Hello.
I am Jose Carvalho,
a statistician at Statistic Consulting in Campinos, Brazil.
I thank you for the opportunity to show an application of JMP to clinical trials
where a major improvement movement came from a statistical discovery.
As a result of that discovery,
one trial ended with the expected and very desired results.
Subsequent trials on the same syndrome will be much cheaper and faster.
The problem is the bleeding after birth or postpartum haemorrhage, P PH for short.
P PH accounts for 125,000 deaths per year.
Even in developed countries like the United States,
it's the cause of 11% of the maternal deaths.
Now, PPH is defined, just for classification,
as blood volume in excess of 500 mL in 24 hours after delivery.
If the volume exceeds 1,000 mL, then it's severe PPH.
It'll be interesting to know the main cause of PPH.
90% of the cause are uterus atony .
It's a failure of the uterus to contract after the delivery.
If the uterus failed to contract, then the bleeding continues.
Then we can treat that by giving drugs to contract the uterus
or by some physical action.
The main cause are trauma
and placental tissue retention and coagulation system failure.
You'll be dealing with uterus atomy and its prevention.
PPH can bring serious threat to woman's life and health.
Its onset must be quickly diagnosed during the delivery and treated.
Treatments include, as I said, drug treatment with additional uterotonics
and as a last resort,
artery irrigation or h ysterectomy, the uterus removal.
New drugs and devices are being developed to prevent PPH.
Every one of those must be tested in clinical trials before they are allowed
to use in the natural deliveries.
We have data on three very large trials.
The first one, the oldest one, was published in 2001.
It was the Misoprostol.
That's the name of a drug
that was compared to the standard treatment and used 18,000 women.
The second one after that,
and that was published in 2012, is the Active Management, not a drug,
but a physical procedure of pulling the umbilical cords.
Now, the Misoprostol didn't prove to be as effective as the standard drug
of treatment, which is oxytocin.
The Active Management did not show any improvement also on PPH.
Now we're going to deal... Sorry, with the Carbetocin trial ,
published in 2018, the largest of all, that enrolled 29,000 women.
In all these trials, the primary outcomes were severe PPH and/or PP H.
Now, to diagnose sPPH and/or PP H, we need to know the blood volume.
The observations were volume, the numbers volumes in m L.
But only the indicators of SPPH and PPH
were considered in the statistical analyses.
That is binomial variance zero, one, yes or no.
Okay, in spite that we had the information about the blood volume.
Before we proceed, just a small explanation
about the two drugs that we'll be dealing with, again.
The standard drug to use in deliveries is oxytocin.
It's given routinely to every delivery work,
every part in the world.
As soon as the baby is delivered, the woman receives a shot of oxytocin.
It's a standard procedure.
Now, oxytocin is very nice.
It reduces the severe PPH rates from 3.84% to 2%.
It helps the incidents or the rates of the sPPH.
But there is a problem, it is a heat-labile substance.
It must be kept in a cold chain at seven centi grades all the time.
Now, in countries with low resources, this can be a problem.
If you do not keep it in this cold chain logistic,
the drug will lose its efficacy, I'm sorry.
Sometimes you can apply a drug that is not effective at all.
Now, carbetocin, it's a new drug which has the same active principle of oxytocin
and just a change in the excipients that makes it heat- stable.
Carbetocin can be kept for six months at 30 centigrades,
which is about room temperature in most places in the world.
Now, there were very high hopes
that carbetocin would be a good replacement for oxytocin,
most of all for use in those low- resource countries.
A clinical trial was devised for PPH, it was done by the WHO
and it was a non- inferiority trial.
The parameters for this trial are in the objective.
The investigators said that, to declare carbetocin non- inferior
to oxytocin, it should preserve 75% of the benefits.
Now, the benefit is this 3.84% minus 2%
so this gives them non-inferiority margin of 0.4 6%.
We are talking about very low rates and the relative risk of 1.23.
Carbetocin would be declared non-inferior to oxytocin
if in the trial we could prove or bring evidence on
that a relative risk is less than 1.23.
This result in just a mazing competition in a sample size with over 30,000 people.
We ended up with a trial with about 29,000.
Those were in several countries as we signed that table before
in the many centres.
It was a very expensive trial, just a data collection
of well over almost two years.
It's a very serious thing.
Why are the trials so large?
Well, the obvious response answers to that question,
is the proportion being compared are small.
