This is an evolving area of research.  Some studies have found an association and others have not.

But two recent meta-analyses suggest that the odds are about 33 to 44% greater due to long-term cell phone usage.

Got your attention?

“But what does this do to my odds of developing a brain tumor?” you may ask.

Before we answer that, we need to explain how the meta-analyses derive this 33 to 44% figure.  Which introduces us to odds ratios.

Case-control studies

Studies of the association between cell phone usage and brain tumor are typically case-control studies.

Such studies are retrospective, as opposed to prospective.[1] They combine a sample of patients (cases) already diagnosed with a brain tumor with a random sample of non-patients (controls) drawn from the general population. Study investigators match controls to each case based on key demographics such as sex, age, and region.

The studies then measure and test for the existence of an association between exposure (cell phone usage) and outcome (brain tumor).[2]

Typically, these case-control studies report their estimated effects, not in terms of odds, but in terms of odds ratios.

So, what is an odds ratio?

Odds ratios

An odds ratio is a measure of association strength. In this case, between cell phone usage and the diagnosis of a brain tumor.

As an example, we can use the results from one of the high-quality studies used in the meta-analyses mentioned above to show how odds ratios are calculated.[3]

The data shown in the following table are from a case-control study conducted in Sweden between 2000 and 2003.[4]  The data are for long term cell phone usage (>= 10 years). The reference category is no cell phone usage.[5]

In an earlier article we learned that the odds of an event occurring are the number of events divided by the number of non-events.

Thus, the odds of a long-term cell phone user in this sample being diagnosed with a brain tumor is (16 / 232) or 0.069; about 1 to 14.

The odds of a non-cell phone user being diagnosed with a brain tumor is (18 / 674) or 0.027; about 1 to 37.

The odds ratio is simply the ratio of the two odds:  (0.069 / 0.027) or 2.582.

So, the odds of a long-term cell phone user being diagnosed with a brain tumor are 2.582 times greater compared to a non-cell phone user.

Alternatively, this can be stated in terms of a % difference. The odds of a long-term cell phone user being diagnosed with a brain tumor are 158% greater compared to a non-cell phone user ((2.582 – 1) * 100).

That is a pretty large effect.[6]

Meta-studies

Now this is just one study.  The two meta-studies alluded to above each combined the results of 7 different, high-quality studies.

They found that the overall odds (across the studies) of a long-term cell phone user (>= 10 years) being diagnosed with a brain tumor (any tumor type) are 33% and (with respect to glioma, a common type of tumor) 44% greater compared to a non-cell phone user.[7]

These meta-studies found no effect due to cell phone usage over a shorter period (i.e., < 10 years).

So, it appears that the risk, if it exists, is associated with long-term usage.  Moreover, using a cell phone on the same side of the head is associated with 46% greater odds of developing a glioma on that side of the head.[8]

Odds of developing a brain tumor

So, back to our original question.  What are the odds of developing a brain tumor from long term cell phone usage?

The odds of developing a brain tumor among the general population is very low to start with.  Annual incidence in the US (2018) is 6.5 per 100,00 or 0.0065%.  In terms of odds, this is about 1 to 15,000.

So, a 44% increase in the odds would mean 9.4 per 100,000 or about 1 to 10,000.  Still quite low.[9]

As one researcher put it, “Your chance of being hurt by distracted driving because you’re using your cell phone wipes out the risk of getting cancer.”

However, in 2011 the World Health Organization’s International Agency for Research on Cancer (IARC) did classify cell phones as a Group 2B carcinogen (i.e., possibly causes cancer).

And there continues to be a healthy debate in both the statistical and public arenas.

Studies are continuing to be released which purportedly finding evidence that recent increasing rates in glioblastomas, an aggressive type of cancer, are tied to cell phone usage.

Skeptics argue that changes in WHO classification of what is considered a glioblastoma may be responsible for any uptick in brain tumor incidence. And that the large, increased risk reported by studies, like the meta-studies discussed above, are inconsistent with the historical trend in brain tumor incidence.[10]

As we said at the outset, this is an evolving area of research, with lots of issues to untangle.

One thing to keep in mind, though, is who is funding the research.  A topic we will cover in a later article.

We have odds ratios to thank

Back to the main point of this article.

Odds facilitate the measurement of the relative likelihood of events.  Epidemiological studies that are retrospective, commonly use the odds ratio as this relative measurement of association strength.

So, the next time you hear that your favorite dietary choice increases your chances of developing cancer, it is probably the result of that not-so-oddity, the odds ratio.

