of cancer deaths, and the transfer of risk across populations. the ddref factor that is used to scale acute radiation exposure data to low-dose and dose-rate radiation exposures. the radiation quality factor (q) as a function of let. space dosimetry the so-called "unknown uncertainties" from the ncrp report no. 126 are ignored by nasa. models of cancer risks and uncertainties life-table methodology the double-detriment life-table approach is what is recommended by the nprc to measure radiation cancer mortality risks. the age-specific mortality of a population is followed over its entire life span with competing risks from radiation and all other causes of death described. for a homogenous population receiving an effective dose e at age ae, the probability of dying in the age-interval from a to a+1 is described by the background mortality-rate for all causes of death, m(a), and the radiation cancer mortality rate, m(e,ae,a), as: q ( e , a e , a ) = m ( a ) + m ( e , a e , a ) 1 + 1 2 [ m ( a ) + m ( e , a e , a ) ] ,a)=,a)}\left}}} the survival probability to age, a, following an exposure, e at age ae, is: s ( e , a e , a ) = ∏ u = a e a − 1 [ 1 − q ( e , a e , u ) ] ,a)=\prod _^\left} the excessive lifetime risk (elr - the increased probability that an exposed individual will die from cancer) is defined by the difference in the conditional survival probabilities for the exposed and the unexposed groups as: e l r = ∑ a = a e ∞ [ m ( a ) + m ( e , a e , a ) ] s ( e , a e , a ) − ∑ a = a e ∞ m ( a ) s ( 0 , a e , a ) ^\lefts(e,a_,a)-\sum _^m(a)s(0,a_,a)} a minimum latency-time of 10 years is often used for low-let radiation. alternative assumptions should be considered for high-let radiation. the reid (the lifetime risk that an individual in the population will die from cancer caused by radiation exposure) is defined by: r e i d = ∑ a = a e ∞ m ( e , a e , a ) s ( e , a e , a ) ^m(e,a_,a)s(e,a_,a)} generally, the value of the reid exceeds the value of the elr by 10-20%. the average loss of life-expectancy, lle, in the population is defined by: l l e = ∑ a = a e ∞ s ( 0 , a e , a ) − ∑ a = a e ∞ s ( e , a e , a ) ^s(0,a_,a)-\sum _^s(e,a_,a)} the loss of life-expectancy among exposure-induced-deaths (lle-reid) is defined by: l l e − r e i d = l l e r e i d uncertainties in low-let epidemiology data the low-let mortality rate per sievert, mi is written m ( e , a x , a ) = m 0 ( e , a x , a ) d d r e f x d x s x t x b x d r ,a)=(e,a_,a)}x_x_x_ where m0 is the baseline mortality rate per sievert and xα are quantiles (random variables) whose values are sampled from associated probability distribution functions (pdfs), p(xa). ncrp, in report no. 126, defines the following subjective pdfs, p(xa), for each factor that contributes to the acute low-let risk projection: pdosimetry is the random and systematic errors in the estimation of the doses received by atomic-bomb blast survivors. pstatistical is the distribution in uncertainty in the point estimate of the risk coefficient, r0. pbias is any bias resulting for over- or under-reporting cancer deaths. ptransfer is the uncertainty in the transfer of cancer risk following radiation exposure from the japanese population to the u.s. population. pdr is the uncertainty in the knowledge of the extrapolation of risks to low dose and dose-rates, which are embodied in the ddref. risk in context of exploration mission operational scenarios the accuracy of galactic cosmic ray environmental models, transport codes and nuclear interaction cross sections allow nasa to predict space environments and organ exposure that may be encountered on long-duration space missions. the lack of knowledge of the biological effects of radiation exposure raise major questions about risk prediction. the cancer risk projection for space missions is found by m j ( e , a e , a ) l j ( e , a e , a ) ∫ d l d f d l l q t r i a l − j ( l ) x l − j (e,a_,a)_(e,a_,a)\int dllq_(l)x_ where d f d l represents the folding of predictions of tissue-weighted let spectra behind spacecraft shielding with the radiation mortality rate to form a rate for trial j. alternatively, particle-specific energy spectra, fj(e), for each ion, j, can be used m j ( e , a e , a ) = m l j ( e , a e , a ) ∑ j ( e ) l ( e ) q t r i a l − j ( l ( e ) ) x l − j (e,a_,a)=m_(e,a_,a)\sum _(e)l(e)q_(l(e))x_ . the result of either of these equations is inserted into the expression for the reid. related probability distribution functions (pdfs) are grouped together into a combined probability distribution function, pcmb(x). these pdfs are related to the risk coefficient of the normal form (dosimetry, bias and statistical uncertainties). after a sufficient number of trials have been completed (approximately 105), the results for the reid estimated are binned and the median values and confidence intervals are found. the chi-squared (χ2) test is used for determining whether two separate pdfs