# Logistic regression burden tests

**URL:** <https://discuss.hail.is/t/logistic-regression-burden-tests/206>\
**Category:** Updates\
**Created:** [May 9, 2017, 1:27pm UTC](https://discuss.hail.is/t/logistic-regression-burden-tests/206 "2017-05-09T13:27:39Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![jbloom](https://yyz2.discourse-cdn.com/flex036/user_avatar/discuss.hail.is/jbloom/32/109_2.png) [@jbloom](https://discuss.hail.is/u/jbloom)\
**Post date:** [September 7, 2018, 10:50pm UTC](https://discuss.hail.is/t/logistic-regression-burden-tests/206/3 "2018-09-07T22:50:07Z")

</div>

Hi Enrique,

Regressions in Hail 0.2 are generic, so there are no longer special command for burden tests. Rather, to do logistic gene burden, annotate and group variants by gene to form a gene-by-sample matrix of scores, and then apply logistic regression per gene. Here’s an example that uses the total number minor alleles as a sample’s gene score (for a biallelic dataset with random phenotype and covariates):

```auto
import hail as hl

interval_ht = hl.import_locus_intervals('genes.37.interval_list')

mt = hl.import_vcf('profile.vcf.bgz')
mt = mt.annotate_cols(y = hl.rand_bool(0.5), x1 = hl.rand_norm(), x2 = hl.rand_norm())
mt = hl.variant_qc(mt)
mt = mt.annotate_rows(gene = interval_ht[mt.locus].target)
mt = mt.filter_rows(hl.is_defined(mt.gene))

gene_mt = mt.group_rows_by(mt.gene).aggregate(
    mac = hl.agg.sum(
        hl.cond(mt.variant_qc.AF[1] <= 0.5,
                mt.GT.n_alt_alleles(),
                2 - mt.GT.n_alt_alleles())))

gene_mt = hl.logistic_regression(y=gene_mt.y, x=gene_mt.mac, covariates=[1, gene_mt.x1, gene_mt.x2], test='wald')
gene_mt.logreg.show()

```

Here’s what’s shown:

```auto
+----------+--------------+-----------------------+---------------+----------------+
| gene | logreg.beta | logreg.standard_error | logreg.z_stat | logreg.p_value |
+----------+--------------+-----------------------+---------------+----------------+
| str | float64 | float64 | float64 | float64 |
+----------+--------------+-----------------------+---------------+----------------+
| ATP6V1E1 | 1.69214e-03 | 1.28280e-03 | 1.31910e+00 | 1.87134e-01 |
| CCT8L2 | 4.03789e-02 | 3.46446e-02 | 1.16552e+00 | 2.43808e-01 |
| CECR1 | 1.29431e-03 | 1.82113e-03 | 7.10716e-01 | 4.77260e-01 |
| CECR2 | 4.90592e-04 | 3.88126e-04 | 1.26400e+00 | 2.06230e-01 |
| CECR5 | -2.90466e-04 | 3.41414e-03 | -8.50774e-02 | 9.32200e-01 |
| CECR6 | 7.20520e-03 | 7.78411e-03 | 9.25630e-01 | 3.54638e-01 |
| GAB4 | 3.14315e-03 | 2.69332e-03 | 1.16701e+00 | 2.43205e-01 |
| IL17RA | 3.40054e-03 | 4.98370e-03 | 6.82333e-01 | 4.95028e-01 |
| OR11H1 | -2.85557e-02 | 5.40733e-02 | -5.28093e-01 | 5.97435e-01 |
| POTEH | -6.64950e-03 | 3.76138e-03 | -1.76784e+00 | 7.70884e-02 |
+----------+--------------+-----------------------+---------------+----------------+

+-------------------------+----------------------+---------------------+
| logreg.fit.n_iterations | logreg.fit.converged | logreg.fit.exploded |
+-------------------------+----------------------+---------------------+
| int32 | bool | bool |
+-------------------------+----------------------+---------------------+
| 3 | true | false |
| 3 | true | false |
| 3 | true | false |
| 3 | true | false |
| 2 | true | false |
| 3 | true | false |
| 3 | true | false |
| 3 | true | false |
| 3 | true | false |
| 3 | true | false |
+-------------------------+----------------------+---------------------+
showing top 10 rows

```

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