Abstract
BackgroundThe Australian Longitudinal Study on Male Health (Ten to Men) used a complex sampling scheme to identify potential participants for the baseline survey. This raises important questions about when and how to adjust for the sampling design when analyzing data from the baseline survey.MethodsWe describe the sampling scheme used in Ten to Men focusing on four important elements: stratification, multi-stage sampling, clustering and sample weights. We discuss how these elements fit together when using baseline data to estimate a population parameter (e.g., population mean or prevalence) or to estimate the association between an exposure and an outcome (e.g., an odds ratio). We illustrate this with examples using a continuous outcome (weight in kilograms) and a binary outcome (smoking status).ResultsEstimates of a population mean or disease prevalence using Ten to Men baseline data are influenced by the extent to which the sampling design is addressed in an analysis. Estimates of mean weight and smoking prevalence are larger in unweighted analyses than weighted analyses (e.g., mean = 83.9 kg vs. 81.4 kg; prevalence = 18.0 % vs. 16.7 %, for unweighted and weighted analyses respectively) and the standard error of the mean is 1.03 times larger in an analysis that acknowledges the hierarchical (clustered) structure of the data compared with one that does not. For smoking prevalence, the corresponding standard error is 1.07 times larger. Measures of association (mean group differences, odds ratios) are generally similar in unweighted or weighted analyses and whether or not adjustment is made for clustering.ConclusionsThe extent to which the Ten to Men sampling design is accounted for in any analysis of the baseline data will depend on the research question. When the goals of the analysis are to estimate the prevalence of a disease or risk factor in the population or the magnitude of a population-level exposure-outcome association, our advice is to adopt an analysis that respects the sampling design.
Highlights
The Australian Longitudinal Study on Male Health (Ten to Men) used a complex sampling scheme to identify potential participants for the baseline survey
It was not feasible to survey remote and very remote regions because of the travel time required for fieldworkers to recruit potential participants into the study, so the study was restricted to sampling from the first three strata, that is, the major cities, inner regional and outer regional areas
Implications for estimating population means, prevalences and totals Estimating means, prevalences or totals from a complex survey as though they were generated from a simple random sample has the potential to generate biased estimates and for the stated precision of these estimates to differ from the variability that we would observe in them under repeated sampling
Summary
Overview of the ten to men sampling design Stratification When stratification is used in a survey design, it refers to the population being partitioned into groups prior to selection of the sample [4]. Individuals in the inner and outer regional strata did, in theory, have equal probabilities of selection (due to the selection of the fixed number of SA1s within each SA2 effectively “cancelling out” the sampling of SA2s with probability proportional to their size), this was violated in practice due to variation in the participation fractions between households, SA1s and SA2s. This variability was an issue for the major cities stratum as well. Details on the calculations of the baseline sampling weights for Ten to Men are given in Appendix 1
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