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Design of Experiments, Basic Concepts

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Contents 1 Introduction 2 Randomisation 3 Replication: 4 Local control 5 Author

Introduction

Designing or planning an experiment in a proper or structured manner, so that maximum interpretation can be done out of the results that come out of the experiment, has become very important in all “scientific” disciplines, but it has become absolutely essential in the field of clinical trials. Let us suppose that we want to test whether a newly discovered drug, B, is safe and effective for use in human beings. It has to undergo clinical trials and it has to be compared with placebo (no drug at all) and with standard drug A, which is already in the market. Let us suppose we decide to test our drug (on the basis of the time, money and energy we have in our possession) on 10 volunteers, then we have to test the placebo on 10 volunteers and the drug A on 10 volunteers for comparison purposes. After conducting the experimental trials, we take the three means, placebo, and and make a comparison and then come to a conclusion. For our conclusion to be valid and acceptable to scientists we have to follow, what are known as “principles of experimental design”.

There are three principles of experimental design, which are the pillars of experimental design. They are randomization, replication and local control. They are shown like this.

Randomisation

In our experiment of testing three treatments, i.e., placebo, drug A and drug B on a group of 30 volunteers; we have to assign placebo to 10 volunteers, drug A to 10 volunteers and drug B to 10 volunteers. This assignment of treatments to volunteers is done by a “randomized” procedure. In this procedure, each volunteer has an equal chance of getting into any of the three treatments. So randomization may be defined as a procedure “which involves giving all the volunteers an equal chance of getting into the sample that takes a particular treatment”.

Randomisation is not a casual process; it is different from “casually” or in a “haphazard” manner allotting treatments to volunteers. Randomisation is a scientific process that ensures that there is no bias in the allotment of treatments to volunteers and that each volunteer has an equal chance of getting into the sample that faces a particular treatment. We can explain with the help of a small example, why “casual” is not the same as “random”. Suppose there are 30 rats in a cage and we want to take 10 rats for placebo, 10 rats for drug A and 10 rats for drug B. Suppose our procedure consists of just opening the door of the cage and casually picking the rats into each treatment group. Then, surely, as we are trying to pick the rats, they will run away from us, and in our attempts to catch them, we usually end up, picking the less lively rats, with less capacity to run, or more obese rats into our first group. The last 10 rats caught are likely to be slim and athletic. So in this casual procedure, the average weight or liveliness of the rats could be different among the three different treatment groups, and unconsciously we allowed “bias” to enter into our experimental design. So a casual sample is not a random sample. A random sample is a sample drawn from a population in such a way that there is no bias, and such that every unit of the population has an equal and defined chance of getting into the sample.

I will explain two methods of drawing a random sample.

1. Since there are 30 volunteers and three treatments we can design a procedure such as the following. We assign numbers 1 to 30 to these volunteers; we write the numbers of all the volunteers (1 to 30) on equal, small slips of papers; we put the slips in a box; we shuffle the box; then we take a slip at random; we call the number and the person with the number goes into the placebo group; them we take a second slip and the call the number and he goes into group A; then we take a third slip and call the number and the volunteer with that number goes into group B, and so on until all the 30 volunteers are allotted the three treatments.
2. Another procedure is the use of Random number tables. These tables are generated with the help of computers and the numbers take random places in these tables. I am reproducing a small sample of random number table from page 99 of Remingtons Pharmaceutical Sciences here.

39	61	09	51	68	81	26	30	52	20	61	41	52
89	35	48	61	72	10	84	34	10	44	72	94	77
37	98	37	56	40	30	70	31	75	03	68	32	15
20	55	68	05	53	73	60	28	96	48	91	81	18

With the help of this table we can randomly allot the three treatments to the 30 patients. We first set down our rules like this:

1. We enter the random number table, randomly, i.e. at any point we like.
2. From there we can freely go horizontally or vertically and record the numbers, as we go, until our sample is filled.
3. For example, we have to select a sample of 10 volunteers from a population of 30 volunteers into our placebo group. I enter the above table randomly at “10” in the second row; from here I go on entering three digit numbers, horizontally; like this; 108, 434, 104, 474 and so on. After taking the number, I divide it by 30, and I take the remainder into the sample. Like this.

       (1.)   30) 108 (3                       (2)     30) 434 (14
                   90                                       30
                --------                                ------------- 
                  18                                        134
                 --------                               --------------       
                                                             14         
                                                        --------------

Volunteer no. 18 goes into the first or the placebo group. Then no. 14 follows into placebo group. Then again the number 14 has come, so we discard it and proceed to the next number. Like this we go on until the first group is filled. If we get the remainder as 0, then we take volunteer number 30. After the placebo group is filled, we proceed to take the next 10 numbers into the second or the A group. If a number has already entered the first group or has been repeated, we discard it. In this way we choose volunteers into treatment groups in a randomized manner. Thus we ensure that there is no bias in our experiment.

Replication:

The second important thing in experimental design is replication. If we test our drug on 10 volunteers and get a result we have a certain level of confidence in it. If we can test it on 20 volunteers, our confidence in the result is doubled. So, as the “size of the sample” increases, the standard error and the sampling error decrease, and our confidence in the result increases.

But we cannot go on increasing the “size of the sample” as we like, because of limitations, such as, money, time, energy and convenience. Clinical trials have to be done in extremely controlled and defined circumstances and are extremely costly. All biological experimentation involving animals is costly and time consuming. That is why it takes a lot of time and money for a new drug to enter the market.

Replication then, means the repetition of an observation. The more numbers of times we can make the observation, the more error free is our result and the more confidence we can have in them. The number of replications is controlled by own time, money, energy, convenience, ethical considerations (even if we have all facilities why should we subject animals / human beings to suffering unnecessarily?) and by our design of experiment.

Local control

This is the third important principle of experimental deisgn. However careful we are in taking volunteers, there is usually some heterogeneity in the population, in terms of their age, health status etc. So we ensure in certain experimental designs, that heterogeneity is controlled, such that, the population is divided into blocks of equal size, and in each block, each treatment is randomly allotted. We divide such that, each block is homogeneous, and the heterogeneity goes into in between two blocks. For example, I can take a group of 27 volunteers (young males) and divide them into three blocks, such that block A has candidates weighing between 100 to 120 kgs; block B has candidates weighing between 80 to 100 kgs, block C has candidates weighting between 60 to 80 kgs. In each block, there will be 9 candidates. Among these 9 candidates 3 will be randomly selected for placebo, 3 for drug A and 3 for drug B.

So local control involves the principle of controlling the heterogeneity in a population by dividing the population into blocks such that each block is homogeneous, and the heterogeneity goes in between two blocks. This helps in better interpretation of the results and in recognizing “variability” in the volunteers and accounting for them.

There are three basic designs used in experimental design; they are 1. Completely Randomized Design, 2. Randomised Block Design and 3. Latin Square Design. Each has its advantages and disadvantages. As we go from CRD to RBD to LSD, randomisation decreases, replication decreases, and local control increases.

Completely Randomised Design : In this design, the treatments are allotted to the volunteers in a totally randomized manner. All the volunteers are considered homogeneous in their characteristics. Even if one result misses by any chance, the results can be interpreted and analys can be done. The scheme is the scheme of one way analysis of variance. It will look something like this.

Treatments

Volunteers
	X1	X3	X4
	X18	X29	X5
	X14	X26	X9
	X22	X11	X12
	X20	X13	X15
	X16	X6	X17
	X2	X7	X23
	X8	X28	X24
	X10	X21	X25
	X30	X19	X27

Author

Prof.Vijaya Ratna

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