How to annotate a new "dict" class with TypedDict?

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I have the following classes:

from typing import Any, TypedDict

class RawDict(TypedDict):
    key1: str
    key2: int

class MyDict(dict):
    def __init__(self, data: RawDict) -> None:
        self._validate(data)
        super().__init__(data)

    def _validate(self, data: RawDict) -> None:
        # validate data and raise if invalid

    def some_other_method(self) -> Any:
        # do anything interesting

I would like to be able to annotate every instance of MyDict with the RawDict type. Currently, it results in a typing error (MyPy 0.930):

var: RawDict = MyDict({"key1": "value", "key2": 1})
# error: Incompatible types in assignment (expression has type "MyDict", variable has type "RawDict")

On the other hand, if we annotate it with MyDict, we won’t know the exact types of values in that dict:

var: MyDict = MyDict({"key1": "value", "key2": 1})
var1 = var["key1"]  # recognized as Any
var2 = var["key2"]  # recognized as Any

In my actual implementation, the RawDict type is more complex, e.g. it’s keys are other TypedDicts or lists of TypedDicts.

How can I combine MyDict and RawDict so that my variables “know” about their actual keys and available methods?

I tried inheriting class MyDict(RawDict):, but it made MyPy fail with error: Invalid statement in TypedDict definition; expected "field_name: field_type".

I’m using Python 3.8.