libprosic/model/priors/

tumor_normal.rs

use std::f64;

use bio::stats::{LogProb, Prob};
use itertools::Itertools;
use itertools_num::linspace;
use ordered_float::NotNan;

use model::{AlleleFreq, ContinuousAlleleFreqs, DiscreteAlleleFreqs, PairPileup, Variant};

use priors::InfiniteSitesNeutralVariationModel;
use priors::PairModel;

/// Tumor-normal prior model using ploidy, heterozygosity (in normal tissue) and tumor mutation rate
/// per effective cell division.
/// The latter is the quotient mu/beta, with mu being the mutation rate and beta being the fraction
/// of effective cell divisions (both lineages survive). Alone, the parameters are not observable.
/// However, mu/beta can be estimated from e.g. SNV calls. It is the slope of the linear model
/// `y = mu/beta * (x -  1 / fmax)``, with `x` being the reciprocal of the observed allele frequencies
/// and y being the number of observed mutations corresponding to each frequency
/// (see Williams et al. Nature Genetics 2016).
///
/// Based on the Williams model, the tail probability of a somatic allele frequency F > f can be expressed
/// as
/// `Pr(F > f) = M(f) / n = mu/beta (1 / f - 1 / fmax) / n`
/// with `n` being the size of the genome and `fmax` is the expected allele frequency of clonal variants
/// at the beginning of tumor evolution.
/// From this, we can obtain the cumulative distribution function as `Pr(F <= f) = 1 - Pr(F > f)`.
/// Consequently, the density becomes the first derivative, i.e. `Pr(F = f) = - M(f)' / n = mu/beta * 1/n * 1/f²` for f>=fmin
/// with `fmin = sqrt(mu/beta * 1/n)`.
///
/// The prior probability for a germline allele frequency f (e.g. 0.0, 0.5, 1.0) in the tumor is
/// calculated with an `InfiniteSitesNeutralVariationModel`. This is valid since clonal variants
/// come from the underlying normal tissue and Williams model assumes that allele frequencies
/// do not change during tumor evolution (no genetic drift, no selection).
///
/// For the final prior, we consider a given tumor purity and calculate the combined prior
/// for all possible allele frequency combinations satisfying `af = purity * af_tumor + (1-purity) * af_normal`.
pub struct TumorNormalModel {
    pub normal_model: InfiniteSitesNeutralVariationModel,
    effective_mutation_rate: f64,
    deletion_factor: f64,
    insertion_factor: f64,
    genome_size: u64,
    pub allele_freqs_tumor: ContinuousAlleleFreqs,
    pub allele_freqs_normal: DiscreteAlleleFreqs,
    pub grid_points: usize,
    af_min: AlleleFreq,
    ploidy: u32,
}

impl TumorNormalModel {
    /// Create new model.
    ///
    /// # Arguments
    ///
    /// * `ploidy` - the ploidy in the corresponding normal sample (e.g. 2 for diploid)
    /// * `effective_mutation_rate` - the SNV mutation rate per effective cell division in the tumor
    /// * `deletion_factor` - ratio of deletions compared to SNV mutation rate
    /// * `insertion_factor` - ratio of insertions compared to SNV mutation rate
    /// * `genome_size` - the size of the genome
    /// * `heterozygosity` - expected heterozygosity in the corresponding normal
    pub fn new(
        ploidy: u32,
        effective_mutation_rate: f64,
        deletion_factor: f64,
        insertion_factor: f64,
        genome_size: u64,
        heterozygosity: Prob,
    ) -> Self {
        assert!(effective_mutation_rate < genome_size as f64);
        let af_min = AlleleFreq((effective_mutation_rate / genome_size as f64).sqrt());

