Is getting a PhD position in the US easier with a prior degree from the US? I'm currently an undergrad in Statistics from India, with a keen interest to pursue higher studies in Biostatistics/Bioinformatics. Is getting a PhD position in US easier for students who did their degree in the US, because the admission committees are more likely to trust a degree from the US itself? I intend to complete my Master's here before applying for a PhD.
Yes and no. In principle, the admissions committee doesn’t care where your previous studies were. However it is easier to evaluate qualifications from a university or system that they are familiar with. 

US PhD admissions committees will be more familiar with US universities in general. However, it really depends on the specific institution. Non-US universities like McGill, Oxford, Cambridge, ENS, ETH-Z, Tsinghua, Shanghai Jiao Tong, Sharif, IIT-K, etc. all have established reputations for producing strong students. So a degree from them is probably better for PhD admissions than from a weak US university.

Of course, more important than where you studied is what you individually did! A degree from Stanford won’t help you get into a PhD program if your recommendation letters are terrible.