's the ratio of the concentrations that are constant.
We call that K before. If you remember, that's the law of mass action.
If you multiply the concentration, if you like, of three receptors,
but the concentration of the drug divided by the concentration of bound receptors
that is constant in a reversible reaction at equilibrium by the law of mass action.
So we rearrange it. We move the RF to the other side.
And since we know that the total number of receptors is already plus RF,
we can substitute for RF and we get this thing at the bottom and that it rearranged.
Gives you this. Where the proportion occupied now is the number of receptors bound to the drug over the total number of receptors.
And so what we get at the end is this proportion occupied is the concentration of the drug
divided by the constant K plus the concentration of the drug relatively simple equation.
What does this mean? What is this constant? Well, when the constant equals the concentration of the drug.
That thing becomes on the left becomes that thing on the right.
And that's just a half. So we've now defined our constant.
The constant is the concentration of drug at which occupancy is half maximal.
And that's commonly called the K-T or the dissociation constant.
And the lower the dissociation constant, the more potent the drug is or the higher affinity it has for the receptor because you
need less drug to saturate or to occupy half of the receptors in this case for CD.
So the lower the CD, the more affinity, the more efficacious, if you like, technical term, the drug is at the receptor.
And here I've put it in a different way. The amount of drug bound there is set to be over the amount that can maximally bend that the b max.
Which is the proportion of receptors occupied as drug over CD plus drug concentration.
And this is the equation of a rectangular hyperbola.
Like that. That's what it looks like.
So if you draw B over B max on the horizontal axis, on the vertical axis, the concentration, the numbers don't matter.
On the horizontal axis, you get this rectangular hyperbola.
And what this shows you is that when you don't have any drag, there's no binding.
As you increase the amount of drag, there's more and more binding, but you can't occupy more receptors than there are to be occupied.
And so you reach a maximum now without going into the details.
Oh, yes. And when you draw, this is a logarithmic.
Concentration curve, you get what's known as the sigmoid curve. It looks like the shape of a long X.
And that is a typical curve for the binding of drugs to receptors.
Notice that that's pretty linear in the middle section from about 20 to 80%.
This is long linear and that's useful for modelling responses in that range.
This is also true without going through all the intermediate steps for the effect
that binding to the receptor produces and we can change B to E binding to effect,
and we find that the ratio of E to Emacs,
in other words, the proportional effect you can produce with a drug that's binding to receptor is
exactly the same in the relationship to the amount of drug that you're using.
And if we rearrange that, we put the emacs on top.
We change constant now instead of 2kd, which is the 50% binding.
We call it D 50, which is the concentration of the drug that produces 50% of the maximum possible effect.
Then that is the dose response curve equation.
And again, if we draw of a re max against log concentration, we get a sigmoid curve, typical dose response curve.
And again. 20 to 80% of it is on the long linear part of the curve.
So the law of mass action applies to receptor drug interactions, it predicts dose responsiveness,
and it's relevant to both benefits and harms of medicines, adverse drug reactions and the like.
The law of Mass Action has many, many more later with many more, many more applications.
For example, enzyme kinetics have exactly the same equation in the same rectangular hyperbola transport,
active transport of ions across cell membranes,
exactly the same equation the control of acidity and alkalinity in cells, the Henderson Halbach equation exactly the same equation.
Wherever you have things going on chemically in the body, the law of mass action applies and you get the same equation out at the end.
It's universal. Now let's move on to some real dose response curves here.
This paper by Steve Stephenson, published in what used to be called British Journal of Pharmacology and Chemotherapy.
Now, just British Journal of Pharmacology in the 1950s shows the effects of a series
of salts of tri missile ammonium on the contraction of guinea pig ileum.
So you put up a guinea pig piece of guinea pig gut in a water bath and you
add these things to it and you measure the contraction using a tension gauge.
And the more you put in, the bigger the effect dose response curve.
But what you can see here is there are three different classes of drug.
There's these three beautiful style in detail. Notice they're all parallel.
They have the same effect exactly on whatever it is that the receptor.
But they're apart because some are more potent than others.
So you need less of the beautiful to produce the same effect.
So there's a difference between potency and efficacy, which is the effect you can produce.
What you see is that these three produce the maximum effect. You can't get the gut to contract any more than that.
They are what are known as full agonists. They produce the full effect.
But these three peptide cocktail and. No, no, don't do that.
You can occupy as many receptors as you like. You never produce the maximum effect.
