## Survey design

Here we are concerned with the estimation of a simple proportion (or percentage). We calculate this proportion using data from the sample and use it to infer the corresponding proportion in the underlying population. One vital component of this process is to ensure that the sampled population from which we have drawn our subjects is as close as possible to that of the target population about which we want to draw conclusions. We also require the sample to be drawn from the sample population in an objective and unbiased way. The best way of achieving this is through some sort of random sampling mechanism. Random sampling implies that whether or not a subject finishes up in the sample is determined by chance. Shuffling and dealing a hand of playing cards is an example of a random selection process called simple random sampling. Here every possible hand of, say, five cards has the same probability of occurring as any other. If we can list all possible samples of a fixed size, then simple random sampling implies that they all have the same probability of finishing up in our survey. It also implies that each possible subject has the same probability of being selected. But note that the latter condition is not sufficient to define a simple random sample. In a systematic random sample, for example, we have a list of possible people to select (the sampling frame) and we simply select one of the first 10 (say) subjects at random and then systematically select every 10th subject from then on. All subjects have the same probability of selection, but there are many samples which are impossible to draw using this mechanism. For example, we can select either subject 2 or subject 3 with the same probability (1/10), but it is impossible to draw a sample which contains both.

What other forms of random sampling mechanisms might be used? Perhaps the most common is a stratified random sample. Here we divide our sampled population into mutually exclusive groups or strata (men and women, or five separate age groups, for example). Having chosen the strata, we proceed, for example, to take a separate simple random sample from each. The proportion of subjects sampled from each of the strata (i.e. the sampling fraction) might be constant across all strata (ensuring that the overall sample has the same composition as the original population), or we might decide that one or more strata (e.g. the elderly) might have a higher representation. Another commonly used sampling mechanism is multistage cluster sampling. For example, in a national prevalence survey we might chose first to sample health regions or districts, then to sample post codes within the districts, and finally to select patients randomly from each selected post code. (See

Kessler(6) and Jenkins et al.{d. for discussions of complex multistage surveys of psychiatric morbidity.)

One particular design that has been used quite often in surveys designed to estimate the prevalence of psychiatric disorders is called two-phase or double sampling. Psychiatrists frequently refer to this as two-stage sampling. This is unfortunate, since it confuses the two-phase design with simple forms of cluster sampling in which the first stage involves drawing a random sample of clusters and the second stage a random sample of subjects from within each of the clusters. In two-phase sampling, however, we first draw a preliminary sample (which may be simple, stratified, and/or clustered) and then administer a first-phase screening questionnaire such as the General Health Questionnaire (see Ch.a.piei,,2.Z). On the basis of the screen results we then stratify the first-phase sample. Note that we are not restricted to two strata (likely cases versus the rest), although this is perhaps the most common form of the design. We then draw a second-phase sample from each of the first-phase strata and proceed to give these subjects a definitive psychiatric assessment. The point of this design is that we do not waste expensive resources interviewing large numbers of subjects who not appear (on the basis of the first-phase screen) to have any problems. Accordingly, the sampling fractions usually differ across the first-phase strata. However, it is vital that each of the first-phase strata have a reasonable representation in the second phase, and it is particularly important that all of the first-phase strata provide some second-phase subjects. The reader is referred to Pickles and Dunn (8) for further discussion of design issues in two-phase sampling (including discussion of whether it is worth the bother).

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