@article{bhat_single_2009,
	title = {Single molecule detection in nanofluidic digital array enables accurate measurement of {DNA} copy number},
	volume = {394},
	issn = {1618-2650},
	doi = {10.1007/s00216-009-2729-5},
	abstract = {Digital polymerase chain reaction (PCR) is a promising technique for estimating target DNA copy number. PCR solution is distributed throughout numerous partitions, and following amplification, target DNA copy number is estimated based on the proportion of partitions containing amplified DNA. Here, we identify approaches for obtaining reliable digital PCR data. Single molecule amplification efficiency was significantly improved following fragmentation of total DNA and bias in copy number estimates reduced by analysis of short intact target DNA fragments. Random and independent distribution of target DNA molecules throughout partitions, which is critical to accurate digital PCR measurement, was demonstrated by spatial distribution analysis. The estimated relative uncertainty for target DNA concentration was under 6\% when analyzing five digital panels comprising 765 partitions each, provided the panels contained an average of 212 to 3,365 template molecules. Partition volume was a major component of this uncertainty estimate. These findings can be applied to other digital PCR studies to improve confidence in such measurements.},
	language = {eng},
	number = {2},
	journal = {Analytical and bioanalytical chemistry},
	author = {Bhat, Somanath and Herrmann, Jan and Armishaw, Paul and Corbisier, Philippe and Emslie, Kerry R},
	month = may,
	year = {2009},
	pmid = {19288230},
	keywords = {Computer Simulation, DNA, Gene Dosage, Microfluidics, Oligonucleotide Array Sequence Analysis},
	pages = {457--467}
}

@article{dube_mathematical_2008,
	title = {Mathematical analysis of copy number variation in a {DNA} sample using digital {PCR} on a nanofluidic device},
	volume = {3},
	issn = {1932-6203},
	doi = {10.1371/journal.pone.0002876},
	abstract = {Copy Number Variations (CNVs) of regions of the human genome have been associated with multiple diseases. We present an algorithm which is mathematically sound and computationally efficient to accurately analyze CNV in a DNA sample utilizing a nanofluidic device, known as the digital array. This numerical algorithm is utilized to compute copy number variation and the associated statistical confidence interval and is based on results from probability theory and statistics. We also provide formulas which can be used as close approximations.},
	language = {eng},
	number = {8},
	journal = {PloS one},
	author = {Dube, Simant and Qin, Jian and Ramakrishnan, Ramesh},
	year = {2008},
	pmid = {18682853 PMCID: PMC2483940},
	keywords = {Algorithms, Confidence Intervals, DNA, Genetic, Genetic Variation, Genome, Human, Humans, Models, Oligonucleotide Array Sequence Analysis, Polymerase Chain Reaction},
	pages = {e2876}
}

@Article{roediger2015r,
  Title                    = {R as an Environment for the Reproducible Analysis of DNA Amplification Experiments},
  Author                   = {R{\"o}diger, Stefan and Burdukiewicz, Micha{\l} and Blagodatskikh, Konstantin and Schierack, Peter},
  Journal                  = {The R Journal},
  Year                     = {2015},
  Number                   = {2},
  Pages                    = {127--150},
  Volume                   = {7}
}

@Article{brown_2001,
  Title                    = {Interval Estimation for a Binomial Proportion},
  Author                   = {Brown, Lawrence D. and Cai, T. Tony and DasGupta, Anirban},
  Journal                  = {Statist. Sci.},
  Year                     = {2001},

  Month                    = {May},
  Number                   = {2},
  Pages                    = {101--133},
  Volume                   = {16},

  Doi                      = {10.1214/ss/1009213286},
  Fjournal                 = {{Statistical Science}},
  Publisher                = {The Institute of Mathematical Statistics},
  Url                      = {http://dx.doi.org/10.1214/ss/1009213286}
}

@Article{dorazio_statistical_2015,
  Title                    = {Statistical {Models} for the {Analysis} and {Design} of {Digital} {Polymerase} {Chain} {Reaction} ({dPCR}) {Experiments}},
  Author                   = {Dorazio, Robert M. and Hunter, Margaret E.},
  Journal                  = {Analytical Chemistry},
  Year                     = {2015},