The effects are necessarily even smaller.
Not so obvious, but it's still obvious,
that the triumph needs to be so large because we are losing a great deal
of information by mapping V, the volume, into two categories, like this.
On this histogram here we have the actual distribution of the blood loss volume
for the 29,000 subjects of the trial and then the cut- off point, thousands .
Just imagine,
just looking at the histogram, how much information is lost
by taking all the niceties of the frequency of the histogram
in zero, one left to the thousand line, right to the thousand line.
But that's the way it was done,
because for some reasons people like to use this dichotomization.
If it's over 1,000, it's severe PPH.
If not, it's not.
I don't know even if that's well too associated
with any further consequence on the health of the women.
That's the way it's done.
The classification is that.
Now JMP helped us to discover
that the distribution of the blood loss volume is log normal.
There is a story behind it.
We set forth to analyze the experiment as decided by the investigators
used in the binomial distribution.
But we saw that very easily that the two distributions
of carbetocin and oxytocin, the blood loss volume distribution
were pretty much the same.
We were not very happy with this dichotomization to begin with,
but we had to do it.
That's what the protocol said.
Now, once we the statisticians at the trial, we found beyond any doubt
that the distribution was log normal.
When I say the distribution of blood loss volume is log normal,
I mean a big if, it is,
it is not an approximation, a nice fit, things that we statisticians like.
No, we had 29,000 points and the fit you are going to see was perfect.
Then we went to do some homework and we found from physics
that the blood loss volume distribution... Excuse me, the fluid volume
in pipes has a log normal distribution,
and that has been known since the 19th century.
Coming from physics.
Of course, we realized that our pipes are blood vessels, so they are elastic.
The viscosity of the blood changes because of coagulation.
But still, we have sort of a model.
We have fluid in pipes, flowing in pipes, and the data showed that.
We were very excited with that.
We went further to see the consequence of using V for the estimation of the risk
and we got nice results.
Now then we had to convince the investigators.
Such a large trial has lots of investigators, big shots.
The physicians, they own the problem,
so they have the last word and everything.
They thrown at the idea.
Some of them really didn't like.
They said, "Well, we use no hypothesis
since it just binomial variant, it has no model."
It has, but they think it doesn't.
People think it's too simple.
What if the log normal distribution is not correct?
We can have wrong results.
Then we did exactly what we're going to do right here.
Now, we did the analysis in front of them,
and that with JMP was very compelling, and I hope you agree with that.
JMP helped also on the communication
of the discovery to the investigators in a very compelling way.
Just then, to advance the result,
using the lognormal distribution saves the results of the experiment.
That's part of the story.
We went on then to publish those results
after the publication of the experiment was done, because the experiment failed.
You'll see that it's a nice story.
But then we published the results with the lognormal distribution
as a secondary analysis.
That touched the hearts of the European authorities,
like the ADMA.
Right now, carbetocin is very happily
being used in low- resource countries, where it is needed.
We are very happy with that.
Let me show you how it went.
First of all, the measurement.
You see on the left, a sort of collector to collect the blood.
It's used in many case in deliveries.
As I told you, sometimes
you have to take very fast action when the woman is bleeding too much.
People can evaluate the blood loss by just seeing the stain
in the bed, in the floor.
But in many case, people use that collector.
That collector has a scale that I enlarged on the right.
In the first two trials,
the blood loss volume was evaluated with that.
Then they changed.
They changed because it was no good, not perfect for our experiments,
the three of them that's been running for about 20 years now.
Let me show you how it goes with JMP.
Let's see.
I feel more comfortable with JMP.
Here is a data table with all the 71,000 case
of the three trials.
Miso prostol.
Here they are.
Mis oprostol, A ctive Management, and Carbetocin .
Let's see the distribution of the blood loss volume
for three of them by trial, not by treatment.
The difference by treatment is so small
that it won't matter for this short demonstration here.
I'm not analyzing the experiment yet.
Here is for Misoprostol distribution.
You see that it's a very nice log normal, isn't it?
Can be something else, but it is log normal.
It looks like a nice distribution, but it has problems.
It's hiding the problems, actually, not for fitting a log normal,
but for analyzing the way it was with the binomial variants.
Let's use the Grabber tool and change the pins of the histogram.
Make them thinner.
Okay, there we go.
What we see, we see spikes in distribution.
