The Linear no-threshold model (LNT) is a way of predicting the maximum biological risk from ionizing radiation. While cancer is only one of the possible problems from radiation (others include acute radiation sickness), it's a common concern, and so will be the focus of this discussion. Eventually, Energy Education would like to have a reasonably full treatment of the biological effects of radiation, but doesn't yet.
The linear no-threshold model is based on biological responses at high radiation doses and dose rates. Of course, the higher the dose and dose rate, the higher the biological response; the lower the dose and dose rate, the lower the response. This model assumes the simplest possible relationship, a straight line. Data collection to confirm or deny this model in humans is quite difficult because people will (obviously) not willingly expose themselves to radiation at (or even close to levels that are known to be) harmful levels. The assumptions of the LNT are used specifically to get around the problem of predicting radiation harm at levels where no data exist.
Another difficulty with determining the biological response comes from the time delay between when an organism is exposed to a carcinogen (something that causes cancer, usually hazardous chemicals, but radiation can be carcinogenic) and when the cancer develops. This period of time is called the latency period. This is particularly difficult with cancer specifically (as opposed to acute radiation sickness), since a large fraction of the population will develop cancer for other reasons than radiation; roughly 40% of people living their full lifespan will be diagnosed with cancer, but not everyone will die of the cancer, and many people won't live that long for other reasons. Many things cause cancer; different populations have different cancer risks, but radiation is probably very rarely the cause of cancer.
This model is primarily a policy model in order to set limits on exposure to radiation and is widely used. This model is deliberately conservative; it almost certainly overestimates the risk associated with radiation exposure.
The data to make the LNT model came from Japanese survivor data from World War II. The bomb victims of Nagasaki and Hiroshima who received the highest amount of radiation exposure displayed an increased risk response. From this correlation, data were then extrapolated to the origin, assuming a linear no-threshold relationship between dosage and the risk of getting cancer. Part of the difficulty is that at low dose rates of radiation it is difficult to differentiate between natural background cancer rates and those caused by radiation.
The linear relationship that exists between cancer risk and dosage has the following assumptions:
As with most models, the assumptions above are almost certainly not true, but the question becomes: are they good approximations for reality? If these assumptions are 'true enough,' then the LNT is a good scientific model; if the assumptions are inaccurate, then it's a poor scientific model.
In either case, because the model is primarily for setting public policy, the important point is that the model gives an overestimation of risk. Detractors from the LNT claim that this has made the public overly concerned about the biological effects of radiation, leading to unnecessary levels of panic in events like the Fukushima nuclear accident. Detractors of the model also point to the financial cost to making nuclear power very expensive and not actually saving human lives, an idea for which energy education will eventually have a page to explore in depth.
One of the biggest arguments against the LNT model is that it does not consider human defense mechanisms. The human body produces enzymes that repair DNA damage with an efficiency of 99.99% for single stranded breaks and 90% for double stranded breaks. Some studies have shown that apoptosis (when cells commit suicide) can be stimulated by low-level radiation. Radiation has also been shown to alter cell cycle timing, thereby increasing the time before the next cell division. (mitosis) This gives a cell more time to notice the DNA damage and go into apoptosis before mitosis, ultimately preventing the cell from becoming cancerous. Naturally the human body suffers DNA damage via corrosive chemicals and thermal processes millions of times per day; however, only about one DNA damage per cell per day remains unrepaired.
There are many models of biological response to radiation that show that the LNT model is unreasonable at low doses. One surprising model is radiation hormesis, which essentially states that there are benefits from low-level ionizing radiation stimulation. Other scientists have noticed that humans often have an adaptive phase response: low-level ionizing radiation seems to be able to condition cells to have better responses to higher amounts of radiation dose. Some models assume a higher risk at lower dose rates (a super-linear model), but this model doesn't seem to mesh well with what's known about this biology, and the data aren't there to support this idea.
Biological effects of radiation remains an active area of research in the scientific community.