  Month                    = nov,
  Number                   = {21},
  Pages                    = {10886--10893},
  Volume                   = {87},

  Abstract                 = {Statistical methods for the analysis and design of experiments using digital PCR (dPCR) have received only limited attention and have been misused in many instances. To address this issue and to provide a more general approach to the analysis of dPCR data, we describe a class of statistical models for the analysis and design of experiments that require quantification of nucleic acids. These models are mathematically equivalent to generalized linear models of binomial responses that include a complementary, log?log link function and an offset that is dependent on the dPCR partition volume. These models are both versatile and easy to fit using conventional statistical software. Covariates can be used to specify different sources of variation in nucleic acid concentration, and a model?s parameters can be used to quantify the effects of these covariates. For purposes of illustration, we analyzed dPCR data from different types of experiments, including serial dilution, evaluation of copy number variation, and quantification of gene expression. We also showed how these models can be used to help design dPCR experiments, as in selection of sample sizes needed to achieve desired levels of precision in estimates of nucleic acid concentration or to detect differences in concentration among treatments with prescribed levels of statistical power.},
  Doi                      = {10.1021/acs.analchem.5b02429},
  ISSN                     = {0003-2700},
  Url                      = {http://dx.doi.org/10.1021/acs.analchem.5b02429},
  Urldate                  = {2016-02-29}
}

@article{burdukiewicz_methods_2016,
	title = {Methods of comparing digital {PCR} experiments},
	volume = {28},
	issn = {2214-7535},
	doi = {10.1016/j.bdq.2016.06.004},
	abstract = {The estimated mean copy per partition (λ) is the essential information from a digital PCR (dPCR) experiment because λ can be used to calculate the target concentration in a sample. However, little information is available how to statistically compare dPCR runs of multiple runs or reduplicates. The comparison of λ values from several runs is a multiple comparison problem, which can be solved using the binary structure of dPCR data. We propose and evaluate two novel methods based on Generalized Linear Models (GLM) and Multiple Ratio Tests (MRT) for comparison of digital PCR experiments. We enriched our MRT framework with computation of simultaneous confidence intervals suitable for comparing multiple dPCR runs. The evaluation of both statistical methods support that MRT is faster and more robust for dPCR experiments performed in large scale. Our theoretical results were confirmed by the analysis of dPCR measurements of dilution series. Both methods were implemented in the dpcR package (v. 0.2) for the open source R statistical computing environment.},
	language = {eng},
	number = {9},
	journal = {Biomolecular Detection and Quantification},
	author = {Burdukiewicz, Michał and Rödiger, Stefan and Sobczyk, Piotr and Schierack, Peter and Mackiewicz, Paweł},
	year = {2016},
	pmid = {27551672},
	keywords = {multiple comparison dPCR GLM},
	pages = {14--19}
}

@article{10.2307/1391186,
 ISSN = {10618600},
 URL = {http://www.jstor.org/stable/1391186},
 abstract = {All-pairwise comparisons among a set of t treatments or groups are one of the most frequent tasks in applied statistics. Users of statistical software are accustomed to the familiar lines display, in which treatments that do not differ significantly, are connected by a common line or letter. Availability of the lines display is restricted mainly to the balanced analysis of variance setup. This limited availability is at stark variance with the diversity of statistical methods and models, which call for multiple comparisons. This article describes a general method for graphically representing any set of t(t-1)/2 all-pairwise significance statements (p values) for t treatments by a familiar letter display, which is applicable regardless of the underlying data structure or the statistical method used for comparisons. The method reproduces the familiar lines display in case of the balanced analysis of variance. Its broad applicability is demonstrated using data from an international multienvironment wheat yield trial and from a fish catching survey.},
 author = {Hans-Peter Piepho},
 journal = {Journal of Computational and Graphical Statistics},
 number = {2},
 pages = {456-466},
 publisher = {[American Statistical Association, Taylor & Francis, Ltd., Institute of Mathematical Statistics, Interface Foundation of America]},
 title = {An Algorithm for a Letter-Based Representation of All-Pairwise Comparisons},
 volume = {13},
 year = {2004}
}
