diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 59910c2af..2a0c539b3 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -31,6 +31,7 @@ jobs:
     - name: Run pre-commit
       uses: pre-commit/action@v2.0.0
     - name: Check for Sphinx doc warnings
+      if: contains(matrix.python-version, '3.8')
       run: |
         cd docs
         make html SPHINXOPTS="-W --keep-going -n"
diff --git a/docs/conf.py b/docs/conf.py
index 5b36f47e3..9976c2d47 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -94,7 +94,11 @@ def filter(self, record: pylogging.LogRecord) -> bool:
 
 autosummary_generate = True
 
-nitpick_ignore = [("py:class", "sgkit.display.GenotypeDisplay")]
+nitpick_ignore = [
+    ("py:class", "sgkit.display.GenotypeDisplay"),
+    ("py:class", "numpy.typing._dtype_like._DTypeDict"),
+    ("py:class", "numpy.typing._dtype_like._SupportsDType"),
+]
 
 
 # FIXME: Workaround for linking xarray module
diff --git a/setup.cfg b/setup.cfg
index 09fc1876e..47902334a 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -144,6 +144,9 @@ ignore_missing_imports = True
 ignore_missing_imports = True
 [mypy-sgkit.*]
 allow_redefinition = True
+[mypy-sgkit.io.bgen.*]
+# avoid warning on unused ignore for Python 3.8, but not unused for 3.7
+warn_unused_ignores = False
 [mypy-sgkit.*.tests.*]
 disallow_untyped_defs = False
 disallow_untyped_decorators = False
diff --git a/sgkit/io/bgen/bgen_reader.py b/sgkit/io/bgen/bgen_reader.py
index 83c194481..eef2b93ce 100644
--- a/sgkit/io/bgen/bgen_reader.py
+++ b/sgkit/io/bgen/bgen_reader.py
@@ -23,12 +23,20 @@
 import xarray as xr
 import zarr
 from cbgen import bgen_file, bgen_metafile
+from numpy.typing import DTypeLike
 from rechunker import api as rechunker_api
 from xarray import Dataset
 
 from sgkit import create_genotype_dosage_dataset
 from sgkit.io.utils import dataframe_to_dict, encode_contigs
-from sgkit.typing import ArrayLike, DType, PathType
+from sgkit.typing import ArrayLike, PathType
+
+try:
+    # needed to avoid Sphinx forward reference error for DTypeLike
+    # try block is needed since SupportsIndex is in Python 3.7
+    from typing import SupportsIndex  # type: ignore # noqa: F401
+except ImportError:  # pragma: no cover
+    pass
 
 logger = logging.getLogger(__name__)
 
@@ -60,7 +68,7 @@ def __init__(
         self,
         path: PathType,
         metafile_path: Optional[PathType] = None,
-        dtype: DType = "float32",
+        dtype: DTypeLike = "float32",
     ) -> None:
         self.path = Path(path)
         self.metafile_path = (
@@ -202,8 +210,8 @@ def read_bgen(
     chunks: Union[str, int, Tuple[int, int, int]] = "auto",
     lock: bool = False,
     persist: bool = True,
-    contig_dtype: DType = "str",
-    gp_dtype: DType = "float32",
+    contig_dtype: DTypeLike = "str",
+    gp_dtype: DTypeLike = "float32",
 ) -> Dataset:
     """Read BGEN dataset.
 
@@ -394,7 +402,7 @@ def pack_variables(ds: Dataset) -> Dataset:
     return ds
 
 
-def unpack_variables(ds: Dataset, dtype: DType = "float32") -> Dataset:
+def unpack_variables(ds: Dataset, dtype: DTypeLike = "float32") -> Dataset:
     # Restore homozygous reference GP
     gp = ds["call_genotype_probability"].astype(dtype)
     if gp.sizes["genotypes"] != 2:
@@ -423,7 +431,7 @@ def rechunk_bgen(
     chunk_length: int = 10_000,
     chunk_width: int = 1_000,
     compressor: Optional[Any] = zarr.Blosc(cname="zstd", clevel=7, shuffle=2),
-    probability_dtype: Optional[DType] = "uint8",
+    probability_dtype: Optional[DTypeLike] = "uint8",
     max_mem: str = "4GB",
     pack: bool = True,
     tempdir: Optional[PathType] = None,
@@ -533,7 +541,7 @@ def bgen_to_zarr(
     chunk_width: int = 1_000,
     temp_chunk_length: int = 100,
     compressor: Optional[Any] = zarr.Blosc(cname="zstd", clevel=7, shuffle=2),
-    probability_dtype: Optional[DType] = "uint8",
+    probability_dtype: Optional[DTypeLike] = "uint8",
     max_mem: str = "4GB",
     pack: bool = True,
     tempdir: Optional[PathType] = None,
diff --git a/sgkit/io/utils.py b/sgkit/io/utils.py
index f11331c54..e93d50797 100644
--- a/sgkit/io/utils.py
+++ b/sgkit/io/utils.py
@@ -6,13 +6,14 @@
 import numpy as np
 import xarray as xr
 import zarr
+from numpy.typing import DTypeLike
 
