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bam2bcf.c
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/* bam2bcf.c -- variant calling.
Copyright (C) 2010-2012 Broad Institute.
Copyright (C) 2012-2022 Genome Research Ltd.
Author: Heng Li <[email protected]>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE. */
#include <math.h>
#include <stdint.h>
#include <assert.h>
#include <float.h>
#include <htslib/hts.h>
#include <htslib/sam.h>
#include <htslib/kstring.h>
#include <htslib/kfunc.h>
#include "bam2bcf.h"
extern void ks_introsort_uint32_t(size_t n, uint32_t a[]);
#define CALL_DEFTHETA 0.83
#define DEF_MAPQ 20
#define CAP_DIST 25
bcf_callaux_t *bcf_call_init(double theta, int min_baseQ, int max_baseQ,
int delta_baseQ)
{
bcf_callaux_t *bca;
if (theta <= 0.) theta = CALL_DEFTHETA;
bca = (bcf_callaux_t*) calloc(1, sizeof(bcf_callaux_t));
bca->capQ = 60;
bca->openQ = 40; bca->extQ = 20; bca->tandemQ = 100;
bca->min_baseQ = min_baseQ;
bca->max_baseQ = max_baseQ;
bca->delta_baseQ = delta_baseQ;
bca->e = errmod_init(1. - theta);
bca->min_frac = 0.002;
bca->min_support = 1;
bca->per_sample_flt = 0;
bca->npos = 100;
bca->ref_pos = (int*) malloc(bca->npos*sizeof(int));
bca->alt_pos = (int*) malloc(bca->npos*sizeof(int));
bca->iref_pos= (int*) malloc(bca->npos*sizeof(int));
bca->ialt_pos= (int*) malloc(bca->npos*sizeof(int));
bca->nqual = 60;
bca->ref_mq = (int*) malloc(bca->nqual*sizeof(int));
bca->alt_mq = (int*) malloc(bca->nqual*sizeof(int));
bca->iref_mq = (int*) malloc(bca->nqual*sizeof(int));
bca->ialt_mq = (int*) malloc(bca->nqual*sizeof(int));
bca->ref_bq = (int*) malloc(bca->nqual*sizeof(int));
bca->alt_bq = (int*) malloc(bca->nqual*sizeof(int));
bca->fwd_mqs = (int*) malloc(bca->nqual*sizeof(int));
bca->rev_mqs = (int*) malloc(bca->nqual*sizeof(int));
return bca;
}
void bcf_call_destroy(bcf_callaux_t *bca)
{
if (bca == 0) return;
errmod_destroy(bca->e);
if (bca->npos) {
free(bca->ref_pos); free(bca->alt_pos);
free(bca->iref_pos); free(bca->ialt_pos);
bca->npos = 0;
}
free(bca->ref_mq); free(bca->alt_mq);
free(bca->iref_mq); free(bca->ialt_mq);
free(bca->ref_bq); free(bca->alt_bq);
free(bca->fwd_mqs); free(bca->rev_mqs);
bca->nqual = 0;
free(bca->bases); free(bca->inscns); free(bca);
}
static int get_aux_nm(bam1_t *rec, int32_t qpos, int is_ref)
{
uint8_t *nm_tag = bam_aux_get(rec, "NM");
if ( !nm_tag ) return -1;
int64_t nm = bam_aux2i(nm_tag);
// Count indels as single events, not as the number of inserted/deleted
// bases (which is what NM does). Add soft clips as mismatches.
int i;
for (i=0; i < rec->core.n_cigar; i++)
{
int val = bam_get_cigar(rec)[i] & BAM_CIGAR_MASK;
if ( val==BAM_CSOFT_CLIP )
{
nm += bam_get_cigar(rec)[i] >> BAM_CIGAR_SHIFT;
}
else if ( val==BAM_CINS || val==BAM_CDEL )
{
val = bam_get_cigar(rec)[i] >> BAM_CIGAR_SHIFT;
if ( val > 1 ) nm -= val - 1;
}
}
// Take into account MNPs, 2% of de novo SNVs appear within 20bp of another de novo SNV
// http://www.genome.org/cgi/doi/10.1101/gr.239756.118
nm -= is_ref ? 1 : 2;
if ( nm < 0 ) nm = 0;
if ( nm >= B2B_N_NM ) nm = B2B_N_NM - 1;
return nm;
}
// position in the sequence with respect to the aligned part of the read
static int get_position(const bam_pileup1_t *p, int *len,
int *sc_len, int *sc_dist) {
int i, j, edist = p->qpos + 1;
int sc_left = 0, sc_right = 0;
int sc_left_dist = -1, sc_right_dist = -1;
// left end
for (i = 0; i < p->b->core.n_cigar; i++) {
int cig = bam_get_cigar(p->b)[i] & BAM_CIGAR_MASK;
if (cig == BAM_CHARD_CLIP)
continue;
else if (cig == BAM_CSOFT_CLIP)
sc_left += bam_get_cigar(p->b)[i] >> BAM_CIGAR_SHIFT;
else
break;
}
if (sc_left)
sc_left_dist = p->qpos+1 - sc_left;
edist -= sc_left;
// right end
for (j = p->b->core.n_cigar-1; j >= i; j--) {
int cig = bam_get_cigar(p->b)[j] & BAM_CIGAR_MASK;
if (cig == BAM_CHARD_CLIP)
continue;
else if (cig == BAM_CSOFT_CLIP)
sc_right += bam_get_cigar(p->b)[j] >> BAM_CIGAR_SHIFT;
else
break;
}
if (sc_right)
sc_right_dist = p->b->core.l_qseq - sc_right - p->qpos;
// Distance to nearest soft-clips and length of that clip.
