It's maybe more "parallel" than "ahead", but one major area the Soviet Union pursued that the West mostly ignored was bacteriophage therapy. Phage therapy is the injection of viruses into the body that target and kill bacteria.

In the Soviet Union, availability of modern broad-specturm antibiotics like penicillin was limited which necessitated an alternative. Phages can be more effective with fewer downsides as they only kill the disease-causing bacteria, not beneficial "good" bacteria. The downside is they are difficult to target because they only kill one specific strain of bacteria. It's possible a given disease could be caused by 10 slightly different strains of bacteria. For phage therapy your doctor would have to run tests and determine the precise strain and administer the correct phage. In the West they would just give you an antibiotic that kills all 10 and send you on your way.

With the recent discoveries of antibiotic resistant bacteria and increased access to former Soviet states there is a renewed interest in bacteriophages.

I'm not a doctor or historian, but most of what I know is from The Forgotten Cure by Anna Kuchment, or articles like Phage therapy gets revitalized and Bacteriophage Therapy

Soviet industrial plans through the year 2000 have emphasized greater variety and higher quality in metals production to keep heavy industry competitive with the West. But the machinery and production systems available to Soviet metallurgists in 1989 showed no signs of improving the inconsistent record the industry had established in meeting such goals. Following the Stalinist pattern, great success in some areas was hampered by breakdown in others. In the late 1980s, escape from this dilemma seemed no more likely than in earlier years.

Since the 1970s, the Soviet Union has led the world in the production of iron, steel, and rolled metals. In 1987 it produced about 162 million tons of steel, 114 million tons of rolled metal, and 20 million tons of steel pipe. Each of these figures was an increase of more than 2.5 times over those of 1960. Metallurgy has been the largest and fastest growing branch of Soviet industry, and metals supply remained vital to growth in virtually all other branches of industry. But yearly production increases were becoming more difficult because the cost of raw materials rose consistently in the 1980s, especially for metals such as molybdenum, nickel, magnesium, and rare earth metals, which were in increasing demand for high-quality steel alloys.

In the mid-1980s, the metallurgy industry was not meeting its goals for supplying high-quality finished metal to the manufacturing industries. Those industries were demanding higher-quality and stronger metals for new applications, such as high-pressure pipelines for oil and gas, high-capacity dump trucks and excavators, industrial buildings with large roof spans, corrosion-resistant pipe for the chemical industry, coated and treated rolled metals, and steel with high conductivity for electrical transformers. As military equipment became more sophisticated, it too required improved quality and performance from metal products. On the development side, advances in lightmetal alloys using aluminum, magnesium, and titanium did provide materials for military aircraft and missiles that were among the best in the world.

One could argue that their were ahead on certain areas of space exploration. The U.S. had the capability to launch a satellite about a year before the Soviets but interagency conflicts prevented it. That said the Russians still pulled significant achievements especially around space probes. Their rocket engines have been recognised as one the best until few years ago.

Their research may have been ahead in several areas but the lack of information around it and the anonymity of the researchers makes very difficult to actually assess it. For instance I know Russians explore the use of viruses to combat cancer decades ago.