To pool or not to pool, from whether to when: applications of pooling to biospecimens subject to a limit of detection

Abstract

Pooling of biological specimens has been utilised as a cost-efficient sampling strategy, but cost is not the unique limiting factor in biomarker development and evaluation. We examine the effect of different sampling strategies of biospecimens for exposure assessment that cannot be detected below a detection threshold (DT). The paper compares use of pooled samples to a randomly selected sample from a cohort in order to evaluate the efficiency of parameter estimates. The proposed approach shows that a pooling design is more efficient than a random sample strategy under certain circumstances. Moreover, because pooling minimises the amount of information lost below the DT, the use of pooled data is preferable (in a context of a parametric estimation) to using all available individual measurements, for certain values of the DT. We propose a combined design, which applies pooled and unpooled biospecimens, in order to capture the strengths of the different sampling strategies and overcome instrument limitations (i.e. DT). Several Monte Carlo simulations and an example based on actual biomarker data illustrate the results of the article.

Figure 1

Normally distributed data constrained by a detection threshold (shaded area represents unobserved data). DT, detection threshold.

Figure 2

The Monte Carlo averages of the numerical sample sizes. DT, detection threshold.

Figure 3

Chi-square distributed data constrained by a detection threshold (shaded area represents unobserved data). DT, detection threshold.

Figure 4

Efficiency of the maximum likelihood estimators: $\underset{N\to \infty }{lim}log(N\times var(\widehat{\mu }))$ and $\underset{N\to \infty }{lim}log(N\times var(\widehat{\sigma }))$ are plotted by graphs (a) and (b) respectively. Curves (------), (——) and (·········) correspond to databases Z, Z^(p) and {Z_i, i = 1,…, n} respectively.

Figure 5

Logarithm of the Monte Carlo estimators of E(μ̂ − μ) and E(σ̂ − σ_X) [graphs (a) and (b) respectively], where the pooling error is in effect. Curves (------), (——) and (·········) correspond to databases Z, Z^(p) (with pooling errors) and {Z_i, i = 1,…, n} respectively.