if (sc_left_dist >= 0) {
if (sc_right_dist < 0 || sc_left_dist < sc_right_dist) {
*sc_len = sc_left;
*sc_dist = sc_left_dist;
}
} else if (sc_right_dist >= 0) {
*sc_len = sc_right;
*sc_dist = sc_right_dist;
} else {
*sc_len = 0;
*sc_dist = 0;
}
*len = p->b->core.l_qseq - sc_left - sc_right;
return edist;
}
void bcf_callaux_clean(bcf_callaux_t *bca, bcf_call_t *call)
{
memset(bca->ref_pos,0,sizeof(int)*bca->npos);
memset(bca->alt_pos,0,sizeof(int)*bca->npos);
memset(bca->iref_pos,0,sizeof(int)*bca->npos);
memset(bca->ialt_pos,0,sizeof(int)*bca->npos);
memset(bca->ref_mq,0,sizeof(int)*bca->nqual);
memset(bca->alt_mq,0,sizeof(int)*bca->nqual);
memset(bca->iref_mq,0,sizeof(int)*bca->nqual);
memset(bca->ialt_mq,0,sizeof(int)*bca->nqual);
memset(bca->ref_bq,0,sizeof(int)*bca->nqual);
memset(bca->alt_bq,0,sizeof(int)*bca->nqual);
memset(bca->fwd_mqs,0,sizeof(int)*bca->nqual);
memset(bca->rev_mqs,0,sizeof(int)*bca->nqual);
if ( call->ADF ) memset(call->ADF,0,sizeof(int32_t)*(call->n+1)*B2B_MAX_ALLELES);
if ( call->ADR ) memset(call->ADR,0,sizeof(int32_t)*(call->n+1)*B2B_MAX_ALLELES);
if ( call->SCR ) memset(call->SCR,0,sizeof(*call->SCR)*(call->n+1));
if ( call->SCR ) memset(call->SCR,0,sizeof(*call->SCR)*(call->n+1));
if ( bca->fmt_flag&B2B_FMT_NMBZ )
{
memset(call->ref_nm,0,sizeof(*call->ref_nm)*(call->n+1)*B2B_N_NM);
memset(call->alt_nm,0,sizeof(*call->alt_nm)*(call->n+1)*B2B_N_NM);
}
else
{
memset(call->ref_nm,0,sizeof(*call->ref_nm)*B2B_N_NM);
memset(call->alt_nm,0,sizeof(*call->alt_nm)*B2B_N_NM);
}
memset(call->QS,0,sizeof(*call->QS)*call->n*B2B_MAX_ALLELES);
memset(bca->ref_scl, 0, 100*sizeof(int));
memset(bca->alt_scl, 0, 100*sizeof(int));
memset(bca->iref_scl, 0, 100*sizeof(int));
memset(bca->ialt_scl, 0, 100*sizeof(int));
}
/*
Notes:
- Called from bam_plcmd.c by mpileup. Amongst other things, sets the bcf_callret1_t.QS frequencies
which are carried over via bcf_call_combine and bcf_call2bcf to the output BCF as the INFO/QS and FMT/QS annotations.
Later it's used for multiallelic calling by `call -m`, `call -mG` and `+trio-dnm`.
- ref_base is the 4-bit representation of the reference base. It is negative if we are looking at an indel.
*/
/*
* This function is called once for each sample.
* _n is number of pilesups pl contributing reads to this sample
* pl is pointer to array of _n pileups (one pileup per read)
* ref_base is the 4-bit representation of the reference base. It is negative if we are looking at an indel.
