Random and Quasi-random Allocation

Background Surprisingly many researchers do not understand the concept of random allocation. For example, a Professor of Psychiatry criticising the WHI study’s findings that HRT increased all cause dementia, was critical because the researchers failed to measure the genetic susceptibility of the women to Alzheimer’s Disease.

As one researcher put it “Whilst it is possible for all or the majority of the 16,000 women with a genetic susceptibility to dementia to be allocated into the HRT arm it is about as likely as Elvis Presley landing a UFO on top of the Loch Ness monster”. BUT – I believe Elvis Presley lives!

What Randomisation is NOT Randomisation is often confused with random SAMPLING. Random sampling is used to obtain a sample of people so we can INFER the results to the wider population. It is used to maximise external or ecological validity.

Random Sampling If we wish to know the ‘average’ height and weight of the population we can measure the whole population. Wasteful and very costly. Measure a random SAMPLE of the population. If the sample is RANDOM we can infer its results to the whole population. If the sample is NOT random we risk having biased estimates of the population average.

Random Allocation Random allocation is completely different. It has no effect on the external validity of a study or its generalisability. It is about INTERNAL validity the study results are correct for the sample chosen for the trial.

The Quest for Comparable Groups It has been known for centuries to to properly evaluate something we need to compare groups that are similar and then expose one group to a treatment. In this way we can compare treatment effects. Without similar groups we cannot be sure any effects we see are treatment related.

Why do we need comparable groups? We need two or more groups that are BALANCED in all the important variables that can affect outcome. Groups need similar proportions of men & women; young and old; similar weights, heights etc. Importantly, anything that can affect outcome we do NOT know about needs to be evenly distributed.

The unknown unknowns Those things we know about we can measure (e.g., age); Those things we know are unknown (health status) we can often control for (e.g, proxy for health status SF36?); Those things that affect outcome that we do not know or cannot know is why we randomise.

Non-Random Methods Quasi-Alternation Dreadful method of forming groups. This is where participants are allocated to groups by month of birth or first letter of surname or some other approach. Can lead to bias in own right as well as potentially being subverted.

Born in August and British? BAD Luck. August born children get a raw deal from the UK educational system as they are young for their year and consequently comparisons between August children and September children show August children do better. Consequently quasi-alternation by month of birth will be biased towards the September group.

Non-random methods: “True “ Alternation Alternation is where trial participants are alternated between treatments. EXCELLENT at forming similar groups if alternation is strictly adhered to. Austin Bradford-Hill one of the key developers of RCTs initially advocated alternation because: It is easy to understand by clinicians; Leads to balanced groups if done properly. BUT Problems because allocation can be predicted and lead to people withholding certain participants leading to bias.

Randomisation Randomisation is superior to non- random methods because: it is unpredictable and is difficult for it to be subverted; on AVERAGE groups are balanced with all known and UNKNOWN variables or co- variates.

Methods of Randomisation Simple randomisation Stratified randomisation Paired randomisation Minimisation

Simple Randomisation This can be achieved through the use of random number tables, tossing a coin or other simple method. Advantage is that it is difficult to go wrong.

Simple Randomisation: Problems Simple randomisation can suffer from ‘chance bias’. Chance bias is when randomisation, by chance, results in groups which are not balanced in important co-variates. Less importantly can result in groups that are not evenly balanced.

Why is chance bias a problem? Unless you are able to ‘adjust’ for co- variates in the analysis imbalance can result in bias. For small samples it is possible for a numerical imbalance to occur with a consequent loss of power.

Other reasons? Clinicians don’t like to see unbalanced groups, which is cosmetically unattractive (even though ANCOVA will deal with covariate imbalance) Historical – Fisher had to analyse trials by hand, multiple regression was difficult so pre-stratifying was easier than post-stratification.

Stratification In simple randomisation we can end up with groups unbalanced in an important co-variate. For example, in a 200 patient trial we could end up with all or most of the 20 diabetics in one trial arm. We can avoid this if we use some form of stratification.

Blocking A simple method is to generate random blocks of allocation. For example, ABAB, AABB, BABA, BBAA. Separate blocks for patients with diabetes and those without. Will guarantee balance on diabetes.

Blocking and equal allocation Blocking will also ensure virtually identical numbers in each group. This is NOT the most important reason to block as simple allocation is unlikely to yield wildly different group sizes unless the sample size is tiny.

