Stochastic Sampling Effects Research Articles

Stochastic sampling effects favor manual over digital contact tracing

Isolation of symptomatic individuals, tracing and testing of their nonsymptomatic contacts are fundamental strategies for mitigating the current COVID-19 pandemic. The breaking of contagion chains relies on two complementary strategies: manual reconstruction of contacts based on interviews and a digital (app-based) privacy-preserving contact tracing. We compare their effectiveness using model parameters tailored to describe SARS-CoV-2 diffusion within the activity-driven model, a general empirically validated framework for network dynamics. We show that, even for equal probability of tracing a contact, manual tracing robustly performs better than the digital protocol, also taking into account the intrinsic delay and limited scalability of the manual procedure. This result is explained in terms of the stochastic sampling occurring during the case-by-case manual reconstruction of contacts, contrasted with the intrinsically prearranged nature of digital tracing, determined by the decision to adopt the app or not by each individual. The better performance of manual tracing is enhanced by heterogeneity in agent behavior: superspreaders not adopting the app are completely invisible to digital contact tracing, while they can be easily traced manually, due to their multiple contacts. We show that this intrinsic difference makes the manual procedure dominant in realistic hybrid protocols.

Comparison of BEAMing and Droplet Digital PCR for Circulating Tumor DNA Analysis.

Circulating tumor DNA (ctDNA) assays are increasingly used for clinical decision-making, but it is unknown how well different assays agree. We aimed to assess the agreement in ctDNA mutation calling between BEAMing (beads, emulsion, amplification, and magnetics) and droplet digital PCR (ddPCR), 2 of the most commonly used digital PCR techniques for detecting mutations in ctDNA. Baseline plasma samples from patients with advanced breast cancer enrolled in the phase 3 PALOMA-3 trial were assessed for ESR1 and PIK3CA mutations in ctDNA with both BEAMing and ddPCR. Concordance between the 2 approaches was assessed, with exploratory analyses to estimate the importance of sampling effects. Of the 521 patients enrolled, 363 had paired baseline ctDNA analysis. ESR1 mutation detection was 24.2% (88/363) for BEAMing and 25.3% (92/363) for ddPCR, with good agreement between the 2 techniques (κ = 0.9l; 95% CI, 0.85-0.95). PIK3CA mutation detection rates were 26.2% (95/363) for BEAMing and 22.9% (83/363) for ddPCR, with good agreement (κ = 0.87; 95% CI, 0.81-0.93). Discordancy was observed for 3.9% patients with ESR1 mutations and 5.0% with PIK3CA mutations. Assessment of individual mutations suggested higher rates of discordancy for less common mutations (P = 0.019). The majority of discordant calls occurred at allele frequency <1%, predominantly resulting from stochastic sampling effects. This large, clinically relevant comparison showed good agreement between BEAMing and ddPCR, suggesting sufficient reproducibility for clinical use. Much of the observed discordancy may be related to sampling effects, potentially explaining many of the differences in the currently available ctDNA literature.

The Polymerase Step Reaction (PSR) Method for Gene and Library Synthesis.

Current gene synthesis methods often incorporate a PCR-amplifying step in order to yield sufficient final product that is detectable and resolvable from multiple off-products. This amplification step can cause stochastic sampling effects that propagate errors during the synthesis and lower the variability when applied towards the construction of randomized libraries. We present the method for polymerase step reaction (PSR), a simple DNA polymerase-based gene synthesis reaction that assembles DNA oligonucleotides in a unidirectional fashion without the need for a PCR-type amplification (Lee et al., BioTechniques 59:163-166, 2015). The PSR method is simple and efficient with little off-product production, undetected stochastic sampling effects, and maximized variability when used to synthesize phage display libraries.

Gene and library synthesis without amplification: polymerase step reaction (PSR).

Current gene synthesis methods often incorporate a PCR amplification step in order to yield final material sufficient for resolution from multiple off-products. These amplification steps can cause stochastic sampling effects that propagate errors in gene synthesis or decrease variability when applied to the construction of randomized libraries. We have developed a simple DNA polymerase-based gene synthesis reaction, polymerase step reaction (PSR), that assembles DNA oligonucleotides in a unidirectional fashion without the need for amplification. We demonstrate that PSR is efficient, with little off-product production, no detectable error propagation, and maximized variability in the synthesis of a phage display library.

