Should adjustment for covariates be used in prevalence estimations?

Background Adjustment for covariates (also called auxiliary variables in survey sampling literature) is commonly applied in health surveys to reduce the variances of the prevalence estimators. In theory, adjusted prevalence estimators are more accurate when variance components are known. In practice, variance components needed to achieve the adjustment are unknown and their sample estimators are used instead. The uncertainty introduced by estimating variance components may overshadow the reduction in the variance of the prevalence estimators due to adjustment. We present empirical guidelines indicating when adjusted prevalence estimators should be considered, using gender adjusted and unadjusted smoking prevalence as an illustration. Methods We compare the accuracy of adjusted and unadjusted prevalence estimators via simulation. We simulate simple random samples from hypothetical populations with the proportion of males ranging from 30% to 70%, the smoking prevalence ranging from 15% to 35%, and the ratio of male to female smoking prevalence ranging from 1 to 4. The ranges of gender proportions and smoking prevalences reflect the conditions in 1999–2003 Behavioral Risk Factors Surveillance System (BRFSS) data for Massachusetts. From each population, 10,000 samples are selected and the ratios of the variance of the adjusted prevalence estimators to the variance of the unadjusted (crude) ones are computed and plotted against the proportion of males by population prevalence, as well as by population and sample sizes. The prevalence ratio thresholds, above which adjusted prevalence estimators have smaller variances, are determined graphically. Results In many practical settings, gender adjustment results in less accuracy. Whether or not there is better accuracy with adjustment depends on sample sizes, gender proportions and ratios between male and female prevalences. In populations with equal number of males and females and smoking prevalence of 20%, the adjusted prevalence estimators are more accurate when the ratios of male to female prevalences are above 2.4, 1.8, 1.6, 1.4 and 1.3 for sample sizes of 25, 50, 100, 150 and 200, respectively. Conclusion Adjustment for covariates will not result in more accurate prevalence estimator when ratio of male to female prevalences is close to one, sample size is small and risk factor prevalence is low. For example, when reporting smoking prevalence based on simple random sampling, gender adjustment is recommended only when sample size is greater than 200

Approximating Optimal Behavioural Strategies Down to Rules-of-Thumb: Energy Reserve Changes in Pairs of Social Foragers

Functional explanations of behaviour often propose optimal strategies for organisms to follow. These ‘best’ strategies could be difficult to perform given biological constraints such as neural architecture and physiological constraints. Instead, simple heuristics or ‘rules-of-thumb’ that approximate these optimal strategies may instead be performed. From a modelling perspective, rules-of-thumb are also useful tools for considering how group behaviour is shaped by the behaviours of individuals. Using simple rules-of-thumb reduces the complexity of these models, but care needs to be taken to use rules that are biologically relevant. Here, we investigate the similarity between the outputs of a two-player dynamic foraging game (which generated optimal but complex solutions) and a computational simulation of the behaviours of the two members of a foraging pair, who instead followed a rule-of-thumb approximation of the game's output. The original game generated complex results, and we demonstrate here that the simulations following the much-simplified rules-of-thumb also generate complex results, suggesting that the rule-of-thumb was sufficient to make some of the model outcomes unpredictable. There was some agreement between both modelling techniques, but some differences arose – particularly when pair members were not identical in how they gained and lost energy. We argue that exploring how rules-of-thumb perform in comparison to their optimal counterparts is an important exercise for biologically validating the output of agent-based models of group behaviour