0:12

I'm going to talk about Simple randomization schemes,

Restricted randomization schemes and Adaptive randomization schemes.

These are, admittedly, somewhat abbreviated overviews

of the various types of randomization schemes

that can be employed in a clinical trial. Simple randomization is probably

what most of us are familiar with, it's analogous to the coin toss again.

It's just a complete randomization.

Each time you toss the coin is independent of

the last time you tossed the coin, so it

doesn't matter if you got a heads or tails

the last time, this next flip is totally independent and

has a 50-50 chance of either heads or tails.

The advantage of having a Simple randomization scheme where the last

assignment doesn't tell you anything about the next assignment, and the

actual probability of the treatment assignments stays fixed

from assignment to assignment, from coin toss to coin toss, is that each assignment

is completely unpredictable.

The fact that a patient was assigned to treatment A yesterday will

tell you nothing about what this new patient is going to be assigned to.

And in the long run, if you have enough patients, it will equal out if you have a

truly, scientifically designed randomization process, and you use a

Simple Randomization scheme, the number of patients assigned to each

group should be about equal, assuming you have large enough numbers.

1:49

So the risks associated with a Simple

Randomization procedure, is that you may indeed imbalances.

These imbalances could be related to the number of

patients assigned to each treatment group, for example, you could

end up in a trial of 100 patients with 40

assigned to one group and 60 assigned to the other

group, when your ideal was a one to one

allocation with 50 patients in each group, and that

in itself, will lower the statistical power or could

lower the statistical power, associated with your clinical trial.

Also, you can have an imbalance related to important

confounding factors, if there are prognostic factors associated with

the outcome and in a Simple Randomization scheme

the chips are going to fall where they may.

So you could just by chance have more people with severe disease assigned to one

group than than the other, or more women assigned to one group than the other.

So, there's no control on the

characteristics of the patients by treatment group.

And if

you have large numbers of patients in a trial,

that's not such a problem because your large numbers

favor the probability that you really will get comparable

distribution of potential confounding factors across the treatment groups.

But with small numbers, you're more likely to run into imbalances.

And again, that can lower the statistical power of your trial.

And even if these imbalance, either in the number of patients, or the types of

patients, or both, don't really affect the results of your trials, they

really are not too severe in terms of numbers, and the factors that they're,

the groups are imbalanced on, really don't have an association with the outcome.

It still can diminish the credibility of your,

results. It can make people questions things.

Well, why, why didn't they have equal numbers in both groups?

Or, more commonly, oh, well, of course they had the sickest patients

were in treatment group A, so that's why treatment group B looked better.

And sometimes you can never really address those credibility issues fully,

and they can really undermine the results of your trial and

give people reasons to not accept the results.

As I referred to before, these risks

are inversely associated with the number of participants.

The more participants you have in a trial, the more that

the properties of probability are going to be working in your favor.

So, how have clinical trialists and biostatisticians addressed this issue?

Well, they've imposed restrictions to the randomization

scheme to ensure balance across important factors in the design of, of experiments.

So, when somehow there's a constraint added to produce the expected

assignment ratio, in the example we've been using, one to one.

According to time that the study's been going on,

or on specified covariates, such as severity of disease,

or gender, or clinic. And the two primary maneuvers that

are used in this restricted randomization are blocking and stratification.

And I'll go over each and one of them separately.

5:21

First we'll start with blocking.

So let me just tell you what blocking is before I tell you why we do it.

A block, if you want to define the block, is a list of treatments that achieves the

treatment assignment ratio.

Again, we're sticking with that example of one to one.

So, a block of two would be an A and a B that we achieve their ratio of one to one.

If we use the block size of four, that means that

a block would have two As and two Bs in it.

And we talk about permuted blockticides, which means,

every possible way you could list those two As and those two Bs and you see listed

out on the slide is the six possible ways you could order two As and two Bs.

You can have AABB, ABAB, and I'll let you read the rest for yourselves.

But that's the list of permutations of the order

of the treatment assignments inside a block of four,

for a one to one treatment assignment.

Another important point is that the size of the smallest possible block

to use, is the sum of the integers defined in the treatment allocation ratio.

