This article presents rules of thumb for the design and analysis of studies. The word “studies” is used as a shorthand term for clinical trials and experiments. These rules enunciated is this article will apply to both of the groups (i.e., clinical trials and experiments).
- I. Randomisation puts systematic effects into the error term
- i. The concept of randomisation as a basis for the design of studies in attributable to R.A. Fisher (1935). The idea took time getting established. As late as 1940, W.S. Gossett was convinced that of researchers really knew what they were doing, it would be counterproductive to randomise.
- Rule of thumb
- i. Randomisation puts systematic sources of variability into the error term.
- i. Suppose the Environmental Protection Agency wants to measure fuel economy in passenger cars. It selects 100 cars at random (just exactly how to do this is not easy) and gets fuel economy estimates from the next tankful. The average of the sample is a valid estimate of the passenger fleet fuel economy and the sample standard deviation provides the basis for an interval estimate. This is also a valid estimate. The variability in fuel economy is a function of many factors such as driving condition, city or highway, type of vehicle, driver characteristics and other factors. The haphazard selection ensures that the effects of all these factors become part of the random variability.
- Basis of the Rule
- i. The basis of the rule is the threefold purpose of randomisation. First, by randomisation, systematic effects are transformed into error. Second, there is an expected balance in the assignment of known and unknown factors that might influence the outcome. Third, randomisation provides that basis for statistical procedure such as tests of significance, analysis of variance and confidence intervals.
- Discussions and Extensions
- i. This formulation of the rule for randomisation is because of Dr. D. B. DeLury of the University of Toronto.
- ii. If, in the illustration, the assignment of cars to fuels had not been random, all kinds of objections could have been raised by interested third parties. The nature of the objections would be determined by whether a significant difference had been found or not.
- iii. Lack of randomisation leads to arm-waving. The most general non-randomised study is the examination study. The lack of randomisation in such studies invariably leads to debate about the interpretation of the results. Epidemiologists come closest to making observational studies as clean as possible through, for example, case-control studies. But even in this situation there is debate about the validity and execution of outcomes. A vigorously debated issue is the relationship between air pollution and morality (Samet et al., 2000a.b.). Epidemiological evidence for such effects is based on time series analysis of daily deaths and daily pollution level at central monitoring stations. One reason for the debate is that such data are observational so they lack the compelling feature of a randomised study.
- iv. Randomisation is essential for a plausible inference. Observational studies may provide correct answers but the degree of certainty is much less than for randomised studies.
- II. Blocking is the key to reducing variability
- i. While randomisation is the key ingredient in the validity of statistical inference, it does have the disadvantage of generating a potentially large error term. One way around this drawback is to establish homogeneous subsets of experimental units (blocks) and assigning treatments randomly to the units within these subsets.
- Rule of thumb
- i. By randomly assigning treatment to experimental units within blocks (i.e., blocking) systematic effects between the blocks can be eliminated with a resultant decrease of within-treatment variability and increased precision.
- i. In the previous illustration some of the variability in fuel economy was attributable to conditions in which driving was carried out, city or highway. If comparisons are only made within cities, the standard deviation of fuel economy among the city-driven cars will be smaller than the overall standard deviation. Hence, for sample size calculations a smaller sample size will be needed to establish the significance of the putative fuel enhancement. The factor, driving conditions, is said to be a blocking factor.
- Basis of the Rule
- i. The total variability in a population can be divided into two components: among blocks and within blocks. By assigning treatments within blocks, between block variability is eliminated. If the background variability in the blocks is of lower magnitude, that is the blocks form units possessing same characteristics, then by blocking more precise estimates are obtained.
- Discussion and Extensions
- i. The term blocking has an agricultural origin where treatments were compared within blocks of land. Each block was partitioned into “plots” upon which the treatments were carried out. In clinical trials, animal studies, or other investigations the blocks can be people, animals, treatment sessions, cities, school districts, or any group that is more homogeneous than the general population. This applies to observational studies as well.
- ii. The “paired study” is a good example of blocking. For example, in studying and comparing the effectiveness of two treatments for epilepsy, one design randomly allocates treatments to groups of subjects with epilepsy and compares, suppose, seizure frequency after 12 weeks of treatment. The error term would then would be the variability in response among the subjects within the subjects—between-subject variability. An alternative design tests both treatments on the same subject. The sequence of treatments is allocated randomly (the source of randomisation), and comparisons are within subjects. A paired study is perhaps the most extreme of blocking; all between-subject variability is removed in this design. Blocking is not always efficient.
- iii. There is a simple test for the effectiveness of blocking: the variability within the blocks must be less than the variability between blocks. This can be assessed by means of an analysis of variance or, in the case of paired data, by correlating the pairs of observations.
- iv. Any factor that co-varies with the outcome variable may be a candidate blocking factor. It should not be in the casual chain between treatment and outcome.
- v. The question may raise, why not make blocks as fine as possible? The solution is that there is a trade-off with generalizability of the results.
- vi. The concept of blocking is intuitively appealing. Blocking occurs in many situations. In multi-centre clinical trials each clinic may be considered a block and treatments are assigned randomly to subjects within the clinic so that there is balance at the clinic level. This eliminates clinic variability from treatment comparisons.
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