Control for stochastic sampling variation and qualitative sequencing error in next generation sequencing

BackgroundClinical implementation of Next-Generation Sequencing (NGS) is challenged by poor control for stochastic sampling, library preparation biases and qualitative sequencing error. To address these challenges we developed and tested two hypotheses. MethodsHypothesis 1: Analytical variation in quantification is predicted by stochastic sampling effects at input of (a) amplifiable nucleic acid target molecules into the library preparation, (b) amplicons from library into sequencer, or (c) both. We derived equations using Monte Carlo simulation to predict assay coefficient of variation (CV) based on these three working models and tested them against NGS data from specimens with well characterized molecule inputs and sequence counts prepared using competitive multiplex-PCR amplicon-based NGS library preparation method comprising synthetic internal standards (IS). Hypothesis 2: Frequencies of technically-derived qualitative sequencing errors (i.e., base substitution, insertion and deletion) observed at each base position in each target native template (NT) are concordant with those observed in respective competitive synthetic IS present in the same reaction. We measured error frequencies at each base position within amplicons from each of 30 target NT, then tested whether they correspond to those within the 30 respective IS. ResultsFor hypothesis 1, the Monte Carlo model derived from both sampling events best predicted CV and explained 74% of observed assay variance. For hypothesis 2, observed frequency and type of sequence variation at each base position within each IS was concordant with that observed in respective NTs (R2=0.93). ConclusionIn targeted NGS, synthetic competitive IS control for stochastic sampling at input of both target into library preparation and of target library product into sequencer, and control for qualitative errors generated during library preparation and sequencing. These controls enable accurate clinical diagnostic reporting of confidence limits and limit of detection for copy number measurement, and of frequency for each actionable mutation.

Abstract 4892: Methods for accurate reporting of confidence intervals in clinical applications of next generation sequencing (NGS)

Abstract BACKGROUND: A challenge to clinical implementation of Next-Generation Sequencing (NGS) is lack of appropriate quality control including control for: a) adequate sample loading, b) variation in target amplification efficiency, and c) variation in loading of prepared NGS specimen onto sequencing platform. Polymerase chain reaction steps used in preparation for NGS can yield a large number of sequencing reads from a small number of starting nucleic acid molecules (e.g. small and/or degraded samples from FNA specimens or FFPE tissue), resulting in large stochastic sampling variation. At present, methods to quantify the analyzable fraction of target nucleic acid are not available or are not suitable for small specimens. As a result, current practice is to rely on sequencing coverage data that may provide false assurance of adequate specimen sampling during molecular analysis, and this has potential to negatively impact patient care. We hypothesize that coefficient of variation (CV) for amplicon-based NGS assay measurements is largely predicted by Poisson (i.e. stochastic) sampling effects for a nucleic acid target at two key points: 1) input molarity (i.e. number of intact molecules) and 2) sequencing coverage (i.e. read counts). METHODS: To test this hypothesis we developed three working models using Monte Carlo simulation and derived equations to predict expected CV based on sequence read count and/or intact molecules mesaured for a given nucleic acid target. These expectation models were tested against empirically derived data from cross-mixtures of two cell lines (H23 and H520) known to be homozygous for opposite alleles at four polymorphic sites (rs769217, rs1042522, rs735482 and rs2298881). Cell lines were mixed to produce limiting inputs of one allele relative to the other, then prepared for NGS such that a broad range of combinations of limiting allelic molecule inputs and/or sequence read counts were observed (46 sets of allelic measurement at all 4 loci). Intra-assay measurement of intact and amplifiable molecules was accomplished using recently described competitive multiplex-PCR amplicon-based NGS specimen preparation (Blomquist, et. al. 2013). RESULTS: Observed CV for measurement at varying input copies and sequencing read counts were compared to expected CV. Actual measured CV was on average 13- and 1.5-fold higher than expected CV based on sequencing reads or molecule input measurements alone, respectively. For the model derived from both sequencing reads and molecule input measurements, expected CV was very close to measured (average [measured CV/expected CV] = 1.01) and explained 74% of observed assay variance. CONCLUSIONS: NGS-based diagnostic tests that do not take into account both input concentration of intact target nucleic acid material and associated sequencing read coverage may not provide accurate reporting of confidence intervals in specimens with limited or degraded material. Citation Format: Erin L. Crawford, Thomas Blomquist, James C. Willey. Methods for accurate reporting of confidence intervals in clinical applications of next generation sequencing (NGS). [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 4892. doi:10.1158/1538-7445.AM2015-4892

Evaluation of the RapidHIT™ 200, an automated human identification system for STR analysis of single source samples.