So, you can't meet the treatment allocation ratio, if you have a block that

is smaller than the sum of the integers. So, I think an example illustrates

this best.

If the allocation ratio is one to one, the smallest block size is 1 plus 1 is 2.

That's the smallest block you can have, to get a one to one ratio.

So, if you have a different allocation ratio, say two to one, the smallest

possible block size is three because you'd have to have two As and one B.

And, if you wanted to go and

use larger block sizes, and I'll discuss reasons for using different block

sizes in a few minutes, the larger block sizes need to be multiples

of the smallest one, so in order to meet the treatment allocation ratio

of two to one, the smallest block size you can have is three.

The next one is six because that is a multiple of the smallest block size

and, it goes up accordingly. So, because within a block size of six,

you could meet that allocation ratio of two to one.

You could have four As and two Bs.

Now if you have a block size of seven that wouldn't work, or even a

block size of eight, you couldn't meet

that treatment allocation ratio within that block size.

So the larger

block size are multiples of the, of the smallest one.

8:10

And then, when we apply this blocking principle and use

blocks of treatment assignments, what we really do is produce

all possible permutations of the block, similar to how I

have listed as the second sub-bullet under the first bullet.

We list all the possible ways a block

of four could be ordered.

And then, when we go to develop a randomization scheme or a ran, a list of

the treatment assignments, what we do is randomly choose those block sizes.

Randomly choose, from those permutations of a block size of four.

So, I think the example we'll come upon

in a few slides will help illustrate this point.

So why do we do this?

It seems sort of confusing, and if it

does seem confusing when you first look at this,

this is common, that blocking, is one of

the more difficult, simple concepts that we deal with.

Once you get it, it's very clear. But just that first

time understanding exactly what blocking is may take some quiet moments alone

looking at it.

But the reason we bother to do this is that

it ensures balance in the treatment assignment ratio over time.

And this makes sense, right? Because if we're using that block size of

four, that means after every four patients, even if we have a sample size

of 400, after every four patients, we're ensured that we've met the allocation

ratio, that two have been assigned to A and two to B.

As we go along in the trial, we can't have long

runs of As or long runs of Bs that you might

have in a simple randomization design, that would be associated with

time because it takes time to accrue patients to a trial.

You can't have that problem if you use the block size.

You'll only

have runs of one particular treatment assignment, the

longest run possible within a particular block size, and you can see with a

block size of four and a one to one allocation ratio,

the longest possible run of a treatment is two, for two patients.

10:32

So, how do you figure out how many permuted blocks do

you have with a particular block size? Well, when you start with small block

sizes, it's fairly easy, so, if you have the allocation ratio is one to one, right?

If the size of the block is two, the number of possible blocks you can have is

two, it's AB and BA. And the way you can figure that out is

to write them down, or you can use this multinomial coefficient you see

illustrated at the bottom of the slide in blue with the factorial signs.

Now, don't be scared of, of this formula, it's quite simple.

So again, if you are back to a block size of four with the one to one allocation

ratio, I showed you on the last page and

have listed out all the possible blocks and that

is six.

But, we can come up with that number six by using the multinomial coefficient.

So, the numerator is the factorial of four and you see that 4!,

which translates to 4 times 3 times 2 times 1.

And then the denominator is the number of each kind of

thing, so in this example, in a block size of four,

we're going to have two As and two Bs.

So the R, we have an R1 and an R2, and both of them equal 2 in this case.

So you can see that the 4 factorial is divided by 2 factorial times 2

factorial, and you get the number of possible permuted blocks for a

block size of four is six blocks. And I'll let you go through that on your

own for block size of six, where it starts to get more

complicated and you don't want to have to sit down and write out

all possible blocks, in this case 20, and you'd rather be able to figure

that out more easily using this shortcut of the multinomial coefficient.

12:38

So, once we've decided that we're going to have a blocked randomization design,

commonly referred to as permuted blocks, and this is

probably one of the most common features of a randomized

clinical trial design, that most trials do use blocking,

but there are some considerations when implementing a block design.

First you have to use the same allocation ratio, throughout the trial.