        TumorNormalModel {
            normal_model: InfiniteSitesNeutralVariationModel::new(1, ploidy, heterozygosity),
            effective_mutation_rate: effective_mutation_rate,
            deletion_factor: deletion_factor,
            insertion_factor: insertion_factor,
            genome_size: genome_size,
            allele_freqs_tumor: ContinuousAlleleFreqs::inclusive(0.0..1.0),
            // TODO make max_amplification parameter (=1) configurable and consider it properly
            // in the normal model.
            allele_freqs_normal: DiscreteAlleleFreqs::feasible(ploidy),
            grid_points: 51,
            af_min: af_min,
            ploidy: ploidy,
        }
    }

    pub fn somatic_prior_prob(&self, af_somatic: AlleleFreq, variant: &Variant) -> LogProb {
        // af_somatic can become negative, meaning that at some point a variant from normal was lost
        // in one cell (LOH!!). Again, the frequency corresponds to time in tumor evolution since the model
        // assumes that all frequencies stay constant. Hence, we can simply take the absolute value
        // of af_somatic here. This is equivalent to calculating
        // af_tumor = af_normal - af_somatic
        // for that case.
        let af_somatic = af_somatic.abs();

        // mu/beta * 1 / (af**2 * n)
        if af_somatic <= *self.af_min {
            return LogProb::ln_one();
        }

        // adjust effective mutation rate by type-specific factor
        let factor = match variant {
            &Variant::Deletion(_) => self.deletion_factor.ln(),
            &Variant::Insertion(_) => self.insertion_factor.ln(),
            &Variant::SNV(_) => 0.0, // no factor for SNVs
            &Variant::None => 0.0,   // no factor for potential homozygous reference sites
        };

        LogProb(
            self.effective_mutation_rate.ln() + factor
                - (2.0 * af_somatic.ln() + (self.genome_size as f64).ln()),
        )
    }

    pub fn normal_prior_prob(&self, af_normal: AlleleFreq, _: &Variant) -> LogProb {
        let m = *af_normal * self.ploidy as f64;
        if relative_eq!(m % 1.0, 0.0) {
            // if m is discrete
            self.normal_model.prior_prob(m.round() as u32)
        } else {
            // invalid allele frequency
            LogProb::ln_zero()
        }
    }
}

impl PairModel<ContinuousAlleleFreqs, DiscreteAlleleFreqs> for TumorNormalModel {
    fn prior_prob(
        &self,
        af_tumor: AlleleFreq,
        af_normal: AlleleFreq,
        variant: &Variant,
    ) -> LogProb {
        // af_tumor = af_normal + af_somatic
        let af_somatic = af_tumor - af_normal;
        let p = self.somatic_prior_prob(af_somatic, variant)
            + self.normal_prior_prob(af_normal, variant);
        assert!(*p <= 0.0);
        p
    }

    fn joint_prob(
        &self,
        af_tumor: &ContinuousAlleleFreqs,
        af_normal: &DiscreteAlleleFreqs,
        pileup: &mut PairPileup<ContinuousAlleleFreqs, DiscreteAlleleFreqs, Self>,
    ) -> LogProb {
        let prob = LogProb::ln_sum_exp(
            &af_normal
                .iter()
                .map(|&af_normal| {
                    let p_tumor: LogProb;
                    {
                        let mut density = |af_tumor| {
                            let af_tumor = AlleleFreq(af_tumor);
                            self.prior_prob(af_tumor, af_normal, &pileup.variant)
                                + pileup.case_likelihood(af_tumor, Some(af_normal))
                        };

