Relevant: I have personally carried out a large number of LED-years of testing, operating numerous strings of LEDs in series for many months each and monitoring light output change with time.
It is common for LED light output to increase during the early stages of their life, in some cases. What you are seeing is completely usual behaviour.
Light output and Vf (LED forward voltage may not be well correlated here)
While Andy's explanation about changing Vf with aging MAY be true and may even be the predominant affect that you are seeing, I would expect that variation in brightness with aging would explain what is being seen.
Factors of relevance to aging include:
Whether the LEDs are all nominally the same or differ in batch or model or manufacturer.
Whether the LEDs are run near or above or well above or well below their current and power ratings
What temperature they are operated at, whether they are heatsunk and whether they all experience equal cooling and ambient conditions.
If they ar all the same and treated the same way then it would be less usual to see significant differences in aging BUT what you are seeing is within the range of normal.
If they are different products or batches or if some are more exposed to cooling or they are on a heatsink with a temperature gradient, then differences would be expected.
In my testing I used a simple constant current supply per string (using one LM317 and one resistor). This is easy, not very expensive and removes the sort of uncertainty that you now have. All LEDs were nominally identical I also had a reference LED in the string which was shorted during normal operation and allowed to operate during testing. As the string was constant current driven, adding or removing the reference LED made no difference to the operation of the other LEDs but gave a sanity check on current constantness, instrumentation and measurement variations and measurement techniques.
Getting repeatable measurements between LEDs and between sampling periods requires careful design and operation. I made a sampling cone that seated very repeatedly over each LED fixed permanently to a light meter head. The reference LED provided a check on method etc.
Introducing the LED into an averaging sphere would work if you have such.
Lifetime depends on current and temperature independently. While the two are related thermally via power and heat sinking and ..., LEDS at the same temperature and varying current age differently. LEDs at the same current and differing temperatures age differently. Philips has some good material on this sunder Lumen maintenance.
Some real LEDs out to 300 hours:
This is for 60 mA rated LEDs run at 40 mA.
Look half reasonable.
Same LEDs run at 60 mA.
Result was similar at 40 mA but slower.
Red line is ~= manufacturer's claim.