You can't modify your allocation

ratio, as you go along, and we'll see an

example of that when we talk about adaptive randomization.

So if you're going to use blocking, you've bought

into the fact that your allocation ratio is going

to be, the same throughout the trial, which again,

is very common, not to change the allocation ratio.

Second, it's important to understand that block

sizes, and information about the block sizes used

in a clinical trial are really on a need to know basis.

They in general shouldn't be written down in

the protocol that the investigators are going to be

looking at, because it gives you a hint

about how the randomization scheme is going to work.

And if you know the block size, then you'll start

to be able to predict what the next assignment is.

And that's one of the whole points of randomization,

is to make the next assignment unpredictable,

so investigators or people won't be influenced by

that knowledge about who to enroll in the trial, or when to enroll, roll them.

So I've heard people say, well, they see

the block size written down in the protocol.

You really shouldn't write it down there.

Now, there should be separate documentation

of the treatment assignment scheme and

how it was generated, but generally, the details in the

protocol should be limited to those that the clinician

needs to know in order to execute the protocol,

and be knowledgeable about the general experimental design.

14:42

Now, one of the tricks that we use to maintain that lack of knowledge

about upcoming treatment assignments, is to use more than one block size.

Because then, the overall sequence of how treatment assignments

are allocated is going to appear to be more random.

If you use the standard block size of two in the one to one

allocation ratio, people are going to be able to start figuring that out that if,

if the first assignment was an A, the next one's going to be a B.

And if they know the block size, then they'll know

that block's complete and then they're back in the next,

when the next block opens up, they're back to not

knowing whether it's going to be an A or a B.

But once that third assignment is issued,

they are going to know the fourth assignment.

And it gets a little bit more complicated with larger block sizes.

But nonetheless,

it takes away from the unpredictability aspects of randomization.

And so the way that we try to deal with that, is to use more than one block size

so that the treatment assignments appear to be more like

a simple randomization scheme, and are less likely to be predicted accurately.

And this is especially important in unmasked trials.

Because, if you know the treatment in a

masked trial, and you know which treatment's going to come

up, A or B, and it's masked, well, if

it's effectively masked, you still don't know that much.

You know that it will be a different

treatment, but you don't know which treatment it is.

If it's a unmasked trial, and you start to figure the block sizes, then you

are going to know the actual treatment that's going

to be administered to the next patient, or

have a good idea.

And certainly that opens the door to more selection bias creeping

into the trial or again back to that confounding by indication.

16:43

Okay, so what are some of the benefits and risks associated with blocking?

Well some of the advantages associated with blocking are, that

it helps to guarantee overall balance, especially in smaller trials.

So, you're more

likely at the end to get equal numbers in both groups.

It also protects against time related

changes that may influence your clinical trial

that could be, those changes could be in the composition of the study population.

So if you start with more severe patients and get to less severe

patients enrolled in the trial as the trial goes on, if you have blocking,

you're more likely to have equal representation of

those different types of patients in both groups.

And those kind of changes, you know, a lot

of things can change over the course of a trial.

The study population, you may have some new

data collection procedures or new instrumentation that is used,

implemented in the course of the trial that

you'd like to have used equally in both groups.

And there could be other forces, outside of the trial, that may influence outcomes

that you would like those external forces

to be equally distributed across the treatment groups.

And by insuring that the allocation ratio is met as you go along

in the trial, blocking protects against some of these time related changes.

Also, if you have a case

where a trial is stopped early, either because of efficacy measures, you've

found that a good treatment and you don't believe it's ethical to continue.

Or safety reasons that you're more likely to

have balance groups because you have this blocking that

institutes balance every so often as you go

along, and that leads to a more powerful analyses.

The disadvantages

of blocking, as I mentioned before, is that

they can facilitate the prediction of future assignments.

If you figure out the block size, you can start

to figure out what is likely to be the next assignment.

And that disadvantage is more problematic in unmasked trials, or

trials that are poorly masked, that people can figure out the treatment assignments.

19:02

So now I'm going to go on to

the second common maneuver that's used

to restrict randomization, and that is stratification.