These are known as partial agonists. And that's an important principle in pharmacotherapy.
Choosing drugs that do or do not have partial agonism effect.
I'm not going to talk about that. This is an odd one.
The D'asile, it looks as if it's contracting and then relaxing.
And that's a phenomenon known as harms, which is rare, but has been described and does sometimes occur.
But mostly we have full agonists or partial agonists.
Now, this is fine in vitro. We can do this. We can string up some gut and drop some drugs on them, and we know the concentrations we're using.
It's relatively easy, although very elegantly done.
But you can and you can do this with other systems in vivo, in vitro.
Here's an experiment with adipocytes fat cells, and you incubate them with glucose and you add insulin.
And the more insulin you put in, the more glucose is taken up.
And this is linear scale, and here's the low dose response. Q So that's fine.
Another in vitro experiments this time using human cells, not guinea pig,
but getting in vivo examples is difficult because we can rarely measure the actual
concentration of drug at the site of action for giving a drug that affects the heart.
For example, how do we know what the concentration is in the heart?
Take a biopsy may be difficult. Occasionally you can do it.
And here's an example. These two drugs be met tonight in furosemide are loop diuretics.
You take them totally. They circulate in the blood and they are excreted via the kidneys.
They don't work as diuretics, increasing urine flow until they get into the lumen of the of the kidney tubule.
In other words, they have to be in the urine before they increase the urinary flow, which is a bit of a [INAUDIBLE], really.
You'd want them to do it before they get out. So if there's no urinary flow, they don't work.
Can't kick urinary flow with these drugs. They don't work.
They have to be in the urine before they'll increase the urine. It's a bit of a catch 22, but once they get in, you can measure the concentration.
This case rate of excretion and that's the concentration at the site of action because you're measuring them in the urine.
So here we have dose response codes for the concentration at the site of action versus the rate of it,
in this case, sodium excretion, beautiful dose response curves.
These are American data, really elegant experiments.
So you can sometimes show in vivo that there are dose response scores of the kind that you expect.
And notice I didn't point it out in the previous slide, but here as well, typically dose response curves occur over about two orders of magnitude.
That is very typical. Some are have a different slope, but typically a 100 fold difference is the range over which you expect changes to occur.
Now here's an indirect method of doing it.
Instead of measuring the concentration actually at the site of action, you measure the plasma concentration as a surrogate for that,
and you assume that the plasma concentration somehow is proportional to the site of action concentration.
And this is an experiment that was done some years ago now, a long time ago in 75 for everybody was born, I guess.
Is that right? No propranolol. The beta blocker, which you can give orderly measure the plasma concentration,
and then you exercise the individual and see how much the tachycardia, the increase in heart rate is prevented by the beta blocker.
You can see there's a very good relationship. These are five different patients, each studied three times three symbols for each one.
And you can see there's a very good linear relationship on the log scale with the inhibition of exercise induced tachycardia.
So this is the 20 to 80% linear log,
linear bit of the dose response curve using plasma concentration as a surrogate for the concentration at the site of action.
We call this typically the dose response curve. It's not it's a concentration response curve.
But we call it the dose response curve because we assume that the dose you give is related to the concentration results.
The bigger the dose, the bigger the concentration. Now, these are beneficial effects I've just shown you.
Diuresis slowing the heart rate when you've got a tachycardia.
What about some adverse effects? Well, this is an early classification of adverse drug reactions.
Eddie Wain, who was originally Professor of therapeutics in Sheffield and when I was a medical student, was the Professor of Medicine in Glasgow.
Classified adverse drug reactions as being either predictable and unpredictable.
That's a funny classification, but it lasted until Ruth Levine, an American pharmacologist, talked about dose related and non dose related reactions.
Then on Wade and Linda, Billy Own Wade was professor of clinical pharmacology in Birmingham,
also talked about dose related and non dose related adverse reactions.
And this idea was reinforced by Mike Rollins,
who at that time was professor of clinical pharmacology in Newcastle and later became well known as chairman of Nice and other big committees.
He and his colleague Thomson invented this imaginative classification and B.
Lots of imaginative classifications like that. Type one and type two.
Or. And B or ABCD sometimes.
And they said there are type A reactions and type B they meant dose related and dose related.
But then they realised nobody could remember which was which. This is a bit of a bind.
So they invented a mnemonic. They called them augmented and bizarre.
Augmented means increased, but the dose bizarre means no relation to those.
