to detect an existing risk by application of these methodologies. Analytical epidemiol- ogy intends to estimate the risk as a function of exposure to an agent by application of one of three classical study types: cross-sectional, case–control, and cohort study designs. Theoretically, all three types are capable of detecting an existing risk under ideal con- ditions but differ in their sensitivity to the effects of extraneous and confounding factors. For all study designs, it has to be assumed that exposure to the agent can be assessed with a certain sensitivity and specificity. In the case of mobile phone use, the appropriate exposure metric is unknown. Absorption of electromagnetic energy in the body of the user depends on technical features of the phone and the network, as well as on anatomical features and habits of use. At first glance, this situation does not seem to be much different from, for example, an exposure to an air pollutant that also varies in time and space and which internal dose will depend on physiologic conditions. The problem with mobile telephones is much more profound. What aspect of the complex exposure condition described by “mobile phone use” could be responsible for an effect? It is obvious that given a certain indicator of mobile phone use, such as years of regular use, cumula- tive number of calls, cumulative hours of use, or cumulative absorption of electromagnetic energy in a certain area of the body, there are indefinitely many exposure conditions that are equivalent under the chosen metric and hence induce an equivalence relation in the space of exposure patterns that cannot be assessed as to its suitability with respect to any outcome meas- ure without a sound mechanistic theory. Another essential problem is related to the long induction periods and latencies of tumors in the head and neck region. Mobile phone use that was insignificant before the mid-1990s could not be studied with respect to its influ- ence during induction period because, in almost all users, malignant transformation has likely occurred long before exposure to mobile phones commenced. Although an influence during the initiation phase cannot be ruled out, many researchers have expressed the opin- ion that if there is an effect at all, it is an effect on tumor promotion or progression (Johansen et al. 2001; Muscat et al. 2000; Stang et al. 2001). If this is actually the case, several sce- narios have to be considered. For example, in a summary of acoustic neuroma, Mohyuddin et al. (2003) found that tumor growth is exhib- ited in 48–70% of patients, stable tumor vol- umes in 27–50%, and involution in 2–10%. If mobile phone use influences growth rate, this influence could result in either restarting growth in stable tumors, an increase of growth rate in growing tumors, or an inhibition of involution. The net result would be an earlier onset of symptoms and an earlier diagnosis. If there is an effect of the specified type, the age incidence function in the exposed popula- tion would be shifted compared with that of the unexposed population by a fraction of the exposure duration, as long as duration of use is short compared with the natural history of the disease. Given that the age incidence function has a positive slope, this shift is equivalent to an increased incidence in the exposed popula- tion for any given age. For simplicity, assume that the duration and effect of exposure is constant across all age groups. Taking the slope for the age incidence function for brain tumors as 0.04 [on the log incidence scale (Wrensch et al. 2002)], the estimated inci- dence of brain cancer at any given age would be proportional to exp(age × 0.04) in the population as a whole. If the exposed segment of the population has an age incidence func- tion shifted by 2 years, the estimated incidence at any given age among the exposed would be proportional to exp[(age + 2) × 0.04], resulting in an OR of exp(2 × 0.04) = 1.08 for mobile phone use. Note that the result is independent of the exposure prevalence and depends only on the shift of the age incidence function and its slope. Given the lower number of mobile phone users at an older age, the expected ORs from studies with short exposure durations (and hence small shifts in the age incidence function) are too small to be detected with acceptable power. The third fundamental problem is related to the vast diversity of tumor types to be con- sidered. The World Health Organization dif- ferentiates about 50 types of brain tumors (Kleihues and Cavenee 2000); there are more than a dozen different histologic salivary gland tumors, and so forth. Furthermore, in recent years molecular histopathology revealed many differences within certain types of tumors. For example, there are at least two clusters of glio- blastoma multiforme, the most frequent malig- nant brain tumor in adults: one expresses loss of heterozygosity on chromosome 17p with mutation of the p53 tumor suppressor gene, and the other cluster is characterized by an amplification of the epidermal growth factor receptor oncogene (Schwartzbaum et al. 2006). Is it possible that all of these diverse types of tumors respond uniformly to mobile phone radiation? We cannot hope to extract sensitive types by epidemiologic investigations because of the small numbers for each distinct type. In summary, the three most important conditions for epidemiology to arrive at a conclusion concerning a potential risk of an agent are as follows: • It must be possible to measure (at least by a surrogate marker) the component of the agent that is related to the risk. • For agents that promote the disease in ques- tion, duration of exposure must be a sub- stantial fraction of the history of the disease. Environmental Health Perspectives • volume 117 | number 3 | March 2009 Mobile phones and cancer • There must be good a priori reason to select specific types of diseases that are sufficiently homogenous to support the assumption of more or less uniform etiology. None of these preconditions are met in the study of mobile phone use and cancer. As a consequence, even substantially increased risks might go undetected, and evidence will tend to be equivocal. Do Mobile Phones Cause Brain Tumors? To assess a possible causal relationship between an agent and cancer, a pragmatic dialog approach has been delineated (Kundi 2006). According to this procedure, epidemiologic evi- dence must be assessed concerning four aspects: temporal relation, association, environmental, and population equivalence. If there are no valid counter arguments against the evidence for an association, this suffices for a verdict of causation. If epidemiologic evidence is insuffi- cient, other evidence that increases or decreases confidence in a causal relationship could be included to come to a conclusion. Temporal relation. Assessment of tem- poral relation is not a trivial problem. It is impossible to define the point in time when a brain tumor started. Before a tumor can be diagnosed, which in the case of brain tumors occurs either by coincidence, if it is detected by imaging techniques applied for other rea- sons, or because of symptoms produced by the growing cell mass, the tumor was present for many years or even decades. For menin- gioma, average induction periods of about 20–40 years have been calculated in adults, based on observations of patients exposed to ionizing radiation (Umansky et al. 2008). For acoustic neuroma, slow growth, with an average volume doubling time of about 1.7 years, suggests similar induction periods (Mohyuddin et al. 2003). For glioma, case reports (Kranzinger et al. 2001) and long-term follow-up after childhood radiation therapy of tinea capitis (Sadetzki et al. 2005) also suggest induction periods of decades. Considering a temporal relationship between exposure and the diverse steps of brain tumor development, the following four phases may be differenti- ated: 1) exposure commenced before the first step of malignant transformation; 2) expo- sure started during the induction phase, which could itself last for several years; 3) onset of exposure occurred during the noninvasive growth phase; and 4) exposure started during final (autonomous) growth. In cases 1 and 2, exposure might influence malignant transfor- mation itself and cause de novo occurrence of a brain tumor. In case 3, exposure might influ- ence the fate of the deviating clone and could decrease latency or probability of spontaneous involution and therefore either increase inci- dence because of a shift of latency or because 317