Hi, maybe this response is abit late.
To host a private group stream on Periscope, you will need to go to your Periscope App on your phone, go to settings, then go to Periscope Producer which will bring you to the Source Connection Information. After configuring the settings OBS using the Source Connection Information, start streaming from OBS, you might come across a few issues or errors that you will need to fix on OBS before the preview link is available. Once you are able to successfully view the Stream Preview, you can change the privacy options on the phone..The default is Public, however you can change to stream privately, to a friend or a group. Once you have selected the privacy choice, you can hit the live option on your phone to start the stream.