Consider using the [Rules][1] module (together with `Rules Scheduler`, a sub-module of it), as explained in the 3 steps below.

### Step 1: Create a field to store the appointment date

Add a field to the "user" entity with machine name (say) field_next_appointment. Allow only 1 date (the store the "next" appointment), but don't make it required.

### Step 2: Create a Rules "Component"

Here is the Rules **Component** to be created (in Rules export format, just import it in your own environment via copy-paste):

    { "rules_send_email_notification" : {
        "LABEL" : "Send eMail notification",
        "PLUGIN" : "action set",
        "OWNER" : "rules",
        "REQUIRES" : [ "rules" ],
        "USES VARIABLES" : { "user_to_notify" : { "label" : "User to be notified", "type" : "user" } },
        "ACTION SET" : [
          { "mail" : {
              "to" : [ "user-to-notify:mail" ],
              "subject" : "Friendly reminder about your upcoming event",
              "message" : "This is a reminder about the upcoming event that you have an upcoming event on [user-to-notify:field_next_appointment] ...",
              "from" : "[site:mail]",
              "language" : [ "" ]
            }
          }
        ]
      }
    }

Obviously, the ***Subject*** and ***Content*** of the eMail may need review / tuning, while you might also want to use some other ***From*** eMail ID.

### Step 3: Create a "Rule" using the Rules Component

Here is the **Rules** to be created (in Rules export format, just import it in your own environment via copy-paste):

    { "rules_on_new_user_event_registration" : {
        "LABEL" : "On new user event registration",
        "PLUGIN" : "reaction rule",
        "OWNER" : "rules",
        "REQUIRES" : [ "rules", "rules_scheduler" ],
        "ON" : { "user_update" : [] },
        "IF" : [
          { "entity_has_field" : { "entity" : [ "account" ], "field" : "field_next_appointment" } }
        ],
        "DO" : [
          { "schedule_delete" : {
              "component" : "rules_send_email_notification",
              "task" : "[account:name]"
            }
          },
          { "schedule" : {
              "component" : "rules_send_email_notification",
              "date" : {
                "select" : "account:field-next-appointment",
                "date_offset" : { "value" : 259200 }
              },
              "identifier" : "[account:name]",
              "param_user_to_notify" : [ "account" ]
            }
          }
        ]
      }
    }

Note that this rule above refers to the Rules Component from the previous step.

The ***date_offset*** (=259200) corresponds to "7 days in advance", which may need review / tuning. Also note that `schedule_delete` part of it to ensure that previously "scheduled" reminders get removed when updating the data field.

If needed, you could also use the [Field Permissions][2] module to set field-level permissions to edit, view and create fields on any entity.

**Note**: [Using Rules to send an email X days after a user registers][3] also contains quite some details that may help you.

  [1]: https://www.drupal.org/project/rules
  [2]: https://www.drupal.org/project/field_permissions
  [3]: https://groups.drupal.org/node/62048