The RapidHIT™ 200 Human Identification System was evaluated to determine its suitability for STR analysis of single source buccal swabs. Overall, the RapidHIT™ 200 performed as well as our traditional capillary electrophoresis based method in producing useable profile information on a first-pass basis. General observations included 100% concordance with known profile information, consistent instrument performance after two weeks of buccal swab storage, and an absence of contamination in negative controls. When data analysis was performed by the instrument software, 95.3% of the 85 samples in the reproducibility study gave full profiles. Including the 81 full profiles, a total of 2682 alleles were correctly called by the instrument software, or 98.6% of 2720 possible alleles tested. Profile information was generated from as little as 10,000 nucleated cells, with swab collection technique being a major contributing factor to profile quality. The average peak-height-ratio for heterozygote profiles (81%) was comparable to conventional STR analysis, and while a high analytical threshold was required when offline profile analysis was performed (800 RFU), it was proportionally consistent with traditional methods. Stochastic sampling effects were evaluated, and a manageable approach to address limits of detection for homozygote profiles is provided. These results support consideration of the RapidHIT™ 200 as an acceptable alternative to conventional, laboratory based STR analysis for the testing of single source buccal samples, with review of profile information as a requirement until an expert software system is incorporated, and when proper developmental and internal validation studies have been completed.

Stochastic sampling effects in STR typing: Implications for analysis and interpretation.

The analysis and interpretation of forensic STR typing results can become more complicated when reduced template amounts are used for PCR amplification due to increased stochastic effects. These effects are typically observed as reduced heterozygous peak-height balance and increased frequency of undetected alleles (allelic "dropout"). To investigate the origins of these effects, a study was performed using the AmpFlSTR(®) Identifiler Plus(®) and MiniFiler(®) kits to amplify replicates from a dilution series of NIST Human DNA Quantitation Standard (SRM(®) 2372A). The resulting amplicons were resolved and detected on two different genetic analyzer platforms, the Applied Biosystems 3130xL and 3500 analyzers. Results from our study show that the four different STR/genetic analyzer combinations exhibited very similar peak-height ratio statistics when normalized for the amount of template DNA in the PCR. Peak-height ratio statistics were successfully modeled using the Poisson distribution to simulate pre-PCR stochastic sampling of the alleles, confirming earlier explanations that sampling is the primary source for peak-height imbalance in reduced template dilutions. In addition, template-based pre-PCR sampling simulations also successfully predicted allelic dropout frequencies, as modeled by logistic regression methods, for the low-template DNA dilutions. We discuss the possibility that an accurately quantified DNA template might be used to characterize the linear signal response for data collected using different STR kits or genetic analyzer platforms, so as to provide a standardized approach for comparing results obtained from different STR/CE combinations and to aid in validation studies.

STAR CLUSTERS IN M33: UPDATED UBVRI PHOTOMETRY, AGES, METALLICITIES, AND MASSES

The photometric characterization of M33 star clusters is far from complete. In this paper, we present homogeneous $UBVRI$ photometry of 708 star clusters and cluster candidates in M33 based on archival images from the Local Group Galaxies Survey, which covers 0.8 deg$^2$ along the galaxy's major axis. Our photometry includes 387, 563, 616, 580, and 478 objects in the $UBVRI$ bands, respectively, of which 276, 405, 430, 457, and 363 do not have previously published $UBVRI$ photometry. Our photometry is consistent with previous measurements (where available) in all filters. We adopted Sloan Digital Sky Survey $ugriz$ photometry for complementary purposes, as well as Two Micron All-Sky Survey near-infrared $JHK$ photometry where available. We fitted the spectral-energy distributions of 671 star clusters and candidates to derive their ages, metallicities, and masses based on the updated {\sc parsec} simple stellar populations synthesis models. The results of our $\chi^2$ minimization routines show that only 205 of the 671 clusters ($31\%$) are older than 2 Gyr, which represents a much smaller fraction of the cluster population than that in M31 ($56\%$), suggesting that M33 is dominated by young star clusters ($<1$ Gyr). We investigate the mass distributions of the star clusters---both open and globular clusters---in M33, M31, the Milky Way, and the Large Magellanic Cloud. Their mean values are $\log(M_{\rm cl}/M_{\odot})=4.25$, 5.43, 2.72, and 4.18, respectively. The fraction of open to globular clusters is highest in the Milky Way and lowest in M31. Our comparisons of the cluster ages, masses, and metallicities show that our results are basically in agreement with previous studies (where objects in common are available); differences can be traced back to differences in the models adopted, the fitting methods used, and stochastic sampling effects.