* bca is the settings to perform calls across all samples
* r is the returned value of the call
*/
int bcf_call_glfgen(int _n, const bam_pileup1_t *pl, int ref_base, bcf_callaux_t *bca, bcf_callret1_t *r)
{
int i, n, ref4, is_indel, ori_depth = 0;
// clean from previous run
r->ori_depth = 0;
r->mq0 = 0;
memset(r->anno,0,sizeof(double)*16);
memset(r->p,0,sizeof(float)*25);
r->SCR = 0;
if (ref_base >= 0) {
ref4 = seq_nt16_int[ref_base];
is_indel = 0;
} else ref4 = 4, is_indel = 1;
if (_n == 0) return -1;
// enlarge the bases array if necessary
if (bca->max_bases < _n) {
bca->max_bases = _n;
kroundup32(bca->max_bases);
bca->bases = (uint16_t*)realloc(bca->bases, 2 * bca->max_bases);
}
// fill the bases array
double nqual_over_60 = bca->nqual / 60.0;
int ADR_ref_missed[4] = {0};
int ADF_ref_missed[4] = {0};
for (i = n = 0; i < _n; ++i) {
const bam_pileup1_t *p = pl + i;
int q, b, mapQ, baseQ, is_diff, min_dist, seqQ;
if ( bca->fmt_flag&(B2B_INFO_SCR|B2B_FMT_SCR) && PLP_HAS_SOFT_CLIP(p->cd.i) ) r->SCR++;
if (p->is_refskip || (p->b->core.flag&BAM_FUNMAP)) continue;
if (p->is_del && !is_indel) continue;
++ori_depth;
if (is_indel)
{
b = p->aux>>16&0x3f;
seqQ = q = (p->aux & 0xff); // mp2 + builtin indel-bias
if (q < bca->min_baseQ)
{
if (!p->indel && b < 4)
{
if (bam_is_rev(p->b))
ADR_ref_missed[b]++;
else
ADF_ref_missed[b]++;
}
continue;
}
if (p->indel == 0 && (q < _n/2 || _n > 20)) {
// high quality indel calls without p->indel set aren't
// particularly indicative of being a good REF match either,
// at least not in low coverage. So require solid coverage
// before we start utilising such quals.
b = 0;
q = (int)bam_get_qual(p->b)[p->qpos];
seqQ = (3*seqQ + 2*q)/8;
}
if (_n > 20 && seqQ > 40) seqQ = 40;
baseQ = p->aux>>8&0xff;
is_diff = (b != 0);
}
else
{
b = bam_seqi(bam_get_seq(p->b), p->qpos); // base
b = seq_nt16_int[b? b : ref_base]; // b is the 2-bit base
// Lowest of this and neighbour quality values
uint8_t *qual = bam_get_qual(p->b);
q = qual[p->qpos];
if (p->qpos > 0 &&
q > qual[p->qpos-1]+bca->delta_baseQ)
q = qual[p->qpos-1]+bca->delta_baseQ;
if (p->qpos+1 < p->b->core.l_qseq &&
q > qual[p->qpos+1]+bca->delta_baseQ)
q = qual[p->qpos+1]+bca->delta_baseQ;
if (q < bca->min_baseQ) continue;
if (q > bca->max_baseQ) q = bca->max_baseQ;
baseQ = q;
seqQ = 99;
is_diff = (ref4 < 4 && b == ref4)? 0 : 1;
}
mapQ = p->b->core.qual < 255? p->b->core.qual : DEF_MAPQ; // special case for mapQ==255
if ( !mapQ ) r->mq0++;
if (q > seqQ) q = seqQ;
mapQ = mapQ < bca->capQ? mapQ : bca->capQ;
if (q > mapQ) q = mapQ;
if (q > 63) q = 63;
if (q < 4) q = 4; // MQ=0 reads count as BQ=4
bca->bases[n++] = q<<5 | (int)bam_is_rev(p->b)<<4 | b;
// collect annotations
if (b < 4)
{
r->QS[b] += q;
if ( r->ADF )
{
if ( bam_is_rev(p->b) )
r->ADR[b]++;
else
r->ADF[b]++;
}
}
++r->anno[0<<2|is_diff<<1|bam_is_rev(p->b)];
min_dist = p->b->core.l_qseq - 1 - p->qpos;
if (min_dist > p->qpos) min_dist = p->qpos;
if (min_dist > CAP_DIST) min_dist = CAP_DIST;
r->anno[1<<2|is_diff<<1|0] += baseQ;
r->anno[1<<2|is_diff<<1|1] += baseQ * baseQ;
r->anno[2<<2|is_diff<<1|0] += mapQ;
r->anno[2<<2|is_diff<<1|1] += mapQ * mapQ;
r->anno[3<<2|is_diff<<1|0] += min_dist;
r->anno[3<<2|is_diff<<1|1] += min_dist * min_dist;
// collect for bias tests
if ( baseQ > 59 ) baseQ = 59;
if ( mapQ > 59 ) mapQ = 59;
int len, epos = 0, sc_len = 0, sc_dist = 0;
if ( bca->fmt_flag & (B2B_INFO_RPB|B2B_INFO_VDB|B2B_INFO_SCB) )
{
int pos = get_position(p, &len, &sc_len, &sc_dist);
epos = (double)pos/(len+1) * bca->npos;
if (sc_len) {
sc_len = 15.0*sc_len / sc_dist;
if (sc_len > 99) sc_len = 99;
}
}
int imq = mapQ * nqual_over_60;
int ibq = baseQ * nqual_over_60;
int inm = get_aux_nm(p->b,p->qpos,is_diff?0:1);
if ( bam_is_rev(p->b) )
bca->rev_mqs[imq]++;
else
bca->fwd_mqs[imq]++;
if ( !is_diff )
{
bca->ref_pos[epos]++;
bca->ref_bq[ibq]++;
bca->ref_mq[imq]++;
bca->ref_scl[sc_len]++;
if ( inm>=0 )
{
bca->ref_nm[inm]++;
if ( r->ref_nm ) r->ref_nm[inm]++;
}
}
else
{
bca->alt_pos[epos]++;
bca->alt_bq[ibq]++;
bca->alt_mq[imq]++;
bca->alt_scl[sc_len]++;
if ( inm>=0 )
{
bca->alt_nm[inm]++;
if ( r->alt_nm ) r->alt_nm[inm]++;
}
}
}
// Compensate for AD not being counted on low quality REF indel matches.
