0:12

I'm going to talk about Simple randomization schemes,

Â Restricted randomization schemes and Adaptive randomization schemes.

Â These are, admittedly, somewhat abbreviated overviews

Â of the various types of randomization schemes

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

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

Â It's just a complete randomization.

Â Each time you toss the coin is independent of

Â the last time you tossed the coin, so it

Â doesn't matter if you got a heads or tails

Â the last time, this next flip is totally independent and

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

Â The advantage of having a Simple randomization scheme where the last

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

Â actual probability of the treatment assignments stays fixed

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

Â is completely unpredictable.

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

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

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

Â truly, scientifically designed randomization process, and you use a

Â Simple Randomization scheme, the number of patients assigned to each

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

Â 1:49

So the risks associated with a Simple

Â Randomization procedure, is that you may indeed imbalances.

Â These imbalances could be related to the number of

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

Â end up in a trial of 100 patients with 40

Â assigned to one group and 60 assigned to the other

Â group, when your ideal was a one to one

Â allocation with 50 patients in each group, and that

Â in itself, will lower the statistical power or could

Â lower the statistical power, associated with your clinical trial.

Â Also, you can have an imbalance related to important

Â confounding factors, if there are prognostic factors associated with

Â the outcome and in a Simple Randomization scheme

Â the chips are going to fall where they may.

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

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

Â So, there's no control on the

Â characteristics of the patients by treatment group.

Â And if

Â you have large numbers of patients in a trial,

Â that's not such a problem because your large numbers

Â favor the probability that you really will get comparable

Â distribution of potential confounding factors across the treatment groups.

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

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

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

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

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

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

Â It still can diminish the credibility of your,

Â results. It can make people questions things.

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

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

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

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

Â and they can really undermine the results of your trial and

Â give people reasons to not accept the results.

Â As I referred to before, these risks

Â are inversely associated with the number of participants.

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

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

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

Â Well, they've imposed restrictions to the randomization

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

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

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

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

Â or on specified covariates, such as severity of disease,

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

Â are used in this restricted randomization are blocking and stratification.

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

Â 5:21

First we'll start with blocking.

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

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

Â treatment assignment ratio.

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

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

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

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

Â And we talk about permuted blockticides, which means,

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

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

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

Â But that's the list of permutations of the order

Â of the treatment assignments inside a block of four,

Â for a one to one treatment assignment.

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

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

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

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

Â this best.

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

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

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

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

Â And, if you wanted to go and

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

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

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

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

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

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

Â you could meet that allocation ratio of two to one.

Â You could have four As and two Bs.

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

Â block size of eight, you couldn't meet

Â that treatment allocation ratio within that block size.

Â So the larger

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

Â 8:10

And then, when we apply this blocking principle and use

Â blocks of treatment assignments, what we really do is produce

Â all possible permutations of the block, similar to how I

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

Â We list all the possible ways a block

Â of four could be ordered.

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

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

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

Â So, I think the example we'll come upon

Â in a few slides will help illustrate this point.

Â So why do we do this?

Â It seems sort of confusing, and if it

Â does seem confusing when you first look at this,

Â this is common, that blocking, is one of

Â the more difficult, simple concepts that we deal with.

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

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

Â looking at it.

Â But the reason we bother to do this is that

Â it ensures balance in the treatment assignment ratio over time.

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

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

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

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

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

Â runs of As or long runs of Bs that you might

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

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

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

Â You'll only

Â have runs of one particular treatment assignment, the

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

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

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

Â 10:32

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

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

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

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

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

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

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

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

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

Â ratio, I showed you on the last page and

Â have listed out all the possible blocks and that

Â is six.

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

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

Â which translates to 4 times 3 times 2 times 1.

Â And then the denominator is the number of each kind of

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

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

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

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

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

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

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

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

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

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

Â 12:38

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

Â commonly referred to as permuted blocks, and this is

Â probably one of the most common features of a randomized

Â clinical trial design, that most trials do use blocking,

Â but there are some considerations when implementing a block design.

