7 factors that influence the sample size

Factors Influencing Decision To Sample

Any researcher takes some decision regarding the sampling plan. His decision to sample is influenced by atleast three factors:

1. Size of the Population
2. Cost involved in obtaining the elements
3. Convenience & Accessibility of the elements

1. Size of the population- Decision to sample is directly influenced by the size of the population. If the population is small, for example, it consists of 100 individuals, the investigator may decide to include all in his study & therefore, sampling may not be done. On the other hand, if the size of the population is large, say, it consists of 10,000 individuals, he may decide to select limited number of individuals from the population of 10,000 individuals. It is also important to note that the size of the population is a relative matter, what one researcher regards as a large population, the other may regards it as a small one. In fact, no clear- cut guidance exists for making distinction between large and small population.

1. Cost involved in obtaining the elements- The researcher is also influenced by the cost likely to be incurred in obtaining the elements from the population. If the sampling involves a bigger cost which the researcher cannot meat, the decision to sample may be postponed. On the other hand, if sampling involves a cost which the investigator can readily meet, the sampling work is facilitated.

1. Convenience & Accessibility of the elements- Sometimes the researcher may have to deal with a problem with respect to which sample may not be conveniently available. On the other hand, some researcher may have access to facilities and staff where large amount of data could be easily handled.

Thus, decision to sample effectively is influenced by the size of the population, the anticipated cost of the study and the convenience and accessibility associated with the sample.

This chapter answers parts from Section A(d) of the Primary Syllabus, "Describe bias, types of error, confounding factors and sample size calculations, and the factors that influence them )".  This topic was examined in Question 2 (p.2) from the first paper of 2009.  It is expanded upon in the Required Reading chapter for the Part II exam ("Study power, population and sample size").

In summary, calculation of sample size involves the following factors:

• Alpha value: the level of significance (normally 0.05); i.e. the level of probability you accept as "real", i.e. not due to chance.
• Beta-value: the power (normally 0.2), i.e. the percentage chance of detecting a treatment effect if there actually is one. 
• The statistical test you plan to use
• The variance of the population (the greater the variance, the larger the sample size)
• The effect size (the smaller the effect size, the larger the required sample)
• The control group outcome rate: How many of the control group are expected to develop the treatment effect.
• Study design, i.e. is it an RCT? In randomised controlled trials, there is an additional benefit to randomisation which develops above a certain sample size (N=200).

How many patients does my trial need?

That depends on several factors.

The magnitude of the treatment effect: The larger the effect, the smaller the required sample size. For a truly tiny treatment effect, one would require truly massive numbers.

The control group outcome rate: How many of the control group are expected to develop the treatment effect.

The agreed-upon significance level (alpha): The level of probability you accept as "real", i.e. not due to chance. The greater your demands for significance, the larger the number of patients needs to be enrolled.

The power (beta): the percentage chance of detecting a treatment effect if there actually is one. This is something you decide upon before commencing the trial; the higher the power value, the more patients you will need. Typically, beta is 0.8, so there is a 20% chance (1-beta) of commiting a Type 2 error , or a "false negative".

Obviously, if your trial has too few patients, you are more likely to commit a Type 2 error. The negative results of this trial will force you to discard a treatment which does actually have a beneficial effect, an effect which you and your tiny useless trial have failed to reveal.

The concept of statistical efficiency demands that the randomised controlled trial achieve its goal (discriminating the treatment effect) with the smallest possible number of patients. However, there is probably a minimum.

In randomised controlled trials, there is an additional benefit to randomisation which develops above a certain sample size (N=200). This is the benefit of randomization, which ensures an approximately equal distribution of unknown confounding factors (such as weird genetic variations and other such unpredictable things). In trials smaller than N=200, this effect of randomisation can no longer be relied upon- one simply cannot guarantee that one group is sufficiently similar to the other group in its incidence of unpredictable features.

References

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