There is no age to pursue interest but there is definitely some roadblocks for you to get into an analytics field like you want. Let me also clearly state that data science is over abused word used these days. Any thing that has a data and any insights you create is data science. Let me share two perspectives here
You as a candidate - Nothing stops you from learning data science and nothing will stop you from applying the science you can learn on any domains you want to pursue. Your 15 years does not count here unless your 15 years brings in domain value/functional value or your line of work value. In this case ITIS. ITIS is a terrific place per me where analytics can make a huge impact.
In simple terms and in simplest example, in traditional IT services even a simple support team hardly has any time to actually look at a pattern of tickets. Think of change requests you serve everyday/everyweek, yet you will continue to spend more time fixing an P1/P2/ tickets.
Now imagine what can the data tell you. Can you identify patterns which can bring about system change or user change. The data science here we are taking about may look simple operational efficiency, but as you start to apply that domain knowledge you can start building systems and changing the way the system interacts and works. Look at this wipro paper.
Now from an employer perspective
15 years is too high. I am not sure if you can break in to a new domain/new field simply because there are cheaper fresher alternatives available. A fresh engineer will cost 5 times cheaper and will probably be faster in approach thanks to age being against you and the mundanity you have gained due to management line of work.
You are not affordable for these data science start ups. You may find it very difficult to find someone who is ready to take you.
But here are good news:-
Just theoretical knowledge or even great technical skills like say modelling and building apps may get you a job but not a career.
What will though is the ability to relate to the real life usage. The current state is such that there are great data scientists with minimal functional knowledge. They create cluster, create algorithms and make suggestion say sales in Asia will be lower by 2% for next 5 quarters. This probably the functional head already knows purely by his experience, but if you know the domain you will look for ways to help that function head to attack this issue and look at data to actually make useful investment that will help the manager attack the problem. This is just an example.
So relook at your ask, and see how a course in analytics will help you be a analysts in your current field of work.
Unless you have a penchant for creating tools and applications hands on and create something (i mean start up your own) dont get into too much hands on knowledge of this data science. I know PHDs in statistics currently managing teams creating reports and dashboards. ANd there are PHD’s who are expert in their field of data science that they are building models at levels it will take you years to reach.
Data science will help, but try to connect it to your line of work. Thats where you can lead a team of young data scientists to achieve what you want. YOu are no longer a PPT manager but more of an analytical manager trying to solve problems.