-from ..typing import ArrayLike, DType
+from ..typing import ArrayLike
 from ..utils import encode_array, max_str_len
 
 
 def dataframe_to_dict(
-    df: dd.DataFrame, dtype: Optional[Mapping[str, DType]] = None
+    df: dd.DataFrame, dtype: Optional[Mapping[str, DTypeLike]] = None
 ) -> Mapping[str, ArrayLike]:
     """ Convert dask dataframe to dictionary of arrays """
     arrs = {}
@@ -110,7 +111,7 @@ def zarrs_to_dataset(
 def concatenate_and_rechunk(
     zarrs: Sequence[zarr.Array],
     chunks: Optional[Tuple[int, ...]] = None,
-    dtype: DType = None,
+    dtype: DTypeLike = None,
 ) -> da.Array:
     """Perform a concatenate and rechunk operation on a collection of Zarr arrays
     to produce an array with a uniform chunking, suitable for saving as
diff --git a/sgkit/io/vcf/vcf_reader.py b/sgkit/io/vcf/vcf_reader.py
index 183114f37..4fc02d8e0 100644
--- a/sgkit/io/vcf/vcf_reader.py
+++ b/sgkit/io/vcf/vcf_reader.py
@@ -20,13 +20,14 @@
 import numpy as np
 import xarray as xr
 from cyvcf2 import VCF, Variant
+from numpy.typing import DTypeLike
 
 from sgkit.io.utils import zarrs_to_dataset
 from sgkit.io.vcf import partition_into_regions
 from sgkit.io.vcf.utils import build_url, chunks, temporary_directory, url_filename
 from sgkit.io.vcfzarr_reader import vcf_number_to_dimension_and_size
 from sgkit.model import DIM_SAMPLE, DIM_VARIANT, create_genotype_call_dataset
-from sgkit.typing import ArrayLike, DType, PathType
+from sgkit.typing import ArrayLike, PathType
 from sgkit.utils import max_str_len
 
 DEFAULT_MAX_ALT_ALLELES = (
@@ -104,7 +105,7 @@ def _normalize_fields(vcf: VCF, fields: Sequence[str]) -> Sequence[str]:
 
 def _vcf_type_to_numpy_type_and_fill_value(
     vcf_type: str, category: str, key: str
-) -> Tuple[DType, Any]:
+) -> Tuple[DTypeLike, Any]:
     """Convert the VCF Type to a NumPy dtype and fill value."""
     if vcf_type == "Flag":
         return "bool", False
diff --git a/sgkit/stats/ld.py b/sgkit/stats/ld.py
index c91de9f09..5973fe662 100644
--- a/sgkit/stats/ld.py
+++ b/sgkit/stats/ld.py
@@ -8,10 +8,11 @@
 import pandas as pd
 from dask.dataframe import DataFrame
 from numba import njit
+from numpy.typing import DTypeLike
 from xarray import Dataset
 
 from sgkit import variables
-from sgkit.typing import ArrayLike, DType
+from sgkit.typing import ArrayLike
 from sgkit.window import _get_chunked_windows, _sizes_to_start_offsets, has_windows
 
 
@@ -205,8 +206,8 @@ def _ld_matrix_jit(
     chunk_window_stops: ArrayLike,
     abs_chunk_start: int,
     chunk_max_window_start: int,
-    index_dtype: DType,
-    value_dtype: DType,
+    index_dtype: DTypeLike,
+    value_dtype: DTypeLike,
     threshold: float,
     scores: ArrayLike,
 ) -> List[Any]:  # pragma: no cover
@@ -246,7 +247,7 @@ def _ld_matrix_jit(
 
                 if no_threshold or (res >= threshold and np.isfinite(res)):
                     rows.append(
-                        (index_dtype(index), index_dtype(other), value_dtype(res), cmp)
+                        (index_dtype(index), index_dtype(other), value_dtype(res), cmp)  # type: ignore
                     )
 