And they later on, some years later, in an article in the BMJ, they talked about dose related,
non dose related, exaggerated or a bad, predictable or unpredictable, preventable and so on.
This to me is odd. And this this idea lasted for about 35 years and nobody challenged it.
But it is very odd. Why should anything be not dose related?
Everything is surely related to dose. Let's just see.
Test this question about known dose related adverse reactions.
Here's a statement. That you might or might not agree with.
Toxicologists need many molecules for. They're going to study toxicology.
Pharmacologists study the right amount of molecules.
Immunologists need only one molecule. And well, you know that I'm going to test these assumptions.
At least I'm going to test the immunological assumption. Does anybody here suffer from hay fever?
Yeah, a few. Not as many as I'd expect. Some of you hiding it, maybe, anyway.
You all know about hay fever, too?
Yeah, I have it. Itchy eyes, runny nose, sneezing, bronchospasm, wheeze.
It's not pleasant. Now I'm going to make some statements about hay fever, and I want you to raise your hands.
Don't be shy if you think the statement is true.
Right. Is this statement true? So here's the first statement coming up.
The risk of an attack of hay fever is not related unrelated to the pollen count.
No takers. Not just shy. Nobody believes that statement.
Okay, I'll try a second statement. The risk of an attack of hay fever increases as the pollen count falls.
Still no takers. It's very disappointing, really hoping somebody would raise their hand.
The risk of an attack of hay fever increases, the pollen count rises.
Oh, right. Everybody seems to think that that might be true.
Well, it is true. Of course it's true. The higher the pollen count, the greater the risk of an attack of hay fever.
And you hear on the weather forecast, the pollen count is rising.
It's a warning to all you guys that, you know, take your steroid or your optical or whatever you use.
And here's the evidence. This paper by friends in the Annals of Allergy and Asthma and immunology.
Shows a dose response curve. It's the wrong way round, if you like.
Here's the log pollen count on the vertical axis and the symptom score, but you can see a clear dose response curve.
The higher the pollen count, the bigger the risk of an attack of hay fever in the population is.
Notice that it goes over 1 to 3 or four orders of magnitude.
It's quite a shallow dose response curve, but then pollen counts vary enormously.
And they even say this in their text.
Quantitative Dose Response Models, Nonlinear relationships.
These are classical dose response curves. So the immunological idea, the idea that people have about immunology, that it's not dose related is wrong.
Everything is dose, really. Everything is a poison. So let's examine this in relation to people's ideas about non dose related adverse reactions.
I'm going to show you some theoretical dose response curves just for illustrative purposes.
Here's the dose response curve. Beneficial dose response curve, whatever it is, doesn't matter.
Plotting the response against the low dose concentration. And it has a sigmoid shape.
No, no drug. You get no effect. Linear effect between 20 and 80% and the maximum possible effect achieved.
You wouldn't want to bother using a dose in this range because you don't get any extra benefit.
You'd probably choose a dose in this sort of range here. For maximum benefit that you can achieve, but you have to be worried about adverse reactions.
Now the idea that adverse reactions are of two types A and B is naive and simplistic.
Robin and I suggested three types.
Depending on the dose response relationship, which you can actually measure something you can actually measure and quantify.
And the first time we described what we call hyper susceptibility reactions, people are more susceptible than others are.
These are typically hypersensitivity reactions, allergic reactions, but they don't have to be.
There are other types, so we call them hyper susceptibility rather than hypersensitivity.
And the whole mark of these is that they occur at doses of the drug, which are lower than those responsible for benefit.
Penicillin. Allergy. The problem is, of course,
you give somebody a dose that you think is beneficial and they're at the top of the dose response curve for the adverse reaction,
for the allergic reaction. That's why it appears to be non dose related because it occurs at only one dose.
And if you increase the dose here, you don't get any different effect here because you're already at the top of the dose response curve.
So that's hyper susceptibility. The second type are what we call collateral.
They occur right beside in the same dose range as the beneficial responses.
And these are difficult to handle because means you can't you can't avoid them.
These you can avoid by not giving the drug a pity.
But that's what you have to do.
These if you want to use the drug, then you have to wear the fact that there's going to be likely going to be an adverse reaction.
The things you can do about that, and I'm not going to discuss how you handle that problem,
but collateral reactions do occur and can be difficult to treat.
And then, of course, there are toxic reactions.
These are reactions that occur at doses that are higher than beneficial and should be entirely avoidable by not using high doses.
