That depends a bit on what you mean by Roman 'Empire'.

If you mean the time span from roughly the first century AD to the middle of the fifth (when Emperors ruled), the answer can mostly be found in that same new imperial structure. Initially, many of the social and political structures of the Roman Republic continued to exist and powerful families or factions were still able to hold impressive amounts of power and influence, even without direct support from the Emperor of his household. However, this quickly changed during the first two centuries of the Imperial era. Simply put, it became impossible to hold any important office or position (and therefor to advance in social standing or to have any influence) without somehow gaining the favour of the Imperial court.

This new political system centered around the court also meant that families or individuals who were not part of the traditional republican system (for example because they were relatively low born or not as wealthy) could quickly gain in standing and amass serious influence, simply by being liked by the Emperor. The gradual change towards an imperial monarchy undermined the traditional Roman system of power, social advancement and influence. It was no longer the nobility who made the rules about who held power, but the Emperor.

However, it should be noted that even in the first century BC, when the Roman Republic started to transform into the Empire, the status of Patrician held very little actual influence anymore. While it is true that some of the oldest and most powerful families of that time were of patrician origin, many other powerful factions were of plebeian background, yet at least as rich and as powerful. It simply did not matter anymore near the end of the Republic whether families were patrician or plebeian. If a family had a long history of public service and high social status they could be just as much a part of the nobility. Vice versa, many families which were originally of patrician descent fell into poverty and ruin. The Conflict of the Orders between patricians and plebeian ended in the third century BC and with it any actual distinction between the two classes. The social and political scene adapted to include wealthy plebeian and found other means to exclude the less influental families from power.

A great work on the change from the Roman Republic to the Empire and the shift in the political structure is The Roman Revolution by Ronald Syme.