Harvard has an acceptance rate of around 11% so getting in requires just more than a good GMAT, referees and essay. While the greatest number of applicants are taken from the 1st round that is when the greatest number of applications are considered. I always advise students to go for 1st round but equally I have got students in at the 3rd round and in my view if you meet the criteria and your application is strong you will get an interview. Age is not a factor if you have met the years of experience requirement. For the 2018 class the statistics are 934 enrolled MBAs, 9759 applications, admit of 11%, GMAT middle 80% 690 - 760; median 730; GPA 3.67/4.0. Harvard look for a diverse student body and are looking for candidates that display leadership, are engaged actively with the community, are eager to share their experiences and are ambitious. It is key that all these come out in the essay and also in your referees comments.If they haven’t then you are not likely to get to even the interview stage. How the application is presented is critical and this is often where professional help is vital to get things right. Your GMAT appears to be in the 750 - 800 range; I cannot ascertain what your years of experience are but HBS, unless you are a rae student, require a minimum of 4 years experience. The undergraduate MBBS and Masters of Surgery would not be deemed to be years of experience so you may not have met this basic criteria. I would advise getting expert advice on your eligibility and assitance with presenting the application that meets all the criteria. It is a very competitive world for the entry into the MBA and having specialist advice is more and more important today if you want to get into the elite MBAs.