     return rows
@@ -258,8 +259,8 @@ def _ld_matrix(
     chunk_window_stops: ArrayLike,
     abs_chunk_start: int,
     chunk_max_window_start: int,
-    index_dtype: DType,
-    value_dtype: DType,
+    index_dtype: DTypeLike,
+    value_dtype: DTypeLike,
     threshold: float = np.nan,
     scores: Optional[ArrayLike] = None,
 ) -> ArrayLike:
diff --git a/sgkit/stats/pca.py b/sgkit/stats/pca.py
index 174121d75..707c13c29 100644
--- a/sgkit/stats/pca.py
+++ b/sgkit/stats/pca.py
@@ -4,6 +4,7 @@
 import numpy as np
 import xarray as xr
 from dask_ml.decomposition import TruncatedSVD
+from numpy.typing import DTypeLike
 from sklearn.base import BaseEstimator
 from sklearn.pipeline import Pipeline
 from typing_extensions import Literal
@@ -11,7 +12,7 @@
 
 from sgkit import variables
 
-from ..typing import ArrayLike, DType, RandomStateType
+from ..typing import ArrayLike, RandomStateType
 from ..utils import conditional_merge_datasets
 from .aggregation import count_call_alleles
 from .preprocessing import PattersonScaler
@@ -331,7 +332,7 @@ def _allele_counts(
     ds: Dataset,
     variable: str,
     check_missing: bool = True,
-    dtype: DType = "float32",
+    dtype: DTypeLike = "float32",
 ) -> DataArray:
     if variable not in ds:
         ds = count_call_alternate_alleles(ds)
diff --git a/sgkit/tests/test_preprocessing.py b/sgkit/tests/test_preprocessing.py
index e57e871fb..00defcb81 100644
--- a/sgkit/tests/test_preprocessing.py
+++ b/sgkit/tests/test_preprocessing.py
@@ -5,10 +5,11 @@
 import numpy as np
 import pytest
 import xarray as xr
+from numpy.typing import DTypeLike
 
 import sgkit.stats.preprocessing
 from sgkit import simulate_genotype_call_dataset
-from sgkit.typing import ArrayLike, DType
+from sgkit.typing import ArrayLike
 
 
 def simulate_alternate_allele_counts(
@@ -16,7 +17,7 @@ def simulate_alternate_allele_counts(
     n_sample: int,
     ploidy: int,
     chunks: Any = (10, 10),
-    dtype: DType = "i",
+    dtype: DTypeLike = "i",
     seed: int = 0,
 ) -> ArrayLike:
     rs = da.random.RandomState(seed)
diff --git a/sgkit/typing.py b/sgkit/typing.py
index cf32b0cdb..f86b8df20 100644
--- a/sgkit/typing.py
+++ b/sgkit/typing.py
@@ -1,10 +1,9 @@
 from pathlib import Path
-from typing import Any, Union
+from typing import Union
 
 import dask.array as da
 import numpy as np
 
 ArrayLike = Union[np.ndarray, da.Array]
-DType = Any
 PathType = Union[str, Path]
 RandomStateType = Union[np.random.RandomState, da.random.RandomState, int]
diff --git a/sgkit/utils.py b/sgkit/utils.py
index 46717e859..c560a4f5c 100644
--- a/sgkit/utils.py
+++ b/sgkit/utils.py
@@ -3,15 +3,16 @@
 
 import numpy as np
 from numba import guvectorize
+from numpy.typing import DTypeLike
 from xarray import Dataset
 
 from . import variables
-from .typing import ArrayLike, DType
+from .typing import ArrayLike
 
 
 def check_array_like(
     a: Any,
-    dtype: Union[None, DType, Set[DType]] = None,
+    dtype: Union[None, DTypeLike, Set[DTypeLike]] = None,
     kind: Union[None, str, Set[str]] = None,
     ndim: Union[None, int, Set[int]] = None,
 ) -> None:
diff --git a/sgkit/window.py b/sgkit/window.py
index f0affa8b3..b2e1d1cd8 100644
--- a/sgkit/window.py
+++ b/sgkit/window.py
@@ -2,12 +2,13 @@
 
 import dask.array as da
 import numpy as np
+from numpy.typing import DTypeLike
 from xarray import Dataset
 
 from sgkit.utils import conditional_merge_datasets, create_dataset
 from sgkit.variables import window_contig, window_start, window_stop
 
-from .typing import ArrayLike, DType
+from .typing import ArrayLike
 
 # Window definition (user code)
 
@@ -110,7 +111,7 @@ def moving_statistic(
     statistic: Callable[..., ArrayLike],
     size: int,
     step: int,
-    dtype: DType,
+    dtype: DTypeLike,
     **kwargs: Any,
 ) -> da.Array:
     """A Dask implementation of scikit-allel's moving_statistic function."""
@@ -135,7 +136,7 @@ def window_statistic(
     statistic: Callable[..., ArrayLike],
     window_starts: ArrayLike,
     window_stops: ArrayLike,
-    dtype: DType,
+    dtype: DTypeLike,
     chunks: Any = None,
     new_axis: Union[None, int, Iterable[int]] = None,
     **kwargs: Any,