Scale dependency in the functional form of the distance decay relationship

We examine a novel mathematical approach which posits that the decay of similarity in community composition with increasing distance (aka distance decay) can be modeled as the sum of individual species joint‐probability vs distance relationships. Our model, supported by analyses of these curves from three datasets (North American breeding birds, North American taiga plants, and tropical forest trees), suggest that when sampling grain is large enough to avoid absences due to stochastic sampling effects, and/or sampling extent is large enough to generate species turnover through the deterministic crossing of environmental and/or geographical range limits, species joint‐probability over increasing distance will generally exhibit exponential decay. However, at small scales where occurrence is driven more by stochastic sampling effects, species joint‐probability curves exhibit a power‐law decay form. Lacking a theoretical prediction of how individual species joint‐probability relationships combine to generate community distance decay, we also performed a meta‐analysis of 26 ecological and 4 human‐system datasets, using non‐linear regression to mean and quantile non‐linear regression at tau = 0.95 for linear, exponential, and power‐law decay forms. These analyses demonstrate that the functional form of community distance decay – as shown by comparison of AIC ranks – is largely determined by observational scale, with power law decay prevailing within domains where the species pool remains constant, while exponential decay prevails at larger scales over which the species pool varies, paralleling the patterns predicted in our mathematical approach.

The NGC 5253 star cluster system – I. Standard modelling and infrared-excess sources

Using high-resolution Hubble Space Telescope data, we reexamine the fundamental properties (ages, masses and extinction values) of the rich star cluster population in the dwarf starburst galaxy NGC 5253. The gain in resolution compared to previous studies is of order a factor of two in both spatial dimensions, while our accessible wavelength range transcends previous studies by incorporation of both near-ultraviolet and near-infrared (IR) passbands. We apply spectral synthesis treatments based on two different simple stellar population model suites to our set of medium-, broad-band and H-alpha images to gain an improved physical understanding of the IR-excess flux found for a subset of young clusters (30 of 149). With the caveat that our models are based on fully sampled stellar mass functions, the NGC 5253 cluster population is dominated by a significant number of relatively low-mass (M_cl <= a few 10^4 Msun) objects with ages ranging from a few x 10^6 to a few x 10^7 yr, which is in excellent agreement with the starburst age of the host galaxy. The IR-excess clusters are almost all found in this young age range and have masses of up to a few x 10^4 Msun. The IR excess in the relatively low-mass NGC 5253 clusters is most likely caused by a combination of stochastic sampling effects and colour variations due to the presence of either luminous red or pre-main-sequence stars. We also find a small number of intermediate-age (~ 1 Gyr-old), ~10^5 Msun clusters, as well as up to a dozen massive, ~10 Gyr-old globular clusters. Their presence supports the notion that NGC 5253 is a very active galaxy that has undergone multiple episodes of star cluster formation.

Relationship between iron-meteorite composition and size: Compositional distribution of irons from North Africa

During the past three decades many iron meteorites have been collected from the deserts of North Africa. Almost all are now characterized, and the distribution among classes is found to be very different from those that were in museums prior to the collection of meteorites from hot and cold (Antarctica) deserts. Similar to the iron meteorites from Antarctica, the irons from Northwest Africa include a high fraction of ungrouped irons and of minor subgroups of group IAB. The different distribution is attributed to the small median size of the desert meteorites (∼1.3 kg in North African irons, ∼30 kg in non-desert irons). It appears that a sizable fraction of these small (several centimeter) masses constitute melt pockets produced by impacts in chondritic regoliths; they were never part of a large (meter-to-kilometer) magma bodies. As a result, a meter-size fragment ejected from the regolith of the asteroid may contain several of these small metallic masses. It may be that such stochastic sampling effects enhanced the fraction of IAB-sHL irons among the irons from Northwest Africa. The variety observed in small meteoroids is also enhanced because (relative to large) small fragments are more efficiently ejected from asteroids and because the orbital parameters of small meteoroids are more strongly affected by collisions and drag effects, they evolve to have Earth-crossing perihelia more rapidly than large meteoroids; as a result, the set of small meteoroids tends to sample a larger number of parent asteroids than does the set of larger meteoroids.

