MUI with TypeScript MultiSelect Dropdown Not Selecting or Updating Values

I have been trying to build a multiselect dropdown list with checkboxes. The dropdown is being populated by an API call, and I am trying to updated a set of values to write back to the DB. I can get the dropdown to populate, but I cannot seem to get the checkboxes to be checked or set the values.

Here is my Dropdown:

import * as React from 'react';
import axios from 'axios';
import { Checkbox, FormControl, FormHelperText, InputLabel, Select, MenuItem, ListItemText, OutlinedInput } from '@material-ui/core';
import { FormControl, FormHelperText, InputLabel, Select, MenuItem, ListItemText, OutlinedInput } from '@material-ui/core';


export default function dropdownMultiSelect(props) {
  const { label, name, handleInputChange, prompt, value, url } = props;
  const [options, setOptions] = React.useState([]);

  // Fetch Data for Dropdown list
  React.useEffect(() => {
    const fetchData = async () => {
      const res = await axios.get(url);
      setOptions( res.data);
    };
    fetchData();
  }, []); 

  return (
      <FormControl variant='outlined' >
        <InputLabel>{label}</InputLabel>
        <Select
          multiple
          value={value}
          onChange={handleInputChange}
          renderValue={(selected) => selected.map((x) => x.name).join(', ')}
        >
          {options.map((option, id) => (
            <MenuItem
              key={option.id}
              value={option.id}
            >
              <Checkbox checked={value.includes(option.id)} />
              {option.name}
            </MenuItem>
          ))}
        </Select>
      </FormControl>
  );
}

I am using the same onChange event that I have used for the rest of my form to catch the input change and set the values.

OnChange Event:

  const [values, setValues] = React.useState({} as any);
  const [errors, setErrors] = React.useState({} as any);

  const handleInputChange = e => {
    const { name, value } = e.target;
    setValues({
      ...values,
      [name]: value
    });
    if (validateOnChange) { validate({ [name]: value }); }
  };

Can someone please show me what I am doing wrong so I can get this thing working.