if ( r->ADF && bca->ambig_reads==B2B_INC_AD0 )
{
for (i=0; i<4; i++)
{
r->ADR[0] += ADR_ref_missed[i];
r->ADF[0] += ADF_ref_missed[i];
}
}
else if ( r->ADF && bca->ambig_reads==B2B_INC_AD )
{
int dp = 0, dp_ambig = 0;
for (i=0; i<4; i++) dp += r->ADR[i];
for (i=0; i<4; i++) dp_ambig += ADR_ref_missed[i];
if ( dp )
for (i=0; i<4; i++) r->ADR[i] += lroundf((float)dp_ambig * r->ADR[i]/dp);
dp = 0, dp_ambig = 0;
for (i=0; i<4; i++) dp += r->ADF[i];
for (i=0; i<4; i++) dp_ambig += ADF_ref_missed[i];
if ( dp )
for (i=0; i<4; i++) r->ADF[i] += lroundf((float)dp_ambig * r->ADF[i]/dp);
}
r->ori_depth = ori_depth;
// glfgen
errmod_cal(bca->e, n, 5, bca->bases, r->p); // calculate PL of each genotype
return n;
}
/*
* calc_vdb() - returns value between zero (most biased) and one (no bias)
* on success, or HUGE_VAL when VDB cannot be calculated because
* of insufficient depth (<2x)
*
* Variant Distance Bias tests if the variant bases are positioned within the
* reads with sufficient randomness. Unlike other tests, it looks only at
* variant reads and therefore gives different kind of information than Read
* Position Bias for instance. VDB was developed for detecting artefacts in
* RNA-seq calls where reads from spliced transcripts span splice site
* boundaries. The current implementation differs somewhat from the original
* version described in supplementary material of PMID:22524474, but the idea
* remains the same. (Here the random variable tested is the average distance
* from the averaged position, not the average pairwise distance.)
*
* For coverage of 2x, the calculation is exact but is approximated for the
* rest. The result is most accurate between 4-200x. For 3x or >200x, the
* reported values are slightly more favourable than those of a true random
* distribution.
*/
double calc_vdb(int *pos, int npos)
{
// Note well: the parameters were obtained by fitting to simulated data of
// 100bp reads. This assumes rescaling to 100bp in bcf_call_glfgen().
const int readlen = 100;
assert( npos==readlen );
#define nparam 15
const float param[nparam][3] = { {3,0.079,18}, {4,0.09,19.8}, {5,0.1,20.5}, {6,0.11,21.5},
{7,0.125,21.6}, {8,0.135,22}, {9,0.14,22.2}, {10,0.153,22.3}, {15,0.19,22.8},
{20,0.22,23.2}, {30,0.26,23.4}, {40,0.29,23.5}, {50,0.35,23.65}, {100,0.5,23.7},
{200,0.7,23.7} };
int i, dp = 0;
float mean_pos = 0, mean_diff = 0;
for (i=0; i<npos; i++)
{
if ( !pos[i] ) continue;
dp += pos[i];
mean_pos += pos[i]*i;
}
if ( dp<2 ) return HUGE_VAL; // one or zero reads can be placed anywhere
mean_pos /= dp;
for (i=0; i<npos; i++)
{
if ( !pos[i] ) continue;
mean_diff += pos[i] * fabs(i - mean_pos);
}
mean_diff /= dp;
int ipos = mean_diff; // tuned for float-to-int implicit conversion
if ( dp==2 )
return (2*readlen-2*(ipos+1)-1)*(ipos+1)/(readlen-1)/(readlen*0.5);
if ( dp>=200 )
i = nparam; // shortcut for big depths
else
{
for (i=0; i<nparam; i++)
if ( param[i][0]>=dp ) break;
}
float pshift, pscale;
if ( i==nparam )
{
// the depth is too high, go with 200x
pscale = param[nparam-1][1];
pshift = param[nparam-1][2];
}
else if ( i>0 && param[i][0]!=dp )
{
// linear interpolation of parameters
pscale = (param[i-1][1] + param[i][1])*0.5;
pshift = (param[i-1][2] + param[i][2])*0.5;
}
else
{
pscale = param[i][1];
pshift = param[i][2];
}
return 0.5*kf_erfc(-(mean_diff-pshift)*pscale);