                        p_tumor = if af_tumor.start == af_tumor.end {
                            density(*af_tumor.start)
                        } else {
                            LogProb::ln_simpsons_integrate_exp(
                                density,
                                *af_tumor.start,
                                *af_tumor.end,
                                self.grid_points,
                            )
                        };
                    }
                    let p_normal = pileup.control_likelihood(af_normal, None);
                    println!(
                        "prior model probs: af={} {:?} {:?}",
                        af_normal, p_tumor, p_normal
                    );
                    let prob = p_tumor + p_normal;

                    prob
                })
                .collect_vec(),
        );

        prob
    }

    fn marginal_prob(
        &self,
        pileup: &mut PairPileup<ContinuousAlleleFreqs, DiscreteAlleleFreqs, Self>,
    ) -> LogProb {
        let p = self
            .joint_prob(self.allele_freqs().0, self.allele_freqs().1, pileup)
            .ln_add_exp(
                // add prob for allele frequency zero (the density is non-continuous there)
                self.joint_prob(
                    &ContinuousAlleleFreqs::inclusive(0.0..0.0),
                    &DiscreteAlleleFreqs::new(vec![AlleleFreq(0.0)]),
                    pileup,
                ),
            );
        p
    }

    fn map(
        &self,
        pileup: &mut PairPileup<ContinuousAlleleFreqs, DiscreteAlleleFreqs, Self>,
    ) -> (AlleleFreq, AlleleFreq) {
        let af_case = linspace(
            *self.allele_freqs_tumor.start,
            *self.allele_freqs_tumor.end,
            self.grid_points,
        );
        let (_, (map_normal, map_tumor)) = self
            .allele_freqs_normal
            .iter()
            .cartesian_product(af_case)
            .minmax_by_key(|&(&af_normal, af_tumor)| {
                let af_tumor = AlleleFreq(af_tumor);
                let p = self.prior_prob(af_tumor, af_normal, &pileup.variant)
                    + pileup.case_likelihood(af_tumor, Some(af_normal))
                    + pileup.control_likelihood(af_normal, None);
                NotNan::new(*p).expect("posterior probability is NaN")
            })
            .into_option()
            .expect("prior has empty allele frequency spectrum");

        (AlleleFreq(map_tumor), *map_normal)
    }

    fn allele_freqs(&self) -> (&ContinuousAlleleFreqs, &DiscreteAlleleFreqs) {
        (&self.allele_freqs_tumor, &self.allele_freqs_normal)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use bio::stats::{LogProb, Prob};
    use itertools_num::linspace;
    use model::priors::tests::create_obs_vector;
    use model::priors::PairModel;
    use model::{likelihood, AlleleFreq, ContinuousAlleleFreqs, PairPileup, Variant};

    #[test]
    fn print_priors() {
        let variant = Variant::SNV(b'A');
        let model = TumorNormalModel::new(2, 30000.0, 0.5, 0.5, 3e9 as u64, Prob(1.25E-4));
        for af_normal in &[0.0, 0.5, 1.0] {
            println!("af_normal={}:", af_normal);
            print!("[");
            for p in linspace(0.0, 1.0, 20).map(|af_tumor| {
                model.prior_prob(AlleleFreq(af_tumor), AlleleFreq(*af_normal), &variant)
            }) {
                print!("{}, ", p.exp());
            }
            println!("]");
        }
    }

    #[test]
    fn test_tnm_het_zero() {
        let heterozygosity = Prob(0.0); //Prob(1.25E-4);
        let model = TumorNormalModel::new(2, 3000.0, 0.5, 0.5, 3e9 as u64, heterozygosity);

        // tumor and normal both hom ref
        let af_tumor = ContinuousAlleleFreqs::inclusive(0.0..0.0);
        let af_normal = DiscreteAlleleFreqs::new(vec![AlleleFreq(0.0)]);

        let variant = Variant::SNV(b'T');

        let tumor_sample_model = likelihood::LatentVariableModel::new(1.0);
        let normal_sample_model = likelihood::LatentVariableModel::new(1.0);

        let tumor_obs = create_obs_vector(5, 0);
        let normal_obs = create_obs_vector(5, 0);

        let mut pileup = PairPileup::new(
            tumor_obs.clone(),
            normal_obs.clone(),
            variant.clone(),
            &model,
            tumor_sample_model,
            normal_sample_model,
        );
        assert_eq!(
            model.prior_prob(af_tumor.start, af_normal[0], &variant),
            LogProb::ln_one()
        );
        assert_eq!(pileup.joint_prob(&af_tumor, &af_normal), LogProb::ln_one());
        assert_relative_eq!(
            pileup.posterior_prob(&af_tumor, &af_normal).exp(),
            1.0,
            epsilon = 0.008
        );
        assert_eq!(
            pileup.map_allele_freqs(),
            (AlleleFreq(0.0), AlleleFreq(0.0))
        );
    }