And they can occur either on a separate mechanism.
Or via the same mechanism as benefit, but giving too much, too much of a good thing.
If you give warfarin to prevent the blood from clotting and you give too much, you'll get a risk of bleeding.
So that's a harmful reaction at the top of the same dose response curve as the benefit.
But. Well, what else? That might be, for example,
that the toxic effects of penicillin on the central nervous system are mediated by an action that has nothing to do with its antibiotic effect.
There's something there, but you only get it at very high doses. So some examples.
Well, here's a real example. This is a curious syndrome called the lupus syndrome.
A lupus like syndrome.
It's similar to a disease called lupus erythematosus, but it's induced by drugs such as this one, hydrazine we don't use anymore.
And if you look at the data, you see that it's dose related. So it's a limited allergic reaction, but it's dose related.
You increase the dose. You increase the risk. And there's the sex difference as well.
Women are more susceptible than men. This is another allergic reaction, which, as it happens, Rabin's wife studied when she was a Ph.D. student.
And what she did was to challenge the skin with a substance called di nitroglycerine, benzine.
When you inject not clear benzene, then you get an allergic reaction, which you can measure by the thickness of the skin.
Then you can see that when you challenge the skin, you get increases into each one of these as it is a separate patient, and that's the control.
So you challenge the skin with this stuff, then you get a dose related increase in thickness of the skin.
And the response also depends on the sensitising dose that you used in the first place.
So it's two types of dose response reactions. But despite this, people keep on talking about non dose related side effects and why?
Why do they do that? What makes them think that things are not dose related?
Well, the first problem is they have this idea is that allergic reactions are not dose related, which is wrong, but they think it is the case.
And so they call anything that's an allergic reaction, non dose related.
It's a misnomer. But this side effect of valproate paper isn't in that region.
It's these are probably collateral or toxic reactions.
So why do they call them non dose related? Well, it's because they see them at only one dose sometimes.
Or there may be other reasons of maybe they've only used one dose.
I mean, let's look at some of the possible reasons.
Well, the first reason is that they've seen an event they've associated with the drug, and there's no association at all.
It's just not so. So they've made a mistake in calling it an adverse effect in the first place.
And that could be just because it's a chance finding or there may be methodological problems, confounding factors, biases.
And so here's an example. This is a drug called into Catterall, which dilate shore bronchioles and asthma.
And what these people showed was that there was.
Headache occurring in these patients would be given in the Catterall.
They thought it might be due to vessel Dilatation maybe, but it was also present in the placebo group.
And when you look at another study, you can see that the risk of headache is actually pretty much the same across all doses and all non doses as well.
This is just an it's a non-event. People get headaches and if you're taking into control, you may or may not get a headache.
The fact that it's not dose related makes you assume it's a non dose related effect, but it's not an effect at all.
It never was. So that's one reason why people get it wrong is another reason.
This is a drug called disulphiram. And liver damage was reported.
What's Disulphiram use to treat anybody?
No alcoholism. And it's not surprising that one sees liver damage in people who are taking excess alcohol.
This is confounding by indication. It's not that the drug is causing liver damage.
It's that the drug is associated with another factor that causes liver damage.
Nothing to do with the drug at all. So it's confounding by indication.
Now, here's another reason. The effect has its dose response curve at lower doses than you studied.
This is what I was talking about before. Hyper susceptibility reactions.
So here we're back to our hyper susceptibility curves.
Here's the benefit curve. Here's the harm curve, the susceptibility reaction.
And of course, you give the drug in a beneficial dose.
And so the adverse effect appears to be non dose related because you're at the top of the dose response curve.
There is a dose response curve can easily be shown by giving a test dose, a very low dose of the drug.
And we do this for some drugs has been done for penicillin, for example.
It's not a very good test. We still do it for amphotericin before we give it as an antifungal drug, give a small dose.
If you get an adverse reaction to the test dose, a small reaction that predicts a large reaction, that's a beneficial dose since you don't use it.
If there wasn't a dose response curve, test doses would be totally useless.
You couldn't use them because they'd produce the same effect if there was no dose relationship.
But they do produce different effects. The test dose produces a small effect and if you gave the beneficial, do she get a big effect?
So the test dose predicts the risk. This also reminds us that you can desensitise people with hypersensitivity
reactions by giving them small doses of the drug to which they're sensitive,
and you can then build up the dose gradually and desensitise them.
Couldn't do that if there wasn't a dose response curve. So that's the second reason.