Regularly you have spikes, you can see them here.
Let me change a little bit, yes.
Now you said, well, there's no problem.
It's like numerical integration.
You lose on the one beam then you have access on the other beam
and they alternate and you end up with a nice integration.
Well, not the case here,
because we have a problem
that in 1,000 we have a cut- off here.
Let me take a zoom of distribution around 1,000, which matter most for us.
See here's the spike at 1,000 .
But you see part of this frequency here comes from the left, from the 900.
Because of the reading of that scale,
that scale was rough and people tended to round the numbers.
There is a sort of a digit preference here.
It's very clear that some of the known cases of PPH
were moved to PPH.
It's no trivial quantity for that small frequency here.
That means that in spite of having no model, as my colleague said,
for the binomial variants,
we probably have a positive bias on this estimation.
Now, this problem was taken care of by taking the weight
of the collector device before the collection, before the use,
before the procedure, and then weighing it again after the procedure.
That was done only for the carbetocin trial
that started on the carbetocin trial.
If you go the same trick here, change the beams.
Now you see that we have a nice distribution,
no problem with spikes anymore.
Weighing solved that problem.
Now, let me tell you this collector is not for the experiment.
It's for actual clinical use.
The evaluation of the blood loss and its speed during the delivery
is perfect with that scale.
We cannot remove that and then weigh then to decide that,
you have to take, say, a hysterectomy or thing like that.
It's still in place, it's still used like that.
We just changed it for the trial.
We wait at the end.
That's just for curiosity or something interesting.
That came also from the ability that we have so easily
to do this sort of analysis with JMP.
That's more important than we can even think of.
Now let's go to the real problem.
It is also easy with JMP.
I'm going to analyze the results of the carbetocin trial
but then, so that I don't get mixed up in front of you,
I prepared data set with subset just for the carbetocin trial .
Here it is, 29,000 case only.
That's a subset of that other trial.
Let me take the opportunity to tell you what the data that I have here,
of course, that's not the full data of the trial, that clinical trials.
Clinical trials, you collect the hundreds of columns of [inaudible 00:20:56]
for many reasons and for controlling so on and so forth.
Here we have just the center,
because the experiment was randomized by center so I have to keep it.
Then the arm, it's one and two here but here have the issue that's closed
and I have open treatment and control here the trial is over, of course.
Then the volume, that's all the data we need.
Those two columns here are derivations, are the sPPH indicator and P PH indicator
so they are just very easy to do.
Just an indicator of [inaudible 00:21:48] PPH in this case.
Let's start by analyzing the way protocol SEBs, perhaps in a simple way,
not doing the complete analysis, but let's analyze the SPPH response.
Remember... Not remember, I didn't say that yet.
In the actual trial analysis, we came to the relative risk of 1.26
and the maximum, I told you, for non-inferiority was 1.23.
So it was a near missed situation.
We could not declare non-inferiority
and if you go to the publication of the experiment,
you can find in the reference in the last slide here.
We have to publish that we didn't prove non-inferiority, much to our regrets.
Let's go and do it just to show that's a sort of show off for JMP.
How we need now is a fit Y by X.
It's so simple after all that work.
We have treatment for X
and we have to use block for centers, just to respect randomization.
And there we can explore the results of this here.
But I'm looking just for the relative risk, which is one item in the...
It's one item on the menu here, relative risk.
Well, one is our response and treatment must be in the numerator.
That's our choice.
There we go. We have down here 1.255,
that's the 1.26 that we got with those nice models,
random models for center and things like that.
So it's 1.25. It's a near miss situation.
We didn't prove non-inferiority.
Instead of just weeping over the results,
we went on and tried to do an analysis that was not planned,
but anyway, we published it as a sort of secondary analysis afterwards.
Let's analyze the distribution of v.
To do that, I'm not going to the distribution platform.
Rather, I'm going to use reliability and survival, life distribution
because it's a much richer platform for studying distributions,
except that the variable, the column must be non- negative.
That's the case for volume, okay.
I can use this instead of timing here.
I don't need sensory, nothing like that. There's no such a thing here.
It's just a tool for fitting distributions.
Now let's get down to business here.
I have distribution of both treatment and control,
that is carbetocin and oxytocin.
Let's separate those.
You can do that by a local data filter for treatment
and then I'll choose treatment here, that's carbetocin.
