Re: {MEDSTATS} Re: Randomization and minimization and so on ... continuation of previous post
Peter Flom
Peter
-----Original Message-----
>From: "Bland, M." <mb...@york.ac.uk>
>Sent: Sep 17, 2009 4:57 AM
>To: meds...@googlegroups.com
>Subject: {MEDSTATS} Re: Randomization and minimization and so on ... continuation of previous post
>
>
>Peter,
>
>You want to balance a trial on two or three categorical covariates, with
>four groups and several hundred subjects.
>
>I would certainly not claim to be well up on the current literature in
>this area. However, here are my thoughts.
>
>The obvious thing to do is to stratify. The usual objection to
>stratification is that some strata may be too small. If we have three
>dichotomous covariates we have eight strata. If they are all in the
>ratio 1:2, the smallest stratum would have about 1/27 of the subjects.
>If we want to allocate 400 subjects, this would mean 15 in the stratum.
>If we used a block size of 8, this would work OK. I would suggest
>random block sizes of 4 or 8 to reduce the risk of predicting the next
>allocation. Of course, there may be even fewer in the stratum, but
>would a combination of characteristics which occurs in less than 4% of
>the population be very important anyway?
>
>The alternative is minimisation. For those not familiar with this
>technique, see Altman and Bland on
>
>http://www.bmj.com/cgi/content/full/330/7495/843
>
>and subsequent links. This is presumably why my name came up. The
>rapid responses to that article, including one by Stephen Senn, raise
>objections to this method and suggest other possible approaches. I
>would recommend them to anyone who is interested in using it. One which
>they do not mention is that the largely mechanistic nature of
>minimisation makes it predictable to any recruiter who wants to subvert
>the trial.
>
>I have only used minimisation in cluster randomised trials, where my
>collaborators have have been concerned about the potential for imbalance
>in small numbers of clusters. It seems to work OK, in that it can
>produce balance where stratification would be completely impractical.
>In two of the three trials I had a list of all the clusters at the
>start, so predictability was not a problem. In the third, it might be,
>but allocation is done very remotely from cluster recruitment and I
>don't think the recruiters know what is going on.
>
>I think that concerns about imbalance are often misplaced. Provided we
>adjust for the covariates in the analysis, imbalance will not produce
>spurious differences. The loss of precision/power is usually very
>small. For an efficient analysis, we should adjust for important
>predictors anyway, whether balanced or not. However, collaborators
>worry about imbalance and in large trials I think we stratify for
>cosmetic reasons rather than practical ones.
>
>In minimised trials, there may be imbalance in other variables,
>including unobserved ones. We just have to hope for the best. Also, in
>the small trials for which minimisation was devised we cannot adjust for
>everything because there is too little data.
>
>So, to sum up, in your case I would probably go for stratification using
>a small random block size. Minimisation is designed for small trials
>and would be a bad decision in a trial intended to take a treatment to
>market. But we shouldn't do that based on one small trial anyway.
>
>Hope this helps,
>
>Martin
>
>Peter Flom wrote:
>> Hi all
>>
>> In an earlier message, I think I used the wrong subject line.
>>
>> I am interested in the problem of adjusting random assignment for covariates, so that the arms of a trial are balanced.
>>
>> I started doing some research, and I find the names of people who I think are right here on MEDSTATS.
>>
>> Stephen Senn
>> Doug Altman
>> and
>> Martin Bland
>>
>> are prominent in the reference lists.
>>
>> If they, or anyone else, has some good links, that would be great.
>>
>> Here are some more specifics:
>> There will be 4 arms to the study (Delay then treatment 1, delay then treatment 2, immediate treatment 1, immediate treatment 2)
>> There will probably be 2 covariates, possibly 3, each categorized into either 2 or 3 levels
>> The final N will be several hundred
>> Recruitment and assignment is ongoing
>>
>> Thanks!
>>
>> Peter
>>
>>
>>
>> Peter L. Flom, PhD
>> Statistical Consultant
>> Website: www DOT peterflomconsulting DOT com
>> Writing; http://www.associatedcontent.com/user/582880/peter_flom.html
>> Twitter: @peterflom
>>
>> >
>>
>
>--
>***************************************************
>J. Martin Bland
>Prof. of Health Statistics
>Dept. of Health Sciences
>Seebohm Rowntree Building Area 2
>University of York
>Heslington
>York YO10 5DD
>
>Email: mb...@york.ac.uk
>Phone: 01904 321334 Fax: 01904 321382
>Web site: http://martinbland.co.uk/
>***************************************************
>
>
>>
Peter L. Flom, PhD
Statistical Consultant
Website: www DOT peterflomconsulting DOT com
Writing; http://www.associatedcontent.com/user/582880/peter_flom.html
Twitter: @peterflom
Greg Snow
then you may want to look at the blockrand package for R, it does
these kinds of randomizations and can be used to create randomization
cards for the study coordinator(s) to use when assigning treatments to
patients.