Here's another case of a so-called non dose dependent adverse drug reaction.
It was a very widespread error. Throw down to red skin with flaking of the skins.
Quite unpleasant. You can lose a lot of water through the skin surface in this way, become dehydrated.
These types of rashes can be fatal in some cases.
And this these authors say it's an unusual non dose dependent,
but they say the literature says that adverse reactions are dose dependent with mild reactions at low doses and severe eruptions at high doses,
they set themselves. And they say, we gave this man 800 and he got a rash.
We gave him 600 and he got a rash. So we think it's non dose dependent on this guy.
The dose response curve was up to 600, clearly.
And in fact, there is other evidence here that these reactions are dose dependent.
So there is this misunderstanding. The third.
Reason that we've given here is that there is huge variability in the population studied so that you don't see the dose relationship.
It's hidden in the variability of the results.
Here's a good example. This is a drug called Ember sent, an Amber Sent and is an endothelial receptor antagonist that's used to treat lung,
arterial hypertension, a very unpleasant disease, difficult to treat.
And in this study, there were a whole range of adverse events reported.
I've highlighted two of them nasal congestion and abdominal pain.
Here are the data to contrast. So here's the placebo data in increasing doses of the drug.
These are the numbers of people here, the numbers affected and the percentage affected.
So for nasal congestion, the percentages increase with dose.
Very nice dose response curve. This is probably very likely an adverse effect of the drug, which is dose related.
Here's the abdominal pain. You can see there looks as if there's an effect, but it's very flat.
There's no dose relationship. What's the explanation of this?
Is this a non dose related reaction? Well, I don't think so.
It could be that this is the top of the dose response curve for this adverse reaction.
That's possible. But I think there's a better explanation than that here of the data that I've just shown you for headache now plotted on a graph.
And what I've done now is to add the confidence intervals to those estimates.
Then you can see that you can't tell anything from this information you really don't know.
And if you fit a dose response curve to it, it could well be just like that.
So the study was not big enough to rule out what is probably the true dose relationship between this drug and the headache,
assuming that it's an effect at all, which is suggested by the difference between the placebo and the treated,
although there is quite a bit of variance there as well, which might mean that it's not a true effect.
We can't really tell. Point is that the study wasn't big enough and that's a major problem for pre licensing drug studies.
They're generally not big enough to detect adverse reactions.
They're good at detecting benefits. Because you don't need such big studies.
Most people will respond to the beneficial effect.
That's what you're looking for. But when it comes to harms, where maybe only a few percent are affected, you need much,
much bigger studies and nobody does them pre licensing because they're not really interested in finding out about drugs as adverse effects.
They want to market them for their beneficial effects.
So now a main problem with all of this is that it's very difficult to find data on dose response curves.
Nobody publishes dose response curves that study have just shown you with three doses is very unusual.
Most studies involve one dose or maybe two at most.
And even though they do, they won't you know, they won't publish dose response curve,
certainly not with one or two points only, not even often with three.
And I've never seen a drug study with more than three arms to it.
Maybe there are, but it's very uncommon. So we thought that it would be useful to try and use modern meta analytical techniques in a systematic
review to generate dose response curves by looking for data in the literature from published studies.
A dose here, a dose there, and put them all together in a single model and generate a dose response curve.
So that's what we've done in this paper. And Richards here, he's the chief mover in this,
although Langford was a mathematician who actually did the work and get advised, I think, on the interpretation, very helpful.
And I stood back and let it all happen. Great.
And here's the data we analysed. We looked for trials of a drug called Alogliptin, which is an antidiabetic drug.
It lowers the blood sugar and a measure of the effect of lowering blood sugar.
Is this thing here? HB one C, which is a measure of the efficacy of treatment in diabetes,
gives you long term measure of overall exposure to glucose over weeks or months.
We found 14 studies. And here are all the data from the different studies showing the relationship between dose and change in HB one C.
And you can see it's a hyperbolic curve probably. This is a linear.
Scale. And here's the effect. And it's upside down because we're reducing something rather than increasing it.
But it still looks as if it has the same shape. And so we used a pharmacological model.
You recognise this bit of it I showed you before.
The effect equals the imac's times dose over the 50,
the constant plus the dose so that we added a baseline effect because there's always some HP H1 C in the system.
Most systems you look at have nothing to start with and then it changes.
For HP one C, there's always something there. So you put in a baseline and there's an error term.