}
double calc_chisq_bias(int *a, int *b, int n)
{
int na = 0, nb = 0, i, ndf = n;
for (i=0; i<n; i++) na += a[i];
for (i=0; i<n; i++) nb += b[i];
if ( !na || !nb ) return HUGE_VAL;
double chisq = 0;
for (i=0; i<n; i++)
{
if ( !a[i] && !b[i] ) ndf--;
else
{
double tmp = a[i] - b[i];
chisq += tmp*tmp/(a[i]+b[i]);
}
}
/*
kf_gammq: incomplete gamma function Q(a,x) = 1 - P(a,x) = Gamma(a,x)/Gamma(a)
1 if the distributions are identical, 0 if very different
*/
double prob = kf_gammaq(0.5*ndf, 0.5*chisq);
return prob;
}
static double mann_whitney_1947_(int n, int m, int U)
{
if (U<0) return 0;
if (n==0||m==0) return U==0 ? 1 : 0;
return (double)n/(n+m)*mann_whitney_1947_(n-1,m,U-m) + (double)m/(n+m)*mann_whitney_1947_(n,m-1,U);
}
double mann_whitney_1947(int n, int m, int U)
{
#include "mw.h"
assert(n >= 2 && m >= 2);
return (n < 8 && m < 8 && U < 50)
? mw[n-2][m-2][U]
: mann_whitney_1947_(n,m,U);
}
double mann_whitney_1947_cdf(int n, int m, int U)
{
int i;
double sum = 0;
for (i=0; i<=U; i++)
sum += mann_whitney_1947(n,m,i);
return sum;
}
double calc_mwu_bias_cdf(int *a, int *b, int n)
{
int na = 0, nb = 0, i;
double U = 0;
//double ties = 0;
for (i=0; i<n; i++)
{
na += a[i];
U += a[i] * (nb + b[i]*0.5);
nb += b[i];
// if ( a[i] && b[i] )
// {
// double tie = a[i] + b[i];
// ties += (tie*tie-1)*tie;
// }
}
if ( !na || !nb ) return HUGE_VAL;
// Always work with the smaller U
double U_min = ((double)na * nb) - U;
if ( U < U_min ) U_min = U;
if ( na==1 ) return 2.0 * (floor(U_min)+1) / (nb+1);
if ( nb==1 ) return 2.0 * (floor(U_min)+1) / (na+1);
// Normal approximation, very good for na>=8 && nb>=8 and reasonable if na<8 or nb<8
if ( na>=8 || nb>=8 )
{
double mean = ((double)na*nb)*0.5;
// Correction for ties:
// double N = na+nb;
// double var2 = (N*N-1)*N-ties;
// if ( var2==0 ) return 1.0;
// var2 *= ((double)na*nb)/N/(N-1)/12.0;
// No correction for ties:
double var2 = ((double)na*nb)*(na+nb+1)/12.0;
double z = (U_min - mean)/sqrt(2*var2); // z is N(0,1)
return 2.0 - kf_erfc(z); // which is 1 + erf(z)
}
// Exact calculation
double pval = 2*mann_whitney_1947_cdf(na,nb,U_min);
return pval>1 ? 1 : pval;
}
double calc_mwu_bias(int *a, int *b, int n, int left)
{
int na = 0, nb = 0, i;
double U = 0;
// double ties = 0;
for (i=0; i<n; i++)
{
if (!a[i]) {
if (!b[i]) continue;
nb += b[i];
} else if (!b[i]) {
na += a[i];
U += a[i] * nb;
} else {
na += a[i];
U += a[i] * (nb + b[i]*0.5);
nb += b[i];
// double tie = a[i] + b[i];
// ties += (tie*tie-1)*tie;
}
}
if ( !na || !nb ) return HUGE_VAL;
if ( na==1 || nb==1 ) return 1.0; // Flat probability, all U values are equally likely
double mean = ((double)na*nb)*0.5;
if (left && U > mean) return 1; // for MQB which is asymmetrical
if ( na==2 || nb==2 )
{
// Linear approximation
return U>mean ? (2.0*mean-U)/mean : U/mean;
}
// Correction for ties:
// double N = na+nb;
// double var2 = (N*N-1)*N-ties;
// if ( var2==0 ) return 1.0;
// var2 *= ((double)na*nb)/N/(N-1)/12.0;
// No correction for ties:
double var2 = ((double)na*nb)*(na+nb+1)/12.0;
if ( na>=8 || nb>=8 )
{
// Normal approximation, very good for na>=8 && nb>=8 and reasonable if na<8 or nb<8
return exp(-0.5*(U-mean)*(U-mean)/var2);
}
// Exact calculation
return mann_whitney_1947(na,nb,U) * sqrt(2*M_PI*var2);
}
// A Z-score version of the above function.
