Hide a particular radio box item in a set
To remove the entire field on the form, you can definitely do something like this

function YOURMODULE_form_alter(&amp;$form, &amp;$form_state, $form_id) {

  if ($form_id == "form_id_for_form_you_want_to_modify") {
    if (isset($form["field_you_want_to_remove"])) {
      unset($form["field_you_want_to_remove"]);
    }

  }

  return $form;
}


To change or remove a specific option on the field you can access and alter it with $form['field_your_field']['und']['#options'] 

(note: If your site is multilingual, you'll need to alter more than just ['und']. In this case ['und'] means undefined language code).

You can also alter the field type with:

$form['field_your_field']['#type'] = 'checkboxes';


It all depends on what you're trying to accomplish.