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

Â You can't modify your allocation

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

Â example of that when we talk about adaptive randomization.

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

Â into the fact that your allocation ratio is going

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

Â is very common, not to change the allocation ratio.

Â Second, it's important to understand that block

Â sizes, and information about the block sizes used

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

Â They in general shouldn't be written down in

Â the protocol that the investigators are going to be

Â looking at, because it gives you a hint

Â about how the randomization scheme is going to work.

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

Â to be able to predict what the next assignment is.

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

Â is to make the next assignment unpredictable,

Â so investigators or people won't be influenced by

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

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

Â the block size written down in the protocol.

Â You really shouldn't write it down there.

Â Now, there should be separate documentation

Â of the treatment assignment scheme and

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

Â protocol should be limited to those that the clinician

Â needs to know in order to execute the protocol,

Â and be knowledgeable about the general experimental design.

Â 14:42

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

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

Â Because then, the overall sequence of how treatment assignments

Â are allocated is going to appear to be more random.

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

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

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

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

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

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

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

Â But once that third assignment is issued,

Â they are going to know the fourth assignment.

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

Â But nonetheless,

Â it takes away from the unpredictability aspects of randomization.

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

Â so that the treatment assignments appear to be more like

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

Â And this is especially important in unmasked trials.

Â Because, if you know the treatment in a

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

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

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

Â You know that it will be a different

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

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

Â are going to know the actual treatment that's going

Â to be administered to the next patient, or

Â have a good idea.

Â And certainly that opens the door to more selection bias creeping

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

Â 16:43

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

Â Well some of the advantages associated with blocking are, that

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

Â So, you're more

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

Â It also protects against time related

Â changes that may influence your clinical trial

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

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

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

Â you're more likely to have equal representation of

Â those different types of patients in both groups.

Â And those kind of changes, you know, a lot

Â of things can change over the course of a trial.

Â The study population, you may have some new

Â data collection procedures or new instrumentation that is used,

Â implemented in the course of the trial that

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

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

Â that you would like those external forces

Â to be equally distributed across the treatment groups.

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

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

Â Also, if you have a case

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

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

Â Or safety reasons that you're more likely to

Â have balance groups because you have this blocking that

Â institutes balance every so often as you go

Â along, and that leads to a more powerful analyses.

Â The disadvantages

Â of blocking, as I mentioned before, is that

Â they can facilitate the prediction of future assignments.

Â If you figure out the block size, you can start

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

Â And that disadvantage is more problematic in unmasked trials, or

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

Â 19:02

So now I'm going to go on to

Â the second common maneuver that's used

Â to restrict randomization, and that is stratification.

Â And stratification is used to ensure balance in the

Â treatment groups across groups that can be specified before randomization.

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

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

Â clinic, gender, or some measure of disease severity.

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

Â clinic we are going to meet the allocation ratio.

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

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

Â that there may be plenty of population infrastructure issues that influence

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

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

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

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

Â Generally, if you're going

Â to use stratification, it should be

Â reserved for subgrouping variables that are considered

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

Â They can either be a strong confounder, sort

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

Â prognostic factor that strongly predicts whether you're going to

Â have a good or a bad outcome, or

Â some factor that is actually even an effect modifier that

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

Â So practically, what stratification requires is a separate treatment

Â assignment schedule for each stratum in a Stratified Randomization scheme.

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

Â a randomization scheme that's stratified by clinic,

Â that you'll need three different treatment assignment lists.

Â 21:20

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

Â So the example we're going to use here is

Â for some type of treatment for breast cancer.

Â So we have treatment A or B.

Â Again, back to the one to one

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

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

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

Â We have two different centers.

Â And then we're also going to stratify the

Â treatment assignment based on the patient's postmenopausal status.

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

Â Into this stratified design,

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

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

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

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

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

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

Â Well, if you look under

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

Â potential first block could be the one listed there

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

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

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

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

Â But notice that, that's specifically

Â within Center X within postmenopausal women.