//
// See "Normal approximation and tie correction" at
// https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test
//
// The Z score is the number of standard deviations above or below the mean
// with 0 being equality of the two distributions and +ve/-ve from there.
//
// This is a more robust score to filter on.
double calc_mwu_biasZ(int *a, int *b, int n, int left_only, int do_Z) {
int i;
int64_t t;
// Optimisation
for (i = 0; i < n; i++)
if (b[i])
break;
int b_empty = (i == n);
// Count equal (e), less-than (l) and greater-than (g) permutations.
int e = 0, l = 0, na = 0, nb = 0;
if (b_empty) {
for (t = 0, i = n-1; i >= 0; i--) {
na += a[i];
t += (a[i]*a[i]-1)*a[i]; // adjustment score for ties
}
} else {
for (t = 0, i = n-1; i >= 0; i--) {
// Combinations of a[i] and b[j] for i==j
e += a[i]*b[i];
// nb is running total of b[i+1]..b[n-1].
// Therefore a[i]*nb is the number of combinations of a[i] and b[j]
// for all i < j.
l += a[i]*nb; // a<b
na += a[i];
nb += b[i];
int p = a[i]+b[i];
t += (p*p-1)*p; // adjustment score for ties
}
}
if (!na || !nb)
return HUGE_VAL;
double U, m;
U = l + e*0.5; // Mann-Whitney U score
m = na*nb / 2.0;
// With ties adjustment
double var2 = (na*nb)/12.0 * ((na+nb+1) - t/(double)((na+nb)*(na+nb-1)));
// var = na*nb*(na+nb+1)/12.0; // simpler; minus tie adjustment
if (var2 <= 0)
return do_Z ? 0 : 1;
if (do_Z) {
// S.D. normalised Z-score
//Z = (U - m - (U-m >= 0 ? 0.5 : -0.5)) / sd; // gatk method?
return (U - m) / sqrt(var2);
}
// Else U score, which can be asymmetric for some data types.
if (left_only && U > m)
return HUGE_VAL; // one-sided, +ve bias is OK, -ve is not.
if (na >= 8 || nb >= 8) {
// Normal approximation, very good for na>=8 && nb>=8 and
// reasonable if na<8 or nb<8
return exp(-0.5*(U-m)*(U-m)/var2);
}
// Exact calculation
if (na==1 || nb == 1)
return mann_whitney_1947_(na, nb, U) * sqrt(2*M_PI*var2);
else
return mann_whitney_1947(na, nb, U) * sqrt(2*M_PI*var2);
}
static inline double logsumexp2(double a, double b)
{
if ( a>b )
return log(1 + exp(b-a)) + a;
else
return log(1 + exp(a-b)) + b;
}
void calc_SegBias(const bcf_callret1_t *bcr, bcf_call_t *call)
{
call->seg_bias = HUGE_VAL;
if ( !bcr ) return;
int nr = call->anno[2] + call->anno[3]; // number of observed non-reference reads
if ( !nr ) return;
int avg_dp = (call->anno[0] + call->anno[1] + nr) / call->n; // average depth
double M = floor((double)nr / avg_dp + 0.5); // an approximate number of variants samples in the population
if ( M>call->n ) M = call->n; // clamp M at the number of samples
else if ( M==0 ) M = 1;
double f = M / 2. / call->n; // allele frequency
double p = (double) nr / call->n; // number of variant reads per sample expected if variant not real (poisson)
double q = (double) nr / M; // number of variant reads per sample expected if variant is real (poisson)
double sum = 0;
const double log2 = log(2.0);
// fprintf(stderr,"M=%.1f p=%e q=%e f=%f dp=%d\n",M,p,q,f,avg_dp);
int i;
for (i=0; i<call->n; i++)
{
int oi = bcr[i].anno[2] + bcr[i].anno[3]; // observed number of non-ref reads
double tmp;
if ( oi )
{
// tmp = log(f) + oi*log(q/p) - q + log(2*(1-f) + f*pow(2,oi)*exp(-q)) + p; // this can under/overflow
tmp = logsumexp2(log(2*(1-f)), log(f) + oi*log2 - q);
tmp += log(f) + oi*log(q/p) - q + p;
}
else
tmp = log(2*f*(1-f)*exp(-q) + f*f*exp(-2*q) + (1-f)*(1-f)) + p;
sum += tmp;
// fprintf(stderr,"oi=%d %e\n", oi,tmp);
}
call->seg_bias = sum;
}
/**
* bcf_call_combine() - sets the PL array and VDB, RPB annotations, finds the top two alleles
* @n: number of samples
* @calls: each sample's calls
* @bca: auxiliary data structure for holding temporary values
* @ref_base: the reference base
* @call: filled with the annotations
*
* Combines calls across the various samples being studied
* 1. For each allele at each base across all samples the quality is summed so
* you end up with a set of quality sums for each allele present 2. The quality
* sums are sorted.
