Since this question was asked on different forums, I decided to write this article. To my knowledge, none of the previous or current medical doctors who practice the Buteyko therapy (over 200 people) claimed that this therapy can cure cancer. However, there are certain clinical observations and known scientific facts that I am going to briefly review here.
All available physiological evidence, starting from the Nobel Prize discovery of Dr. Otto Warburg, who in his speech "The Prime Cause and Prevention of Cancer" (1966) said, "In every case, during the cancer development, the oxygen respiration always falls, fermentation appears, and the highly differentiated cells are transformed into fermenting anaerobes, which have lost all their body functions and retain only the now useless property of growth and replication" until all available modern research, indicates that low body oxygenation in the body is still the prime cause of cancer (see http://www.normalbreathing.com/diseases-cancer-1-Hypoxia.php).
The central test of the Buteyko oxygenation therapy and the main tool of the patient or student is stress-free breath holding time, which accurately reflects body oxygenation. [Exhale normally, pinch the nose, close the mouth, and measure your breath holding time but only until the first stress or discomfort. At certain moment of time, this discomfort starts to grow and, if one releases the nose at this moment, the test is correct and the breathing pattern does not change: it is the same after the test as before it.]
A typical Buteyko doctor had hundreds, sometimes thousands of patients who learned the oxygenation therapy to variable degree (starting with less than 20 s for early morning oxygenation and going up to 30, 35, 40, 60, 90 etc. seconds). There were no systematic cancer studies since the Buteyko method is focused mostly on about 15-20 other common diseases (like asthma, heart disease, bronchitis, epilepsy, sinusitis, insomnia, etc.) However, it is known that presence of any chronic condition is a risk factor for cancer. Hence, hundreds of Russian Buteyko patients with cancer experienced corresponding developments (see below), while none of Russian Buteyko doctors could make cancer cure claims based on a few or even several cases in the own practice. When all these cases are gathered together and their conclusions are the same, then we can speak about the following clinical findings.
These doctors consistently observed that when index of body oxygenation gets up to 35-40 s, tumors start to disappear.
It is not a surprise then that Doctor Buteyko, based on these persistent observations in relation to cancer and other diseases of civilization, stated that 60 s of oxygen in the body should be the norm of ideal health, since about 150 chronic diseases, cancer included, are incompatible with this physiological state. [You cannot have 60 s of oxygen in the body 24/7 and tumors at the same time.]
When oxygenation is below 20 s, even for 30 min, inflamed tissues and tumors are likely to grow.
When the breath hold is less than 10 s, the immune system offers little resistance even in the blood. Sepsis and metastasis are possible.
These observations are rather simple and they are in complete agreement with dozens of western professional oncological studies (cancer-tissue hypoxia link). Moreover, oxygenation-based observations are more accurate since they provide a simple measure of cancer development (for worse and for better).
We see that all available evidence, clinical observation and scientific research show that cancer development is based on tissue hypoxia, not on presence or absence of herbs, functional foods, vitamins, or other substances in diet. (Only when we are truly deficient in any essential nutrient, correct supplementation improves the health state and increase body oxygenation. This effect can be easily measured.)
The modern approach to cancer among many people in alternative health area is almost the same as the approach of most doctors in relation to disease and drugs. Instead of the medication or pill, it is suggested to use various supplements, herbs, colloidal silver, enzymes, etc. to fight cancer. For this mental approach, the person with cancer becomes an innocent victim of the vicious disease and the supplement (herb, enzyme, vitamin, substance, etc.) plays the role of the savior. It is the same situation as with medical drugs: innocent patients, treacherous diseases, and a doctor-savior on a white horse delivering the magic medical pill.
Moreover, reduced brain oxygenation, due to heavy breathing, makes cancer sufferers very susceptible to this "sweet supplement" myth when they participate in never-ending games searching for the cure. When the old savior (medical drug or supplement) disappears or gets unpopular, the new savior is immediately found or anticipated. Why are these fantasies so popular? Because these myths create an illusion of innocence and "re-assure" current, physiologically abnormal lifestyle of the sick person.
This has nothing to do with physiology of the human body, cancer pathology, and health, because the person can eat tones of herbs and vitamins, drink canisters of colloidal silver, and do thousands other promoted things, but if the oxygenation remains below 20 s (e.g., due to mouth breathing, or sleeping on one's back, or due to lack of physical activity, or due to inflammation and cortisol deficiency, etc.), no cancer improvement will take place. Hence, prevention of mouth breathing 24/7, prevention of sleeping on one's back, correct posture 24/7, physical activity with strictly nasal breathing, eating only when truly hungry, and many other lifestyle factors and hidden physiological obstacles (cavities, intestinal parasites, fungal infections, etc.) are more important since these, real factors address the foundation of cancer: low body oxygenation.
"Oxygen content in the organism can be found using a simple method: after exhalation, observe, how long the person can pause their breath without stress" Soviet Physiologist, PhD (Physiology), MD Konstantin Buteyko.
"Therefore, I emphasize, the fact established long ago, or the law: the less the depth of breathing, the more oxygen is delivered in the organism, and vice versa, the deeper the breath, the less oxygen is delivered in the organism." Dr. Buteyko speaking about breathing patterns
2010 Update. A clinical trial:
Metastasized breast cancer clinical trial: Fivefold reduction in 3-year mortality for breathing normalization group. One hundred twenty patients with metastasized breast cancer participated in this controlled study published in Oncology Journal (Kiev).