And so the response was modelled using this equation and a lot of fancy computing and this is what we came up with.
We used four different methods and pretty much the same really.
There's the, there's the fit. And you can see we've got.
Confidence intervals on the likelihood that that is the true mean.
And so we were able to. Generate dose response codes.
These two here show you the rarity of high dose experiments and the huge variance on those.
We can ignore that this is the main main bit of the business.
So we thought that was a useful technique. And now I'm going to finish off by showing you some work that we've been doing recently.
It's very early stages, but it's quite interesting already.
And this was a young student who came to work with us, Evie Monahan, who turned out to be an absolute whiz.
She bashed her way through a whole load of data in double quick time, demonstrating it in ways that I couldn't begin to understand.
And I'll show you one of her results. This is a drug called Atorvastatin.
It's a statin that's used to lower blood cholesterol, a particular form of cholesterol called LDL, low density lipoprotein cholesterol.
And it's the statins are widely used. Everybody knows about the statins.
They're used to prevent heart attacks and strokes by lowering cholesterol and they have adverse effects.
They can cause muscle pain and sometimes diabetes if you use too much.
So the question of what the correct dose should be is quite important.
Can you find a dose that satisfactorily lowers the cholesterol and avoids the adverse effects?
So what we did was she went through clinicaltrials.gov looking for trials containing atorvastatin.
She found 600 or so, she screened them, excluded 526.
I think I'll show you the exclusion criteria, but you're not going to read them.
She came up with 73 that looked as if they might be useful and 55 of them were.
The other statines we've studied weren't quite as good as that. This is probably the best I think of the bunch.
That's why I'm showing it. Of course, you always show the best data and call it typical.
Those are the exclusion criteria. So you see why she excluded 500 odd various reasons for not including the data.
But here's her dose response curve. Using the program, the kind of approach that we used for the other Lipton work.
And it's pretty good actually. I was really surprised.
We got such good dose response data and the variances are quite small.
But you'll notice two things about this. First, that the maximum effect occurs at about 50 milligrams.
I shouldn't have to use more than 50 on average and the variance is a very tight.
So it's unlikely that anybody in the population would need more than that.
But the second thing you notice is that nobody, it appears, has studied anything, even approaching the edifice that all using high doses.
And the variance at five mg shows you that there are relatively few studies, even as low as five and none below that.
There's the ED 50, which is around four, by my calculation.
I think it's maybe slightly different. I'm using 50 as the maximum, which may not be the case.
But here's the manufacturer's dosage recommendations.
The bottom line usual starting dose is ten and the maximum is 80.
So are we using doses that are too high? Should we be using lower doses?
Is that why people are now beginning to wonder about diabetes as an adverse effect of the statins?
And could we have less in the way of muscle pain?
If we used lower doses, we might get smaller beneficial effects, of course, and one would have to balance that up.
But the lower your cholesterol is, the better, whatever it is.
And so perhaps we should be thinking again about the doses.
Now, before we did this study, I did a preliminary analysis and I got 8050 values from the literature.
I'm not sure how well defined they have been in the past,
but I plotted them against this measure of how effective the drug is in inhibiting its target enzyme, the HMG, COA reductase.
And you can see there's a reasonably good relationship between those two things and this is a logarithmic scale, of course.
It's like this is linear, it's not bad.
And it does suggest that the ID 50 for reducing LDL cholesterol is somehow related to the mode of action of the drug.
We need to confirm this with the data we've got at the moment, and it may not be as good if only because of regression to the mean I guess.
I don't know. But there's a hint here that there may be something worth thinking about.
So that's my review of some aspects of dose responsiveness.
There are other things. It's useful when you're teaching medical students and training doctors how to use drugs properly to
introduce the idea that things are graded in looking for signals of harms and benefits in big databases,
for example, of anecdotal reports. If a report suggests that there's no difference across a range of doses, you think, well,
is that truly in effect, you expect things to be dose related and benefits as well.
Test doses. I've mentioned a dose titration.
The principle of increasing the dose, reducing the dose, depending on the type of adverse reaction is to that side of the beneficial curve.
Is it in the middle or is it toxic?
The three dose adverse reaction approach and monitoring therapy, biomarkers and so on, and of course in drug development.
So. Don't let anybody tell you.
But any biochemical biomedical phenomenon is not dose related.
And remember, Paracelsus, everything is a poison and nothing is not a poison.
Only the dose determines whether something is or is not a poison.
Did you?