* 3. Using the sorted quality sums we now create the allele ordering array
* A\subN. This is done by doing the following:
* a) If the reference allele is known it always comes first, otherwise N
* comes first.
* b) Then the rest of the alleles are output in descending order of quality
* sum (which we already know the qsum array was sorted). Any allelles with
* qsum 0 will be excluded.
* 4. Using the allele ordering array we create the genotype ordering array.
* In the worst case with an unknown reference this will be: A0/A0 A1/A0 A1/A1
* A2/A0 A2/A1 A2/A2 A3/A0 A3/A1 A3/A2 A3/A3 A4/A0 A4/A1 A4/A2 A4/A3 A4/A4
* 5. The genotype ordering array is then used to extract data from the error
* model 5*5 matrix and is used to produce a Phread likelihood array for each
* sample.
*/
int bcf_call_combine(int n, const bcf_callret1_t *calls, bcf_callaux_t *bca, int ref_base /*4-bit*/, bcf_call_t *call)
{
int ref4, i, j;
float qsum[B2B_MAX_ALLELES] = {0,0,0,0,0};
if (ref_base >= 0) {
call->ori_ref = ref4 = seq_nt16_int[ref_base];
if (ref4 > 4) ref4 = 4;
} else call->ori_ref = -1, ref4 = 0;
// calculate qsum, this is done by summing normalized qsum across all samples,
// to account for differences in coverage
for (i = 0; i < n; ++i)
{
float sum = 0;
for (j = 0; j < 4; ++j) sum += calls[i].QS[j];
if ( sum )
for (j = 0; j < 4; j++) qsum[j] += (float)calls[i].QS[j] / sum;
}
// sort qsum in ascending order (insertion sort)
float *ptr[5], *tmp;
for (i=0; i<5; i++) ptr[i] = &qsum[i];
for (i=1; i<4; i++)
for (j=i; j>0 && *ptr[j] < *ptr[j-1]; j--)
tmp = ptr[j], ptr[j] = ptr[j-1], ptr[j-1] = tmp;
// Set the reference allele and alternative allele(s)
for (i=0; i<5; i++) call->a[i] = -1;
for (i=0; i<B2B_MAX_ALLELES; i++) call->qsum[i] = 0;
call->unseen = -1;
call->a[0] = ref4;
for (i=3, j=1; i>=0; i--) // i: alleles sorted by QS; j, a[j]: output allele ordering
{
int ipos = ptr[i] - qsum; // position in sorted qsum array
if ( ipos==ref4 )
call->qsum[0] = qsum[ipos]; // REF's qsum
else
{
if ( !qsum[ipos] ) break; // qsum is 0, this and consequent alleles are not seen in the pileup
call->qsum[j] = qsum[ipos];
call->a[j++] = ipos;
}
}
if (ref_base >= 0)
{
// for SNPs, find the "unseen" base
if (((ref4 < 4 && j < 4) || (ref4 == 4 && j < 5)) && i >= 0)
call->unseen = j, call->a[j++] = ptr[i] - qsum;
call->n_alleles = j;
}
else
{
call->n_alleles = j;
if (call->n_alleles == 1) return -1; // no reliable supporting read. stop doing anything
}
int has_alt = (call->n_alleles==2 && call->unseen!=-1) ? 0 : 1;
/*
* Set the phread likelihood array (call->PL) This array is 15 entries long
* for each sample because that is size of an upper or lower triangle of a
* worst case 5x5 matrix of possible genotypes. This worst case matrix will
* occur when all 4 possible alleles are present and the reference allele
* is unknown. The sides of the matrix will correspond to the reference
* allele (if known) followed by the alleles present in descending order of
* quality sum
*/
{
int x, g[15], z;
double sum_min = 0.;
x = call->n_alleles * (call->n_alleles + 1) / 2;
// get the possible genotypes
// this is done by creating an ordered list of locations g for call (allele a, allele b) in the genotype likelihood matrix
for (i = z = 0; i < call->n_alleles; ++i) {
for (j = 0; j <= i; ++j) {
g[z++] = call->a[j] * 5 + call->a[i];
}
}
// for each sample calculate the PL
for (i = 0; i < n; ++i)
{
int32_t *PL = call->PL + x * i;
const bcf_callret1_t *r = calls + i;
float min = FLT_MAX;
for (j = 0; j < x; ++j) {
if (min > r->p[g[j]]) min = r->p[g[j]];
}
sum_min += min;
for (j = 0; j < x; ++j) {
