Abstract: Techniques for construction of internal controls for improved accuracy and sensitivity of DNA testing include obtaining first data and determining weights over real numbers for a normalization function in less than a day. The first data indicates a measured amount of reference sequences for nucleic acids from training samples. The reference sequences include a target, for which an abundance is indicative of a condition of interest, and covariates not correlated with the condition of interest. The normalization function involves a sum of abundances of the covariates, as internal controls, each multiplied by a corresponding one of the weights. The weights are determined based on minimizing variance of a Taylor expansion of a ratio of a measured amount of the target divided by a value of the normalization function evaluated with measured amounts of the covariates over a portion of the first data in which the condition is absent.

Abstract: Techniques for measuring abundances of sequences includes obtaining first data that indicates a target sequence at a plurality of loci, wherein the target sequence comprises a plurality of bins of loci for which a relative abundance is indicative of a condition of interest. Second data is determined that indicates alignment with the target sequence of reads of DNA fragments in a sample from the subject. Third data is determined that indicates locus dependent observed variations in abundance. A raw count Hj of reads is determined that start at each locus j; and, a copy number of a first bin is determined based on a sum over all loci in the first bin of expected counts for each partition weighted by the locus dependent observed variations. Output data that indicates condition of the subject based at least in part on the copy number of the first bin is presented.

Abstract: Some techniques for compensating noise in nucleotide sequencing data include smoothing data for a first reference sequence based on amounts of a subset of reference sequences. An amount of each reference sequence of the subset is multiplied by a corresponding smoothing factor for the reference sequence. The smoothing factor for the reference sequence is based on a spread of the amounts of the reference sequence in the training data. Some techniques include applying a hidden Markov model in which hidden states represent normal condition and a condition of interest at each of multiple pairs of complementary fractions of the sample exhibiting the condition. Transitions from a non-normal condition at a first fraction are confined to states at the first fraction. The normal condition at the first fraction can transition to a state of a different fraction only if the different state represents the normal condition at a complementary fraction.

Abstract: Techniques for automated determination or correction of count bias are based on probability of fraction fragment size for a particular fractions, such as a minority fraction contributed to a sample by fetal or tumor DNA. The techniques include determining a probability density function of fragment sizes for a particular fractional component of the sample; and determining a fraction f of the sample associated with the particular fractional component. A raw count of reads that start at each locus in the target sequence is determined for each fragment i of size si. A corrected count is determined by multiplying the raw count for each fragment i with a weighting factor ci that depends on the fraction f and the probability density function value for the fragment size si. The corrected count is used for determining a condition of interest in the particular fractional component.

Abstract: Techniques for construction of internal controls for improved accuracy and sensitivity of DNA testing include obtaining first data and determining weights over real numbers for a normalization function in less than a day. The first data indicates a measured amount of reference sequences for nucleic acids from training samples. The reference sequences include a target, for which an abundance is indicative of a condition of interest, and covariates not correlated with the condition of interest. The normalization function involves a sum of abundances of the covariates, as internal controls, each multiplied by a corresponding one of the weights. The weights are determined based on minimizing variance of a Taylor expansion of a ratio of a measured amount of the target divided by a value of the normalization function evaluated with measured amounts of the covariates over a portion of the first data in which the condition is absent.