Monosaccharides are mainly grouped into aldose having a polyhydroxyl aldehyde structure, ketose having a polyhydroxyl ketone structure, and sugar alcohols obtained by reducing the aldose and the ketose.  Also, monosaccharides are classified depending on amounts by which they are present in the natural world.  More specifically, a rare saccharide is defined as “a saccharide that is rarely present in the natural world” by International Society of Rare Sugars, i.e., it is a monosaccharide present in the natural world in very small amount.  Many of rare saccharides generally have small yields in synthesis reactions based on organic chemical synthesis methods.  For that reason, properties of many rare saccharides are still unknown.  In the current state, therefore, such rare saccharides as aldohexose (aldose of hexose), including D-allose, have many not-yet-known properties. 
In addition to D-allose, examples of rare saccharides belonging to aldohexose include D-gulose, D-idose, D-talose, D-altrose, L-mannose, L-glucose, and L-galactose.  The above-described situations are similarly applied to such rare saccharides as ketohexose (ketose of hexose), including D-psicose.  Examples of rare saccharides belonging to ketohexose include D-psicose, L-psicose, D-sorbose, L-sorbose, D-tagatose, L-tagatose, and L-fructose. 
In connection with the relationships between saccharides and cancers, there have hitherto been known polysaccharides that are effective in preventing cancers, as disclosed in Patent Reference 1, for example.  Also, it has been reported that an oligosaccharide acts to keep the intestine in order and therefore it is effective in relieving constipation for protection against a colon cancer.  Further, there have recently been publicized reports indicating a cancer inhibitory effect of polysaccharides, such as agaricus, and discussing the relations between saccharide chains and metastasis of cancers. 
On the other hand, as an example utilizing the properties of saccharides against active oxygen, an active oxygen inhibitor containing a polysaccharide with active-oxygen inhibitory properties is known as disclosed in, e.g., Patent Reference 2. 
Among rare saccharides, psicose is ketohexose (ketose of hexose).  There are known two optical isomers, i.e., D-psicose and L-psicose.  D-psicose is a known substance, but it is rarely present in the natural world.  Therefore, D-psicose is a “rare saccharide” according to the definition by International Society of Rare Sugars.  With recent commercialization of epimerase (see, e.g., Patent Reference 3), however, D-psicose has become relatively easily available although it is still expensive.  Patent Reference 3 also suggests that prepared D-psicose can be effectively utilized as raw materials, intermediates, etc.  for sweeteners, carbon sources for fermentation, reagents, cosmetic and medicines.  Further, Patent Reference 3 discloses that the sweeteners can be utilized to add sweetness and to improve taste of oral ingesta, such as food and drink, feed, dentifrice, and internal medicines, but it does not include detailed disclosure regarding the use as an edible additive.  With regards to L-psicose, i.e., an optical isomer of D-psicose, Patent Reference 4, for example, discloses in detail that L-psicose can be utilized as an edible additive.     Patent Reference 1 Japanese Patent Laid-Open No.  5-112455    Patent Reference 2 Japanese Patent Laid-Open No.  7-285871    Patent Reference 3 Japanese Patent Laid-Open No.  6-125776    Patent Reference 4 Japanese Patent Laid-Open No.  57-129671