int y;
y = (int)(r->p[g[j]] - min + .499);
if (y > 255) y = 255;
PL[j] = y;
}
}
if ( call->DP4 )
{
for (i=0; i<n; i++)
{
call->DP4[4*i] = calls[i].anno[0];
call->DP4[4*i+1] = calls[i].anno[1];
call->DP4[4*i+2] = calls[i].anno[2];
call->DP4[4*i+3] = calls[i].anno[3];
}
}
if ( call->SCR )
{
for (i=0; i<n; i++)
{
call->SCR[0] += calls[i].SCR;
call->SCR[1+i] = calls[i].SCR;
}
}
if ( call->ADF )
{
assert( call->n_alleles<=B2B_MAX_ALLELES ); // this is always true for SNPs and so far for indels as well
// reorder ADR,ADF to match the allele ordering at this site
int32_t tmp[B2B_MAX_ALLELES];
int32_t *adr = call->ADR + B2B_MAX_ALLELES, *adr_out = call->ADR + B2B_MAX_ALLELES;
int32_t *adf = call->ADF + B2B_MAX_ALLELES, *adf_out = call->ADF + B2B_MAX_ALLELES;
int32_t *adr_tot = call->ADR; // the first bin stores total counts per site
int32_t *adf_tot = call->ADF;
for (i=0; i<n; i++)
{
for (j=0; j<call->n_alleles; j++)
{
tmp[j] = adr[ call->a[j] ];
adr_tot[j] += tmp[j];
}
for (j=0; j<call->n_alleles; j++) adr_out[j] = tmp[j];
for (j=0; j<call->n_alleles; j++)
{
tmp[j] = adf[ call->a[j] ];
adf_tot[j] += tmp[j];
}
for (j=0; j<call->n_alleles; j++) adf_out[j] = tmp[j];
adf_out += call->n_alleles;
adr_out += call->n_alleles;
adr += B2B_MAX_ALLELES;
adf += B2B_MAX_ALLELES;
}
}
if ( bca->fmt_flag & B2B_FMT_QS )
{
assert( call->n_alleles<=B2B_MAX_ALLELES ); // this is always true for SNPs and so far for indels as well
// reorder QS to match the allele ordering at this site
int32_t tmp[B2B_MAX_ALLELES];
int32_t *qs = call->QS, *qs_out = call->QS;
for (i=0; i<n; i++)
{
for (j=0; j<call->n_alleles; j++) tmp[j] = qs[ call->a[j] ];
for (j=0; j<call->n_alleles; j++) qs_out[j] = tmp[j] < BCF_MAX_BT_INT32 ? tmp[j] : BCF_MAX_BT_INT32;
qs_out += call->n_alleles;
qs += B2B_MAX_ALLELES;
}
}
// if (ref_base < 0) fprintf(stderr, "%d,%d,%f,%d\n", call->n_alleles, x, sum_min, call->unseen);
call->shift = (int)(sum_min + .499);
}
// combine annotations
memset(call->anno, 0, 16 * sizeof(double));
call->ori_depth = 0;
call->depth = 0;
call->mq0 = 0;
for (i = 0; i < n; ++i) {
call->depth += calls[i].anno[0] + calls[i].anno[1] + calls[i].anno[2] + calls[i].anno[3];
call->ori_depth += calls[i].ori_depth;
call->mq0 += calls[i].mq0;
for (j = 0; j < 16; ++j) call->anno[j] += calls[i].anno[j];
}
// No need to calculate MWU tests when there is no ALT allele, this should speed up things slightly
if ( !has_alt ) return 0;
calc_SegBias(calls, call);
// calc_chisq_bias("XPOS", call->bcf_hdr->id[BCF_DT_CTG][call->tid].key, call->pos, bca->ref_pos, bca->alt_pos, bca->npos);
// calc_chisq_bias("XMQ", call->bcf_hdr->id[BCF_DT_CTG][call->tid].key, call->pos, bca->ref_mq, bca->alt_mq, bca->nqual);
// calc_chisq_bias("XBQ", call->bcf_hdr->id[BCF_DT_CTG][call->tid].key, call->pos, bca->ref_bq, bca->alt_bq, bca->nqual);
if (bca->fmt_flag & B2B_INFO_ZSCORE) {
// U z-normalised as +/- number of standard deviations from mean.
if (call->ori_ref < 0) { // indel
if (bca->fmt_flag & B2B_INFO_RPB)
call->mwu_pos = calc_mwu_biasZ(bca->iref_pos, bca->ialt_pos,
bca->npos, 0, 1);
call->mwu_mq = calc_mwu_biasZ(bca->iref_mq, bca->ialt_mq,
bca->nqual,1,1);
if ( bca->fmt_flag & B2B_INFO_SCB )
call->mwu_sc = calc_mwu_biasZ(bca->iref_scl, bca->ialt_scl,
100, 0,1);
} else {
if (bca->fmt_flag & B2B_INFO_RPB)
call->mwu_pos = calc_mwu_biasZ(bca->ref_pos, bca->alt_pos,
bca->npos, 0, 1);
call->mwu_mq = calc_mwu_biasZ(bca->ref_mq, bca->alt_mq,
bca->nqual,1,1);
call->mwu_bq = calc_mwu_biasZ(bca->ref_bq, bca->alt_bq,
bca->nqual,0,1);
call->mwu_mqs = calc_mwu_biasZ(bca->fwd_mqs, bca->rev_mqs,