Remove Item Group from invoice via SuiteScript

We have a custom scheduled script that automatically creates invoices from sales orders.  Sometimes we need to invoice a sales order in separate pieces because some items are not fulfilled immediately. 

The script starts out with

var invoice = nlapiTransformRecord('salesorder', id, 'invoice');

We then remove any unfulfilled (or previously-invoiced) line items, in descending order of line numbers, using

invoice.removeLineItem('item', item.line);

and finally

if (invoice.getLineItemCount('item') != 0)
nlapiSubmitRecord(invoice);

We recently started using item groups and we want to wait for the entire item group to be fulfilled so that it can be invoiced at once.  This means that the script needs to be able to remove the line items corresponding to the item group.