Blocking - Disadvantages Can lead to prediction of group allocation if block size is guessed. This can be avoided by using randomly sized blocks. Mistakes in computer programming have led to disasters by allocating all patients with on characteristics to one group.

Too many variables. Many clinicians want to stratify by lots of variables. This will result in cells with tiny sample sizes and can become impracticable to undertake.

Centre Stratification Many, if not most, trials that stratify stratify by centre. This can lead to the predictability of allocation so that subversion can occur.

Stratification Disadvantage In trial steering meetings often large amounts of time are WASTED discussing what variables to stratify by. Many amateur trialists think it is very important to stratify (perhaps it gives them a raison d’etre for being there as they know various obscure clinical characteristics on which to stratify).

Pairing A method of generating equivalent groups is through pairing. Participants may be matched into pairs or triplets on age or other co-variates. A member of each pair is randomly allocated to the intervention.

Pairing - Disadvantages Because the total number must be divided by the number of groups some potential participants can be lost. Need to know sample in advance, which can be difficult if recruiting sequentially. Loses some statistically flexibility in final analysis. Can reduce the statatistical power of the study.

Summary allocation methods If your trial is large (which it should be if you are doing proper research), then I would generally use simple randomisation as this has strong advantages over the other approaches (exception being cluster trials).

The ‘Average Trial’ ON AVERAGE trials are balanced across all variables. But some trials will be unbalanced across some variables. What will happen? Large imbalance in trivial variables (we have more women called Mavis who were born on a Monday in the intervention group); Small imbalance in important variables (e.g., age); Even small imbalances can lead to a biased estimate.

What can we do? “If it exists, we can measure it, if we can measure it, we can put it into a regression equation” (Health Economist). IMPORTANT measurable variables (e.g., age, baseline health status) SHOULD be adjusted for in ANCOVA (regression analysis). This ‘post-stratification’ deals with any chance imbalance, and even if there is no imbalance increases the power of the study.

What about my small cluster trial? Cluster trials are an exception – small units of allocation can easily lead to imbalance at the cluster level. Also, whilst it is possible to adjust using sophisticated statistical methods of cluster level imbalances if we were sure of balance we can use simple cluster means t-test (albeit with some loss of power).

Randomising clusters Two ways to do this: We can use stratified random allocation but with small effective sample sizes we can easily have empty cells. OR we can use minimisation.

Non-Random Methods Minimisation Minimisation is where groups are formed using an algorithm that makes sure the groups are balanced. Sometimes a random element is included to avoid subversion. Can be superior to randomisation for the formation of equivalent groups.

Minimisation Disadvantages Usually need a complex computer programme, can be expensive. Is prone to errors as is blocking. In theory could be subverted.

Cluster trials and balance In cluster trials (where we randomise groups of participants, e.g., patients of GPs) there are usually very few clusters (e.g., or fewer). Chance imbalance can easily occur. Some form of restricted allocation is usually necessary. Because units of allocation are known in advance this avoids subversion.

Example of minimisation We are undertaking a cluster RCT of adult literacy classes using a financial incentive. There are 29 clusters we want to be sure that these are balanced according to important co-variates: size; type of higher education; rural or urban; previous financial incentives.

Example of minimisation ICNext FE Other Rural Urban < Incent No None

Example of minimisation ICNextI = 34 FE Other C = 33 Rural Urban Next goes to C 8+ < Incent No None

What is wrong with? “In this randomised study, we took a random sample of doctors from the Southern area where guideline A was being implemented and compared their outcomes with a random sample of doctors from the Northern area where there was no guideline”

Is this OK? “We randomised doctors into two groups using a telephone randomisation service. We then took a random sample of patients from each group and compared the effect of guidelines on their health status”.

Study A From a database of 2000 heroin addicts we will take a random sample of 1,000 and randomise these into two groups of 500 each. The intervention group will be offered pharmaceutical heroin. The control group will not be contacted. At 6 months both groups will be invited attend a clinic to measure outcomes.

Study B From a database of 2000 heroin addicts we will take a random sample of 500 this group will be offered pharmaceutical heroin. At 6 months we will invite these addicts to attend a clinic to measure outcomes. At the SAME time we will take another random sample of 500 addicts and measure their outcomes.

Which is the RCT? Study A or Study B?

Conclusions Random allocation is USUALLY the best method for producing comparable groups. Alternation even if scientifically justified will rarely convince the narrow minded evidence based fascist that they are justified. Best to use random allocation.