Low copy number typing has yet to achieve “general acceptance”

When processing a small number of starting DNA templates during the PCR, exaggerated stochastic sampling effects will occur, and because of increased sensitivity of detection there is a concomitant increased risk of observing contamination. Caution should be taken with using LCN typing and there should be awareness of the pitfalls that have been encountered by some users of LCN typing. The methodology does not yield reliable results; therefore interpretation strategies have been developed in an attempt to overcome the non-reproducibility of LCN typing. It is troubling that the LCN protocols that are available are scant and leave most of the interpretation to the discretion of the analyst. There is substantial evidence that the interpretation by practitioners often is not based on the results of validation studies and is steeped in practices of bias. In addition, no generally accepted approach(es) to statistical analyses and the values to account for the uncertainty associated with the stochastic phenomena, such as allele drop out, are described.

Validity of low copy number typing and applications to forensic science.

Low copy number (LCN) typing, particularly for current short tandem repeat (STR) typing, refers to the analysis of any sample that contains less than 200 pg of template DNA. Generally, LCN typing simply can be defined as the analysis of any DNA sample where the results are below the stochastic threshold for reliable interpretation. There are a number of methodologies to increase sensitivity of detection to enable LCN typing. These approaches encompass modifications during the polymerase chain reaction (PCR) and/or post-PCR manipulations. Regardless of the manipulations, when processing a small number of starting templates during the PCR exaggerated stochastic sampling effects will occur. The result is that several phenomena can occur: a substantial imbalance of 2 alleles at a given heterozygous locus, allelic dropout, or increased stutter. With increased sensitivity of detection there is a concomitant increased risk of contamination. Recently, a commission reviewed LCN typing and found it to be "robust" and "fit for purpose." Because LCN analysis by its nature is not reproducible, it cannot be considered as robust as that associated with conventional DNA typing. The findings of the commission seem inconsistent with the nature of LCN typing. While LCN typing is appropriate for identification of missing persons and human remains and for developing investigative leads, caution should be taken with its use in other endeavors until developments are made that overcome the vagaries of LCN typing. A more in-depth evaluation by the greater scientific community is warranted. The issues to consider include: training and education, evidence handling and collection procedures, the application or purpose for which the LCN result will be used, the reliability of current LCN methods, replicate analyses, interpretation and uncertainty, report writing, validation requirements, and alternate methodologies for better performance.

An assessment of broad-band optical colours as age indicators for star clusters

We present an empirical assessment of the use of broad-band optical colours as age indicators for unresolved extragalactic clusters and investigate stochastic sampling effects on integrated colours. We use the integrated properties of Galactic open clusters (OCs) as models for unresolved extragalactic clusters. The population synthesis code STARBURST99 (SB99) and four optical colours were used to estimate how well we can recover the ages of 62 well-studied Galactic OCs with published ages. We provide a method for estimating the ages of unresolved clusters and for reliably determining the uncertainties in the age estimates. Our results support earlier conclusions based on comparisons to synthetic clusters, namely the (U - B) colour is critical to the estimation of the ages of star-forming regions. We compare the observed optical colours with those obtained from SB99 using the published ages and get good agreement. The scatter in the (B - V) observed - (B - V) model is larger for lower luminosity clusters, perhaps due to stochastic effects.

Quantifying Change Through Time in Spider Assemblages: Sampling Methods, Indices and Sources of Error

Using a sample dataset from six sites in the Southern Appalachian mountains in the United States, I evaluate the usefulness of diversity indices and similarity/difference indices for monitoring the changes in spider (Order Araneae) assemblages through time. The Shannon index, Brillouin index, Simpson's index and Margalef's index were correlated with each other and were able to detect successional changes in two old clear-cuts as well as disturbance to a Beech gap forest possibly due to Beech Bark Disease. Turnover, Bray-Curtis similarity, and Morisita-Horn similarity also detected successional differences between the forest types and indicated the short-term and long-term changes in a mature forest stand. Seasonal changes (early to late summer) in spider communities were consistently higher than yearly changes. I identify and discuss the implications of various sources of error that will adversely affect the accuracy and efficiency of a monitoring protocol: sensitivity of indices to sample size, sampler bias, inclusion of juveniles, taxonomic uncertainty and stochastic sampling effects. Although gross trends are still apparent in the sample data regardless of these errors, more subtle changes may be obscured. It is these subtle trends which may be more useful to managers attempting to identify disturbance before irreversible damage occurs.