Omit the curly braces:

var Person = {
    name:  'John', 
    age:   21, 
    alive: true,
    siblings: [
        Andrew,
        {
            name:  'Christine',
            age:   19,
            alive: true
        }
    ]    
}

Andrew is a reference to a JavaScript object. The curly brace notation - { foo: 1 } - is an object literal. To use a variable instead of a literal, you omit the entire literal syntax, including the curly braces.

Note that neither of these is JSON or a "JSON object". JSON is a string that happens to match JavaScript Object literal syntax. Once a JSON string has been parsed, it is a JavaScript object, not a JSON object.

For example, this is valid JavaScript, but not valid JSON:

var Person = {
    name: "John",
    birthDate: new Date(1980, 0, 1),
    speak: function(){ return "hello"; },
    siblings: [
        Andrew,
        Christine
    ];
}

JSON cannot instantiate objects such as new Date(), JSON cannot have a function as a member, and JSON cannot reference external objects such as Andrew or Christine.