    #[test]
    fn test_tnm_het_real() {
        let heterozygosity = Prob(1.25E-4);
        let model = TumorNormalModel::new(2, 3000.0, 0.5, 0.5, 3e9 as u64, heterozygosity);

        // tumor and normal both hom ref
        let af_tumor = ContinuousAlleleFreqs::inclusive(0.0..0.0);
        let af_normal = DiscreteAlleleFreqs::new(vec![AlleleFreq(0.0)]);

        let variant = Variant::SNV(b'T');

        let tumor_sample_model = likelihood::LatentVariableModel::new(1.0);
        let normal_sample_model = likelihood::LatentVariableModel::with_single_sample();

        let tumor_obs = create_obs_vector(5, 0);
        let normal_obs = create_obs_vector(5, 0);

        let mut pileup = PairPileup::new(
            tumor_obs.clone(),
            normal_obs.clone(),
            variant.clone(),
            &model,
            tumor_sample_model,
            normal_sample_model,
        );

        // priors assuming: heterozygosity = 1.25E-4, ploidy = 2
        let normal_prior_prob = 0.9998125;
        println!(
            "TNM.somatic_prior_prob(af_tumor.start = {}): {}",
            af_tumor.start,
            model.somatic_prior_prob(af_tumor.start, &variant).exp()
        );
        assert_eq!(
            model.somatic_prior_prob(af_tumor.start, &variant),
            LogProb::ln_one()
        );
        println!(
            "TNM.normal_prior_prob(af_normal[0] = {}): {}",
            af_normal[0],
            model.normal_prior_prob(af_normal[0], &variant).exp()
        );
        assert_relative_eq!(
            model.normal_prior_prob(af_normal[0], &variant).exp(),
            normal_prior_prob,
            epsilon = 0.000001
        );
        println!(
            "TNM.prior_prob(af_tumor.start = {}, af_normal[0] = {}): {}",
            af_tumor.start,
            af_normal[0],
            model
                .prior_prob(af_tumor.start, af_normal[0], &variant)
                .exp()
        );
        assert_relative_eq!(
            model
                .prior_prob(af_tumor.start, af_normal[0], &variant)
                .exp(),
            normal_prior_prob,
            epsilon = 0.000001
        );
        let aft_full = model.allele_freqs().0;
        let afn_full = model.allele_freqs().1;
        assert_relative_eq!(
            pileup.joint_prob(&af_tumor, &af_normal).exp(),
            normal_prior_prob,
            epsilon = 0.0000001
        );
        println!(
            "pileup.joint_prob(af_tumor, af_normal): {}",
            pileup.joint_prob(&af_tumor, &af_normal).exp()
        );
        println!(
            "pileup.joint_prob(full spectrum): {}",
            pileup.joint_prob(&aft_full, &afn_full).exp()
        );
        println!("pileup.marginal_prob: {}", pileup.marginal_prob().exp());
        println!(
            "pileup.posterior_prob: {}",
            pileup.posterior_prob(&af_tumor, &af_normal).exp()
        );
        assert_relative_eq!(
            pileup.posterior_prob(&af_tumor, &af_normal).exp(),
            0.9933008088509733,
            epsilon = 0.00000001
        );
        assert_eq!(
            pileup.map_allele_freqs(),
            (AlleleFreq(0.0), AlleleFreq(0.0))
        );
    }
}