And stratification is used to ensure balance in the

treatment groups across groups that can be specified before randomization.

So by imposing stratification, we can ensure that the treatment assignment

is met within a subgroup of the population and those subgroups are commonly

clinic, gender, or some measure of disease severity.

So, if we stratify by clinic, then we can ensure that at each

clinic we are going to meet the allocation ratio.

And you can imagine that could seem like intuitively an important thing to do.

That if you have clinics scattered across the country or indeed the world,

that there may be plenty of population infrastructure issues that influence

the outcome for those patients just as much as a treatment may.

So you want to ensure that you're balanced in your treatment assignment within

each clinic, so that you have a fair comparison of the treatment assignments.

And those external factors associate with the clinic don't bias comparison.

Generally, if you're going

to use stratification, it should be

reserved for subgrouping variables that are considered

to be strongly related to the outcome, the primary outcome for the trial.

They can either be a strong confounder, sort

of, as we've talked about before, that some

prognostic factor that strongly predicts whether you're going to

have a good or a bad outcome, or

some factor that is actually even an effect modifier that

the treatment effect works differently in different subgroups of the population.

So practically, what stratification requires is a separate treatment

assignment schedule for each stratum in a Stratified Randomization scheme.

So if you have three clinics, that really means, if you're going to institute

a randomization scheme that's stratified by clinic,

that you'll need three different treatment assignment lists.

21:20

So here's an example of both stratification and blocking.

So the example we're going to use here is

for some type of treatment for breast cancer.

So we have treatment A or B.

Again, back to the one to one

treatment allocation ratio, that's what our ideal is.

And we're going to stratify it by two different factors.

One is center, is the patient coming to Center X or Center Y?

We have two different centers.

And then we're also going to stratify the

treatment assignment based on the patient's postmenopausal status.

Is this someone who has gone through menopause or premonopausal person?

Into this stratified design,

we're going to institute a block size of four.

So, if you look at the table, you can see that the first row

indicates the center and then, that sort of divides the actual table in half.

Within each center, you can have postmenopausal or premenopausal women.

So, within each center, you have two types of women.

So, what's the treatment assignment gong to be?

Well, if you look under

clinic X for postmenopausal women, if we are using a block size four,

potential first block could be the one listed there

with the patient gets assignment B, the second patient assignment A,

the third patient assignment B, and then the fourth patient assignment A.

And as I talked about before when we were discussing blocking, walah,

you end up with two As and two Bs after four patients.

But notice that, that's specifically

within Center X within postmenopausal women.

So you actually have a separate list based on the stratification variables.

So, again, if you go to the right one column, we've

got the list for premenopausal women who enrolled at Center X,

and when a premenopausal woman arrives at Center X to be randomized,

she is going to receive an assignment from that second string of As and Bs.

So the first woman who fits that characteristic is

going to get assignment B, the second woman will get assignment

B and the third and fourth women will get assignment

A, because that is the, the first block in that

particular treatment assignment list for

that combination of stratification variables.

So, I hope that's clear.

Now one point that may be a little hard to absorb at first, is that if you

stratify without blocking, there's really no point in stratifying.

Because, what you end up doing is segmenting your

population into small groups.

And then, imposing a Simple Randomization scheme within those segmented groups.

So, you could even be more at risk for imbalances

within those groups because you have smaller numbers of patients.

So it's important to recognize that stratification alone is

not a useful maneuver unless you're going to add blocking to ensure that there is

balance over time and over assignments within

each list that's defined by the stratification variables.

24:51

So, I'm going to go on to discuss some of the practical aspects of stratification.

One thing that you should recognize is that

you have to limit it to a few variables.

Once people are kind of aware of the benefits of stratification, they

tend to think, wouldn't it be nice to have very homogeneous groups?

But that can get you into problems, to have too many stratification variables.

So, you want to pick ones that are highly related to outcomes.

That are really important to control for and sort of a sense of confounding, and

also ones that are logistically possible.

You have to know the stratification variable status before you randomize.

So, you probably don't want to have as a stratification

variable some interpretation of a blood test that takes a few

days or a few weeks to get the results back, because

you can't randomize someone until you know which list to use.