On Sep 17, 2:58 am, Peter Flom <peterflomconsult...@mindspring.com>
wrote:
> >Web site:http://martinbland.co.uk/
> >***************************************************
>
> Peter L. Flom, PhD
> Statistical Consultant
> Website: www DOT peterflomconsulting DOT com
> Writing;http://www.associatedcontent.com/user/582880/peter_flom.html
>
> - Show quoted text -
Helena Oakey
By stratifying we are maintaining one of the fundamental design assumptions-
that within a strata the 'subjects' are (more) homozygous or alike than
subjects from another strata. By stratifying we are also ensuring that we
have a reasonable chance of both treatments being represented within each
level of stratification. But the fundamental aim is to ensure that treatment
differences are not 'polluted' by potential differences in strata. (All
obvious so far and mostly for my benefit!). If you think of a trial of this
sort as a randomised complete block design (RCBD with a continuous variable
and treat strata as random) then essentially we are partitioning the
variation into that due to strata, treatment and error and hopefully as a
result we get better estimate of treatment differences.
Therefore as Martin suggests we should be adjusting for stratifiers in our
model (otherwise in the case of RCBD the treatment variation is lumped in
with the error variation). Essentially this is the 'analyses as you design'
principle.
With respect to whether you should stratify by surgeons. The alternative to
stratification is don't stratify. If you decide on this alternative I would
still put surgeons in the model to account for the fact that patients from
the same surgeon are likely to be more similar than patients from different
surgeons. In this case, it's really recognising that your observations in
your final data set might not be independent.
Getting finally to my point-there seems to be a lot of debate in the
literature as to which is the most appropriate way to account for
stratifiers. The alternatives are to include a surgeon term as either a
random or fixed effect or use a gee's.
For continuous variables I would be inclined to put stratification terms in
the model as random effects (stems from my agricultural background). In this
case for example if you put surgeon in the model as a random effect this
would induce a compound symmetry covariance structure (same variance and
covariance) between observations from the same surgeon.
As the literature is so diverse in it's recommendations, I am still debating
what my preferred option should be when a variable is binomial. Which is the
better alternative-to fit a GLMM or gee or include the stratifier as a fixed
effect? I would be interested to know how other people are adjusting for
stratifiers in their models particularly if their response is binomial.
Regards
Helena
Peter Flom
I don't think HLM or something like that is an option in our case, as we don't have something like "surgeon"; we just have 4 treatment arms, and some covariates.
As to stratifying vs. minimizing, the problem with stratifying, in our case, is that assignment to treatment arm is ongoing. That is, a person comes in, and needs to be assigned to a treatment arm, and then begins treatment more or less immediately. A day or two later, next person comes in, and so on.
I may be revealing my ignorance, but how would stratifying work here?
(I don't worry about revealing my ignorance - it's an opportunity to learn!)
Thanks
And if anyone has a good starting point for this literature, that would be appreciated too.
Peter
-----Original Message-----
>From: Helena Oakey <helena...@adelaide.edu.au>
>Sent: Sep 17, 2009 10:26 PM
>To: meds...@googlegroups.com
John Whittington
>As to stratifying vs. minimizing, the problem with stratifying, in our
>case, is that assignment to treatment arm is ongoing. That is, a person
>comes in, and needs to be assigned to a treatment arm, and then begins
>treatment more or less immediately. A day or two later, next person comes
>in, and so on.
>I may be revealing my ignorance, but how would stratifying work here?
Say you were stratifying just by sex. In effect, that would mean that you
had separate randomisation schedules for each sex. If you did that, this
would therefore ensure that, within a sex, you would be guaranteed to get
roughly equal allocations to possible treatments (within the potential
error determined by randomisation block size). Without such
stratification, if you were very unlucky, you could end up with, say, all
males being allocated to the same treatment.
Such stratification obviously cannot work the other way around (ensure that
you have roughly the same number of males and females for each treatment) -
since you have no control over the sex of patients who present. If nearly
all the eligible patients prove to be male, there's obviously no way that
stratification, per se, could make the sexes within treatment allocations
equal. To achieve that, you would have to have a system which 'turned
away' potential patients if they were of a sex that was already
significantly over-represented in the study - but such an approach presents
lots of problems, not the least ethical and practical ones.
That's how I see it, anyway.
Kind Regards,
John
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Peter Flom
>Say you were stratifying just by sex. In effect, that would mean that you
>had separate randomisation schedules for each sex. If you did that, this
>would therefore ensure that, within a sex, you would be guaranteed to get
>roughly equal allocations to possible treatments (within the potential
>error determined by randomisation block size). Without such
>stratification, if you were very unlucky, you could end up with, say, all
>males being allocated to the same treatment.
>
If the stratification schedules are random, then you still could get very different
proportions of males and females in the two groups, couldn't you? You would have to
get unlucky, but .... well that does happen!
Isn't this the problem minimization is designed to prevent?