are significantly different (denoted p1(ri) and p2(ri), respectively). each p(ri) follows a poisson distribution with variance p ( r i ) )}}} . the χ2 test for n-degrees of freedom characterizing the dispersion between the two distributions is χ 2 = ∑ n [ p 1 ( r n ) − p 2 ( r n ) ] 2 p 1 2 ( r n ) + p 2 2 ( r n ) =\sum _^(r_)+p_^(r_)}}}} . the probability, p(ņχ2), that the two distributions are the same is calculated once χ2 is determined. radiation carcinogenesis mortality rates age-and sex-dependent mortality rare per unit dose, multiplied by the radiation quality factor and reduced by the ddref is used for projecting lifetime cancer fatality risks. acute gamma ray exposures are estimated. the additivity of effects of each component in a radiation field is also assumed. rates are approximated using data gathered from japanese atomic bomb survivors. there are two different models that are considered when transferring risk from japanese to u.s. populations. multiplicative transfer model - assumes that radiation risks are proportional to spontaneous or background cancer risks. additive transfer model - assumes that radiation risk acts independently of other cancer risks. the ncrp recommends a mixture model to be used that contains fractional contributions from both methods. the radiation mortality rate is defined as: m ( e , a e , a ) = [ e r r ( a e , a ) m c ( a ) + ( 1 − v ) e a r ( a e , a ) ] ∑ l q ( l ) f ( l ) l d d r e f ,a)=\leftq(l)f(l)l} where: err = excess relative risk per sievert ear = excess additive risk per sievert mc(a) = the sex- and age-specific cancer mortality rate in the u.s. population f = the tissue-weighted fluence l = the let v = the fractional division between the assumption of the multiplicative and additive risk transfer models. for solid cancer, it is assumed that v=1/2 and for leukemia, it is assumed that v=0. biological and physical countermeasures identifying effective countermeasures that reduce the risk of biological damage is still a long-term goal for space researchers. these countermeasures are probably not needed for extended duration lunar missions, but will be needed for other long-duration missions to mars and beyond. on 31 may 2013, nasa scientists reported that a possible human mission to mars may involve a great radiation risk based on the amount of energetic particle radiation detected by the rad on the mars science laboratory while traveling from the earth to mars in 2011-2012. there are three fundamental ways to reduce exposure to ionizing radiation: increasing the distance from the radiation source reducing the exposure time shielding (i.e.: a physical barrier) shielding is a plausible option, but due to current launch mass restrictions, it is prohibitively costly. also, the current uncertainties in risk projection prevent the actual benefit of shielding from being determined. strategies such as drugs and dietary supplements to reduce the effects of radiation, as well as the selection of crew members are being evaluated as viable options for reducing exposure to radiation and effects of irradiation. shielding is an effective protective measure for solar particle events. as far as shielding from gcr, high-energy radiation is very penetrating and the effectiveness of radiation shielding depends on the atomic make-up of the material used. antioxidants are effectively used to prevent the damage caused by radiation injury and oxygen poisoning (the formation of reactive oxygen species), but since antioxidants work by rescuing cells from a particular form of cell death (apoptosis), they may not protect against damaged cells that can initiate tumor growth. evidence sub-pages the evidence and updates to projection models for cancer risk from low-let radiation are reviewed periodically by several bodies, which include the following organizations: the nas committee on the biological effects of ionizing radiation the united nations scientific committee on the effects of atomic radiation (unscear) the icrp the ncrp these committees release new reports about every 10 years on cancer risks that are applicable to low-let radiation exposures. overall, the estimates of cancer risks among the different reports of these panels will agree within a factor of two or less. there is continued controversy for doses that are below 5 msv, however, and for low dose-rate radiation because of debate over the linear no-threshold hypothesis that is often used in statistical analysis of these data. the beir vii report, which is the most recent of the major reports is used in the following sub-pages. evidence for low-let cancer effects must be augmented by information on protons, neutrons, and hze nuclei that is only available in experimental models. such data have been reviewed by nasa several times in the past and by the ncrp. epidemiology data for low linear energy transfer radiation radiobiology evidence for protons and hze nuclei