On the right here we have the data points, those black dots,.
They are so many, 15,000 of them. Those that were treated with carbetocin,
that they look like a continuous line but those are the points.
They're not having blue, they're nonparametric estimates,
nonparametric estimates [inaudible 00:25:41].
They are the same as the binomial point wise, because they have no sensory.
Then where's the lognormal here?
There's no lognormal in the menu for distributions.
That's because there are zeros in the data.
Then we cannot fit a lognormal with two parameters.
Some women are very lucky enough to have [inaudible 00:26:06] zero
millilitre for blood loss.
Probably that was some mistake.
There were women that went almost to 4000 in the control
and those were probably in shock.
This large span here for the binomial variation was separating just two.
Okay, let's fit the threshold lognormal.
The lognormal that you take a shift so that we can put the zeros in the field.
Now we have three lines here.
The red one is the threshold lognormal.
They are all three. They are hiding themselves, the three of them.
Then people can say "Well, okay, the fit is very nice, perfect."
It's not always like that. If I fit a normal or a smallest value here
things like that , you can see that you come out but that's no need here.
We can find the risk in several place in this result here.
The risk is one minus 0.985. If you don't want to do this sort of subtraction,
we can show the survival curve and the risk is 1.47 for carbetocin.
If I want to see the risk at 1,000
for oxytocin, it's again the same, 1.47. Wow.
We have also confidence interval here.
People will challenge us say,
"T hose distributions, they look the same because of the scale of the graph."
Well, let's take up this challenge.
Let's do a zoom here.
Let's do a zoom around 1,000.
Just because we are caring about that.
Look how close the fit is.
It's very close.
Now I can go even further, like this.
And now we can see even more.
We see that the point estimates this black dot here, if you want,
it's almost the same as the red line, which is the lognormal fence.
My fellow investigators there could see that I don't have expressions or a table.
A table won't say anything. They could even—
I don't know— but they could even think that statisticians were cheating.
Here is the easy way to show it but there is more to see here.
If you see the confidence interval for the lognormal distribution,
it's one third of that of the nonparametric distribution.
Well, since the precision goes with the...
increase with the square root of the experiment size.
We can guess that if we take size one ninth of that
I would get for the lognormal the same confidence interval
that I get for the nonparametric here.
That's interesting.
Instead of using 30,000 women, essentially I could use 3000 and get this result.
That was very good for the investigators, they planned on that.
This reduced
[inaudible 00:29:55] of the confidence interval
came from the lognormal, which was not planned.
So something else to hear.
Well, okay, you're doing fine for the risk .
You're getting the risk from the log normal which is the same as the binomial rate
and you have a closer confidence interval
if the log normal assumption is okay, it is.
Now what about the relative risk ?
Well, we can go and take the logarithm of the V.
You have a normal distribution
so we have a standard apparatus to do some regressions and find the relative risk.
But I remember John Sol talking on this same meeting last year.
His talk has a nice title, Delicate Brute Force.
Let's use the same thing, delicate brute force.
If it's good for John Sol, it's going to be good for us too.
Here is the estimation...
the estimated parameters of the lognormal that we get.
If we can do a bootstrap sample of this,
we can compute the risk, the bootstrap risk.
We have a bootstrap sample for the risk.
We can do that for carbetocin and for oxytocin and that's good.
Then you say, "Well, I have to program this."
"I have to program the bootstrap sample." It's not difficult but you have to program
and then you have to compute 1000 times, 2000 times, whatever it is lognormal fits.
But no, JMP is nice twice. If you click with the right button,
this table, you have bootstrap on the menu.
The suggestion is to take 2500, we can take 5,000 or whatever,
but it takes a long time.
We did that with 1,000.
We were very happy with that.
It takes 10 minutes or so for each of treatment and carbetocin or oxytocin.
I'm not going to make you wait 10 minutes, I didn't want to wait for longer, right.
We did that before
and here is the bootstrap sample for the control.
I mean, that is oxytocin.
The output are the parameters here.
The first line is the actual result of the experiments
and all the rest is 1,000 bootstrap samples that's why we have 1,001 here.
Now this column here
came from the parameters. It's just the risk estimate.
One minus the log normal distribution at the point 1,000 minus threshold,
location and scale.
Fine, easy.
Now here's the same thing for carbetocin.
Now I use a result that I've read the book by [inaudible 00:33:18] ,
the man who knows everything about bootstrap.