So there's a logistical consideration that you

need to have those data available at randomization.

The typical ones that are used in multicenter

clinical trials or clinic, that almost universally considered

an, an important stratification variable, because populations and

treatments do tend to vary quite widely by center.

Sometimes in a surgical trial, because there's concern

about the effect of different skill levels, the stratification

variable will actually be on the surgeon, involved in the

trial, so that you can ensure, that there is

an equal allocation of what procedures were done by surgeon.

You may also stratify by stage of disease if that is

an important prognostic factor, if you have some measure of disease

severity and what's the likely prognosis that you think is strongly related

to the outcome, then you may consider that as a stratification variable.

Probably there's more emphasis than there should

be on demographic characteristics as stratification variables.

But if you thought that it was important to ensure that you had the same

numbers of people in treatment A and treatment B within

subgroups based by gender or race or age categories.

You could also stratify based on that type of characteristic.

27:24

The problem that you can come across with having too

many stratification variables, as you saw on the last slide,

each combination relates in a separate list, is that you get too

many strata. And you can't fill up the blocks, and you

actually are working against yourself because if you have lots of strata.

And each one has a separate list associated with it, and

people are coming into the trial and filling up those blocks what

you'll, you may end up with is a lot

of open blocks, blocks that didn't get completely filled.

So a block size of four would be open

if only three assignments were filled in that block.

And if you have to merge together data from a lot of unopened blocks, you're

likely to end up with an imbalance overall in the treatment group allocation.

So, you've sort of shot yourself in the foot.

So, stratification and blocking are really

the two most common restrictive randomization features.

And so, the take home points here are that blocking is very important in terms

of ensuring that you maintain the design allocation

ratio as you go throughout the trail and

helps control for a number of things that can change over time.

Whereas stratification, is related to baseline characteristics of the

patient, or where the patient is at, that you

can control the balance of the treatment assignment, that

it meets the design assignment within those subgroups of patients.

And indeed, for stratification to be effective, you should also

apply blocking.

29:16

So the final type of scheme I'm

going to talk about is an Adaptive Randomization scheme.

And I'm only going to briefly review this.

An Adaptive scheme is a process in which

the probability of assignment to the treatment i.e the

allocation ratio, does not remain constant over the

course of the trial, but is somehow determined by

the current balance of participants in the trial, or

even the outcomes from patients enrolled in the trial.

There are two common types of Adaptive Randomization schemes.

One is based on minimization, after the first patient the

treatment assignment that yields the smallest in balance is chosen.

So, instead of having stratum to

ensure balance across important characteristics, in a minimization scheme

you can be balancing on a number of characteristics or

prognostic factors as you go on in the trial, and

ensure that your, have balance as the trial goes on.

So then, if you have a patient with a certain set of

characteristics, that you have a relative lack of in a certain treatment group,

their probability to be assigned to that treatment group would be

greater, and you can combine several patient characteristics to do this.

But the allocation scheme can't be determined in advance

if you're using a minimization design, so you have

to have some, you know, real time usually computer

resources to be able to effectively institute a minimization scheme.

In effect, you're sort

of writing or generating the treatment assignment list as

you go along to ensure balance, across the treatment groups.

Again, you have to decide what factors you want

to balance things on, and have data on those factors.

Another type of Adaptive Randomization that relies more on outcome assessment,

is a play the winner design, where you change the treatment allocation to favor

the better treatment based on the primary outcome.

So, if one treatment appears more favorable,

you preferentially assign patients to the betterment treatment.

You give them a greater probability of assigned to the better treatment.

To do this, you have to be able to evaluate outcomes relatively quickly.

So for the prior patient's outcomes to influence this next

patient's treatment assignment, you have to have

those data again to implement this kind

of design, and therefore, need to be

able to evaluate the outcomes relatively, quickly, and

you can implement these designs in stages,

so you might start with a, fixed allocation

ratio and after you get to a

certain number of patients, impliment an adaptive ratio.

Okay,

I know this has been a long section.

We've gone over Simple Randomization,

Restrictive Randomization, and Adaptive Randomization schemes.