In the world of healthcare investing, it's not uncommon to see sectors rise and fall with the tides of the market. But what makes the current situation particularly intriguing is the ASX 200 healthcare index's recent plunge of 27% over six months. This sector rout has left many investors scratching their heads, wondering where the value lies. Personally, I think this is a prime opportunity to delve into the sector and uncover some hidden gems. What makes this particularly fascinating is the diverse range of challenges facing Australian healthcare companies, from currency fluctuations to higher labor and cost pressures. These factors have not only impacted the sector's performance but have also led to some of the largest healthcare shares trading at multi-year lows. In this article, I will explore three ASX 200 healthcare shares that analysts believe are worth buying, despite the sector's current struggles. I will also provide my own interpretation and commentary on why these shares are worth considering, and how they fit into the broader healthcare landscape. From Pro Medicus Ltd to Telix Pharmaceuticals Ltd and Ramsay Health Care Ltd, each of these companies faces unique challenges, but also presents an opportunity for investors to capitalize on the sector's potential. So, let's take a closer look at these three shares and see what makes them worth considering, from a personal perspective.