Why pooling samples

As measuring all the biological subjects in two populations is rarely possible in most situations representatives from a population are randomly selected and measurements are made on these. These are then taken to infer the properties of the population. Let X be the measurable quantity that is being determined in the experiment, e. In the case of one-channel microarray, X could denote the logarithm most commonly base 2 is used of fluorescence intensity or the logarithm of the fluorescence ratio in the case of two-channel microarray.

Let x i c denote the value of X for an individual subject i in the control population c , and x j t that of the individual subject j in the treatment population t.

The two-labelling t -test presented in Zhang and Gant was designed to deal with systematic labelling biases generated during microarray experimentation. The t -test presented in this paper, however, assumes no systematic data biases. In the case of two-colour microarrays this requires a common reference design.

In such an experimental design the labelling biases cancel themselves out in the calculation of the test statistic. In Zhang and Gant , the biological variances of the two populations under comparison do not have to be the same, i. Relaxing this requirement was possible, as in the case of the traditional two-sample t -test with unequal variance Brownlee, , but an exact power function could not be readily obtained. The exact power function obtained in this paper allows evaluation of the effects of pooling biological samples and the effects of taking multiple technical measurements, thus giving researchers quantitative guidance on the practice of pooling samples.

We have implemented the computation of the power function S of Equation 12 as a Java application, which can be accessed at the URL given in the abstract. Here we apply this to microarray comparative studies for finding differentially expressed genes and investigate the effect of pooling RNA samples in the experiments.

We also compare our exact results with some approximate results presented by other authors Shih et al. Based on their approximate formulas, Shih et al. Here we give exact results for the two scenarios to show the difference to the approximate results.

In Table 1 , we present results for different pooling parameter r. The effects of other levels of pooling on the detection power are also shown in Table 1. The minimum number of biological subjects N s and microarrays N m that meet the preset targets is highlighted with bold fonts.

It is clear that as the level of pooling is increased with increasing r , the number of microarrays N m can be reduced, but the number of biological subjects N s has to be increased. For example, in order to reduce the number of arrays from 12 Table 1 , first panel to 8 Table 1 , fourth panel , the number of biological subjects to form the pools must be increased from 12 to For the first scenario described in the text, the detection power of designs with different levels of pooling.

The minimum number of biological subjects N s and microarrays N m that meet the preset targets are highlighted with bold fonts. Similar to the first scenario, as the level of pooling is increased, the number of arrays N m is reduced while the number of subjects increased to meet the preset targets. In Table 2 , we summarize our exact results and the approximate results of Shih et al.

It can be seen that the difference between the two can be very large, indicating the need for exact results. Generally, the approximate formulas of Shih et al. Comparison of our exact results and the approximate results of Shih et al. The last column in each panel gives the cost conditions when pooling samples become beneficial relative to a lower level of pooling shown in this table.

For the first scenario using the actual cost figures given in Shih et al. Therefore for this laboratory pooling samples is not recommended. However, if we use the cost figures of Kendziorski et al. For the second scenario, it is a similar story.

The cost figures of Shih et al. On the other hand, the cost figures of Kendziorski et al. So in Kendziorski et al. We have in this paper presented exact formulas for calculating the power of microarray experimental design with different levels of pooling. These formulas can be used to determine the conditions of statistical equivalence between different pooling setups.

As in Kendziorski et al. However, microarray monitors thousands of genes simultaneously, and the biological and technical variances vary from gene to gene, therefore no single result of statistical equivalence between pooled and non-pooled designs applies equally to all genes on the array.

So in practice how would the formulations in this work be used? The pooled sample is tested first. If negative, all members of the pool can be given a negative result immediately, saving the cost of testing each individual one at a time.

If the pool tests positive, however, then each individual sample within the pool must be re-tested to identify who within the pool is actually causing the pool test to be positive. There is no other way to identify who is positive or if more than one person in the pool is infected. Testing each unit separately would be prohibitively expensive and slow, especially when only a tiny percentage of units are likely to be contaminated.

As a result of this pooled screening of blood for viral pathogens, the probability of receiving contaminated blood is less than 1 in , units. COVID is more transmissible than most other viral infections. Pre-symptomatic and asymptomatic individuals have similarly high viral loads and transmission risk as those with evident symptoms, but without testing they will never know it until it is too late, when many of the friends and family around them become ill super-spreader events. This has placed a very large burden on diagnostics test manufacturers and has far exceeded the ability of the overall testing infrastructure to meet it.

Pooled screening test is most effective when applied to populations with relatively low positivity rates, often at or even below a 10 percent prevalence of COVID in the target population. Misclassification rates obtained by the six classifiers were investigated for individual subjects and pooled samples pool sizes of 2, 3, and 5. The results show that the misclassification rates increase with larger pool sizes Figure 1 , which is in accordance with the study of Telaar et al.

This characteristic can be observed with both small and larger numbers of markers in datasets. Although pooling helps to decrease variances of biological samples, the sample size is reduced when samples are pooled [ 15 ] which can degrade the discriminatory ability of classifiers. In addition, the increase of misclassification rates with raising pool sizes follows a linear pattern.

The difference among the performance of classifiers is larger for higher numbers of markers than for small numbers of markers in the data. Significant differences in the performance of classifiers between individual subjects and various pool sizes become apparent from the Wilcoxon rank sum test Figure 2. In datasets with large number of markers, the performances of classifiers show significant differences in every pair of pool size Figure 2 b.