To have a bootstrap sample of the relative risk,
all I have to do is take those two bootstrap samples here
and join the tables row wise.
It's a Mickey Mouse operation for JMP, like we do with the tables here and so on.
Here's the results.
I kept just the risks column here for carbetocin here and oxytocin.
If you don't want to use this extra point, I don't know why you wouldn't bu t.
We can exclude it to use just the bootstrap.
We have the relative risk here, just the quotient of those two columns.
We're done.
Take the distribution of this bootstrap sample, the relative risks
and here we are, we're almost to celebrate now.
Here's the distribution.
You don't see 1.23 here... Yes, you see, but then
we need now one sided confidence interval with 95% coverage.
I need the 5% quantile, which is not here.
Okay, so we kindly asked JMP
to compute that you can put display options, custom quantiles
and we need 0. 95 quantile, which turns out to be 1.11.
We even have a bonus result which is the confidence interval for this estimate.
If you want to be really safe, we can use the upper,
the upper confidence limit... For the limit of the confidence limit
that's too involved to say. Anyway, it's far away than 1.23.
Then we have proven in some sense,
we have thrown evidence that carbetocin is non- inferior to oxytocin.
That's the result we published.
A s I told you, that publication with some work by the investigators,
it's warmed the hearts of the EMA,
the European authority who was overlooking this trial
and carbetocin is not being used on places where you have no code chain assured.
Let me use your time if I can,
just to show the efficiency that we get.
Let me go back to presentation here.
Let's see the relative efficiency of binomial versus lognormal.
Let's take the problem, not non-inferiority but simple problem
of testing the superiority of a new drug over oxytocin.
The new drug would be declared superior if it's risk
for sPPH is less than 1.5% compared with 2% of oxytocin.
We have here all we need to do a binomial test.
For the lognormal test we need to convert from this piece to the means.
Let's do it.
For the [inaudible 00:37:15] , you have this,
for the lognormal, we just do this.
We want to know the risk,
is the probability of being larger than 1,000 so we take logs on both sides,
no subtract then standardized, which is now a normal variance.
And here for S, the standard deviation, use 0.7.
It's important in every bit that we did,
every inference that we did with those three trials and then a few more,
that we have data available.
Every time the standard deviation came about 0.7.
We called jokingly, this is a universal constant of P PH.
The standard deviation of the logarithm of the blood volume loss is 0.7
we replace S by 0.7. We compute the quantiles at 2% and then 1.5% here
and we solve the equations on them and we have those two means to compare
with a normal distribution.
The difference is 0.08 14.
Okay, now we go back to JMP.
I feel even ashamed of showing that but it's fun
and we did that for our medical team there and it was very compelling, as I told you.
Sorry about all those windows open here.
Very simple. You come to DOE, Sample Size Explorer,
Power, it's mickey mouse stuff.
Let's do that for the sample size for two independent sample proportions.
We have one sided, it's a superiority test.
The proportion under the new is 2%,
under the alternative is 1.5%. It's going to change to too much, 1.5 in hiding here.
Then we want 8% for Power and the sample size is 17,000.
Okay, 17,000 to go old fashioned.
Let's compute the sample size for the lognormal.
Using Sample Size Explorers from DOE,
Power and Power for Two Independent Sample Means.
We have a one sided test.
We have to add the standard deviations which are 0.7 for both groups
and then the difference to detect we had compute 0.0814
and we want 80% Power.
Okay, we came to the result.
Now, the sample size or the experiment size is 1831.
That's about one ninth of the 17000 that we had computed for the binomial
[inaudible 00:40:31].
That's what we got by just inspecting the
the width of the confidence intervals in the reliability platform.
That's how much more efficient using lognormal [inaudible 00:40:48] binomial.
Just to finish...
Just to finish the rap-up is
the lognormal distribution fits very well the blood loss volume distribution
so why not to use it?
Using this fact, the estimates of the risks are much more precise.
We even show that our big trial was saved
in some sense by showing non- inferiority of carbetocin, using the lognormal.
We are very happy to communicate to you
that a new trial is already underway now using the lognormal.
Now this trial would not come to life
because we don't have money for 30,000 people.
But since we are using only less than 4000, that made the trial possible.
It's underway now. It's for treatment, not for prevention like they're of others.
That's what I had to tell you. Thank you very much.
