setTimeout() inside JavaScript Class using "this"

You can do this:

 var that = this;
 setTimeout(function () {
     that.doStuff();
 }, 4000);

You can also bind for more succinct code (as originally pointed out by @Raynos):

setTimeout(this.doStuff.bind(this), 4000);

bind is a standard library function for exactly this coding pattern (ie capturing this lexically).

You can also bind a function to scope.

setTimeout(this.run.bind(this) ,(1000 * randomNumber(1,5)));

Be warned Function.prototype.bind is ES5

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