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

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

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

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

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

Â So the first woman who fits that characteristic is

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

Â B and the third and fourth women will get assignment

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

Â particular treatment assignment list for

Â that combination of stratification variables.

Â So, I hope that's clear.

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

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

Â Because, what you end up doing is segmenting your

Â population into small groups.

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

Â So, you could even be more at risk for imbalances

Â within those groups because you have smaller numbers of patients.

Â So it's important to recognize that stratification alone is

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

Â balance over time and over assignments within

Â each list that's defined by the stratification variables.

Â 24:51

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

Â One thing that you should recognize is that

Â you have to limit it to a few variables.

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

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

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

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

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

Â also ones that are logistically possible.

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

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

Â variable some interpretation of a blood test that takes a few

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

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

Â So there's a logistical consideration that you

Â need to have those data available at randomization.

Â The typical ones that are used in multicenter

Â clinical trials or clinic, that almost universally considered

Â an, an important stratification variable, because populations and

Â treatments do tend to vary quite widely by center.

Â Sometimes in a surgical trial, because there's concern

Â about the effect of different skill levels, the stratification

Â variable will actually be on the surgeon, involved in the

Â trial, so that you can ensure, that there is

Â an equal allocation of what procedures were done by surgeon.

Â You may also stratify by stage of disease if that is

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

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

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

Â Probably there's more emphasis than there should

Â be on demographic characteristics as stratification variables.

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

Â numbers of people in treatment A and treatment B within

Â subgroups based by gender or race or age categories.

Â You could also stratify based on that type of characteristic.

Â 27:24

The problem that you can come across with having too

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

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

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

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

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

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

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

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

Â So a block size of four would be open

Â if only three assignments were filled in that block.

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

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

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

Â So, stratification and blocking are really

Â the two most common restrictive randomization features.

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

Â of ensuring that you maintain the design allocation

Â ratio as you go throughout the trail and

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

Â Whereas stratification, is related to baseline characteristics of the

Â patient, or where the patient is at, that you

Â can control the balance of the treatment assignment, that

Â it meets the design assignment within those subgroups of patients.

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

Â apply blocking.

Â 29:16

So the final type of scheme I'm

Â going to talk about is an Adaptive Randomization scheme.

Â And I'm only going to briefly review this.

Â An Adaptive scheme is a process in which

Â the probability of assignment to the treatment i.e the

Â allocation ratio, does not remain constant over the

Â course of the trial, but is somehow determined by

Â the current balance of participants in the trial, or

Â even the outcomes from patients enrolled in the trial.

Â There are two common types of Adaptive Randomization schemes.

Â One is based on minimization, after the first patient the

Â treatment assignment that yields the smallest in balance is chosen.

Â So, instead of having stratum to

Â ensure balance across important characteristics, in a minimization scheme

Â you can be balancing on a number of characteristics or

Â prognostic factors as you go on in the trial, and

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

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

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

Â their probability to be assigned to that treatment group would be

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

Â But the allocation scheme can't be determined in advance

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

Â to have some, you know, real time usually computer

Â resources to be able to effectively institute a minimization scheme.

Â In effect, you're sort

Â of writing or generating the treatment assignment list as

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

Â Again, you have to decide what factors you want

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

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

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

Â the better treatment based on the primary outcome.

Â So, if one treatment appears more favorable,

Â you preferentially assign patients to the betterment treatment.

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

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

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

Â patient's treatment assignment, you have to have

Â those data again to implement this kind

Â of design, and therefore, need to be

Â able to evaluate the outcomes relatively, quickly, and

Â you can implement these designs in stages,

Â so you might start with a, fixed allocation

Â ratio and after you get to a

Â certain number of patients, impliment an adaptive ratio.

Â Okay,

Â I know this has been a long section.

Â We've gone over Simple Randomization,

Â Restrictive Randomization, and Adaptive Randomization schemes.

Â