For SVMs with both linear and radial kernels, performances of classifiers do not show statistical differences at pool sizes of 2 and 3, respectively. These results could motivate the use of classifiers with different pool sizes in cases where the data is noisy and only a small number of markers are expected.

In order to gain further insight on the performance of different classifiers, the misclassification rate of classifiers with different number of markers from 1 to 10 was investigated Figure 3. RF outperforms other classifiers for every pool size 2, 3, and 5 in our settings with top-ranked features. For other classifiers, the performance-ranked order slightly differs, depending on the pool size. The kernel function helps to map data into higher dimension space.

This could allow the linear hyperplane providing better separation between data points of two classes. The performance variation of classifiers is greater for individual and small pool sizes than for larger pool sizes.

The RF classifier demonstrates a good predictive performance even when most predictive features are noisy and turns out to be robust against overfitting. In earlier studies, it was also reported to produce favorable results [ 32 , 33 ].

In addition, ensemble methods like RF are generally well-suited for reducing the total expected error [ 34 ]. Also performance trends of classifiers with increasing numbers of markers are demonstrated in Figure 3.

The higher the number of markers, the better the classification performance [ 20 ]. This trend is apparent with any number of pooled data. To provide a real-life scenario, we mimicked datasets of human studies and animal in this case mice or rats experiments.

The animal datasets were simulated with a smaller sample size and smaller variance compared to the human scenario see Section 3 , reflecting properties of real-world data [ 28 , 35 ]. For instance, mice experiments are generally conducted with smaller sample sizes.

The variability in mice is smaller than in human settings due to in-bred and genetic homogeneity of populations as well as means to standardize and control experimental conditions e. The effects of pooling samples in the animal scenario are shown in Figure 4. In general, the trends of the animal study simulations Figure 4 are similar to the human scenario Figure 1 , where a larger pool size causes higher error rates for classifiers.

The differences between classifier performances are also larger for bigger numbers of mocked markers in datasets. However, the classifiers produce increased misclassification rates compared to the human scenario despite the lower variance in the animal datasets. The lower variability is compromised by the effect of the sample size. We have investigated the performance of classifiers in the animal study scenario with the same sample size as in the human setting.

As expected, the classifiers in the animal scenario outperform the ones in the human setting Figure 5. In this work, we provide a systematic evaluation of pooling designs on the discriminating ability of classifiers. The results highlight that pooling strategies generally lead to higher error rates of classifiers.

Misclassification rates are likely to increase with pool sizes in a linear pattern, not exponentially. Moreover, with datasets having small number of makers, there is no statistically significant difference of the performance of classifiers between some pairs of pool sizes. Furthermore, a staged approach might also be considered where first a pooling design is used for global profiling of biomarkers in high-dimensional datasets and subsequent model building, followed by qualification steps where individual samples are analyzed and only a subset of biomolecules is targeted for analysis.

This comparative study motivates scientists to consider and balance pros and cons of various designs prior to the execution of biomarker discovery studies.

Thus, scientists are encouraged to make an informed decision to leverage pooling designs as a valid strategy to compensate for limited amounts of samples or high biological variation, or as a remedy to improve analytical cost and time efficiency. In this study, we applied various classifiers with and without feature selection, and systematically explored the effect of relevant parameters on their performance. In general, all considered designs aim at discovering a subset of features via an algorithm that is subsequently used to predict future outcome, such as the disease status.

SVMs perform better with a radial kernel compared to a linear one. We strongly recommend conducting feature selection prior to classification. It aids in picking important features and reducing noise, which in turn yields better performance of classification algorithms. The results highlight the importance of applying feature selection and pooling design according to the individual properties of the classification algorithms.

As a consequence of the selected data properties in the human and animal study scenarios, sample size influences and compromises the performance of classifiers more than variance of the data in our setting. Therefore, even though data of the animal scenario has lower variance in this study, the classifiers do not perform better than in human datasets.

In future studies, we want to include skewed class distributions and correlations between features in our mock datasets and explore the effect of these properties as well as unbalanced study group sample sizes on the performance of classifiers.

Kusonmano carried out the data simulation, established framework for feature selection and classification, analyzed the results, and drafted the paper. Netzer participated in implementation of the framework for feature selection and classification. Graber guided the design of the study.

Kusonmano, A. Graber, M. Netzer, M. Dehmer, C. Baumgartner, and K. Liedl participated in discussion of the results and coordination to draft the paper. All authors read and approved the final paper. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Zhenqiang Su. Received 18 Dec Accepted 10 Jan Published 30 Apr Abstract A pooling design can be used as a powerful strategy to compensate for limited amounts of samples or high biological variation.

Introduction High-throughput technologies generate large amounts of data, which allow analysis of a broad range of biomolecules in living organisms [ 1 , 2 ]. Article Google Scholar. Int J Infect Dis. Wellcome Open Res. Lancet Infect Dis.

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Epub Apr 2. Download references. We acknowledge all lab personnel, skilled technicians who provided help during the research and preparation of the manuscript. The study was not funded by any funding body. It was performed by Biogenix lab as a part of research. Sally A. You can also search for this author in PubMed Google Scholar. SM — conception, design of work, acquisition, analysis, interpretation of data, drafted and substantively revised the manuscript.

EI — conception, design of work, acquisition, analysis, interpretation of data, drafted and substantively revised the manuscript. BT- conception, design of work, interpretation of data, drafted and substantively revised the manuscript. JT- conception, design of work, interpretation of data, drafted and substantively revised the manuscript. PR- conception, design of work, drafted and substantively revised the manuscript. SG-Acquisition, analysis, interpretation of data, drafted and substantively revised the manuscript.

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