Thanks again for all the help
Peter
John Whittington
>John Whittington <Joh...@mediscience.co.uk> wrote
>
> >Say you were stratifying just by sex. In effect, that would mean that you
> >had separate randomisation schedules for each sex. If you did that, this
> >would therefore ensure that, within a sex, you would be guaranteed to get
> >roughly equal allocations to possible treatments (within the potential
> >error determined by randomisation block size). Without such
> >stratification, if you were very unlucky, you could end up with, say, all
> >males being allocated to the same treatment.
>
>If the stratification schedules are random, then you still could get very
>different
>proportions of males and females in the two groups, couldn't you? You
>would have to
>get unlucky, but .... well that does happen!
As I see it .... Only if the study is very small (in relation to
randomisation block size) AND the numbers of each sex are not exact
multiples of the within-sex randomisation block size. If the numbers ARE
exact multiples of the block size, then (even for a small stud) you would
be guaranteed (assuming randomisation in a 1:1 ratio) exactly equal numbers
of allocations to each treatment for males (say Nm in each group) and
exactly equal numbers of allocations to each treatment for females (say Nf
in each group). The proportion of males and females in each group is
therefore identical (Nm:Nf).
If the numbers of patients of each sex are not exact multiples of the block
size, then the extent of impact depends upon the block size and the total
study size. Consider the common situation of a block size of 4 and 1:1
randomisation. The worst case scenario is then that, for one sex, there
are two more patients allocated to treatment A than to treatment B and, for
the other sex, there are two more patients allocated to treatment B than to
treatment A. This 'worst case error' would only result in 'very different
proportions of males and females in the two groups' if the study itself
were very small.
That's how I see it, anyway!
Marc Schwartz
>
> John Whittington <Joh...@mediscience.co.uk> wrote
>
>> Say you were stratifying just by sex. In effect, that would mean
>> that you
>> had separate randomisation schedules for each sex. If you did
>> that, this
>> would therefore ensure that, within a sex, you would be guaranteed
>> to get
>> roughly equal allocations to possible treatments (within the
>> potential
>> error determined by randomisation block size). Without such
>> stratification, if you were very unlucky, you could end up with,
>> say, all
>> males being allocated to the same treatment.
>>
>
> If the stratification schedules are random, then you still could get
> very different
> proportions of males and females in the two groups, couldn't you?
> You would have to
> get unlucky, but .... well that does happen!
>
> Isn't this the problem minimization is designed to prevent?
>
> Thanks again for all the help
>
> Peter
Peter,
For each gender, you set up two series of randomization blocks. If
the subject is male, you use the first set of blocks, if the subject
is female, you use the second set of blocks.
Each series of blocks has a structure such that for each X set of
subjects within each gender group, they are evenly split between the
two treatment arms. So for example, let's say that within each gender
series, you have a block size of 6 and there are 100 blocks. Thus, you
have 600 equal treatment allocations for each gender or a total of
1,200 subjects in the study.
The block sizes themselves can be done using a permuted block size
sequence, where instead of a fixed size of 6, you might use sizes of
2, 4 and 6, and then randomly permute the 3 block sizes, so that for
each set of 12 subjects, you can have differing sequences (eg. 4/6/2,
6/2/4, etc.). Within each block, the treatment allocations are
randomized, so that between the two randomizations, you further
obfuscate the treatment allocation sequences.
Back to the example, for each 6 males and each 6 females, the blocks
of 6 each contain 3 allocations for arm A and 3 allocations for arm B.
Those 6 allocations are randomized within each block. Thus, for each 6
subjects within each gender, you get a random sequence and an equal
allocation to treatment.
The risk of course is that at some point, you have less than 6
subjects to randomize, in which case you can get an imbalance,
especially if the result of the randomization within a block is A/A/A/
B/B/B, which of course can happen. In this scenario, you could
feasibly get 3 more subjects into A than into B. That imbalance is
more problematic in a small study than in a large study.
Thus, you balance the selection of the block size to minimize the risk
of an intolerable imbalance in the covariate of interest, while also
minimizing the ability for a study site to anticipate treatment
allocation.
This is an approach that we take pretty often, though frequently it is
not to balance covariates, but to balance treatment allocation within
each site in a multi-site study. Using this approach along with a
permuted block size schema, we can reasonably achieve a balance in
treatment allocation for each site, so that there are not study sites
that contribute subjects to only one arm.
HTH,
Marc Schwartz
Peter Flom
I'm finally clear on that. I had thought that the subjects in each stratum would be randomly assigned
but now I see (and I am sure it was in the earlier posts by various people) that that is not what is done.
This would certainly be simpler than minimization
Peter
>From: Marc Schwartz <marc_s...@me.com>
>Sent: Sep 23, 2009 9:10 AM
>To: meds...@googlegroups.com
>Subject: {MEDSTATS} Re: Randomization and minimization and so on ... how to adjust for stratifiers
>
>