[1] Prospective cohort studies have also been used (i.e., studies which track subjects over time).  See here for a summary of the advantages and disadvantages of retrospective and prospective studies.

[2] Exposure is determined by answers to a lengthy questionnaire. Hence, one of the criticisms levied against case-control studies is respondent recall bias. That is, whether respondents accurately recall their cell phone usage, particularly over a long period of time.

[3] Studies are graded on a quality scale considering such factors as selection of cases and controls, comparability of cases and controls based on study design, and proper assessment/measurement of exposure.

[4] The results shown in the table are taken from a meta-study which considered this Hardell et al (2006) study.

[5] As cell phone usage becomes more ubiquitous, and fewer people who have never used a cell phone are available in the population, the exposure will need to be increasingly measured in terms of levels/frequency of usage.

[6] The additional risk derived using an odds ratio is closely related to the concept of efficacy, which is derived directly from the concept of relative risk (ratio of probabilities). We covered efficacy in an earlier article. Epidemiologists typically use relative risk to measure association strength in prospective (cohort) studies; odds ratios in case-control studies.

[7] Meta-studies start with a larger number of studies.  They then cull studies from the final sample for various reasons, such as data availability and the quality grade they receive.

[8] All these studies on brain tumors controlled for whether cell phones were being used next to users’ heads.

[9] See for US cancer incidence rates as of 2018.

[10] See also Geoffrey Kabat (2017).

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1 in 1,600,000.

Yep, not very likely.  You are much more likely to die from a dog attack (1 in 86,781) or from a lightning strike (1 in 138,849).

But why odds?

Why not express these likelihoods in terms of probabilities?  Seems like a more natural way to express the chance of an event occurring, doesn’t it?

Odds, however, are commonly used to express event risk.  And of course, the chances of winning a sporting event.

As we write, the odds of the Los Angeles Dodgers repeating as World Series champions in 2021 are 1 in 3.[1]

So, what are odds?

The number of times an event occurs divided by the number of times it does not occur.

In the case of a meteorite strike, for every person that dies, 1.6 million do not.  In the case of the Dodgers, we would expect the Dodgers to win 1 World Series for every 3 they lose.

But this still begs the question, why odds and not probabilities?

Odds and probabilities

It is true that the probability of a low likelihood event is so small that stating it as a % requires a lot of zeros after the decimal (0.0000625% in the case of dying from a meteorite strike).

But that is not an insurmountable objection. For example, the risk of disease is often expressed in terms of rates per 100,000 to make the chances of low likelihood events easier to comprehend. Or we could state the probability of the non-event…not dying from a meteorite strike (99.994%).

A more important reason for using odds is that they facilitate multiplicative comparisons.

A simple example makes clear how probabilities can fall short.

Suppose the probability that Beth will go out to dinner this weekend is 75%. We cannot say, then, that the probability of Jose doing the same is 3 times that of Beth’s probability.

Why?  Probabilities are constrained to lie between 0 and 1. And 3 * 0.75 > 1.0.

So, what do we do?  Enter odds.

Odds are unconstrained

Odds are only bounded on the low end, by 0.  Let’s return to Beth and Jose.

The odds of Beth going out to dinner are 3 or 3/1.  Why 3/1?

Remember odds are the ratio of the events to non-events. Beth is 75% likely to go out. So, if she is faced with 4 opportunities to go out, she will do so 3 times.  In other words, she will go out (event) 3 times for every time she stays home (non-event).  3 to 1.

Now, if Jose is 3 times as likely to go out as Beth, his odds are simply 3 * 3 or 9.  Equivalently, we can express his odds as 9 to 1 or 9/1.

On the odds scale, odds can be 2, 10, 50 times greater…there is no upper limit. And this makes them very useful when we wish to compare the relative likelihood of events occurring.

Two sides of the same coin

It turns out that if we are still interested in the probability, we can easily derive it from the odds.  Odds and probability are two sides of the same coin.

Odds (o) are related to probability (p) by the following:

o = p / (1 – p) = (probability of event / probability of non-event)

Rearranging we find the “other side of the coin” (for an event):

p = o / (1 + o) = (odds of event) / (1 + odds of event)

So, in the case of Beth and Jose we get:

The relationship between odds and probability is shown graphically below.

As the odds increase, the probability also increases but in a non-linear manner.  As shown above, the probability “increases at a decreasing rate” and approaches 1.0 “asymptotically” (i.e., as the odds get very large, the probability approaches but never quite reaches 1.0).[2]

But any finite odds will map to a probability between 0 and 1.

Odds are preferred

When comparing the relative chances of events (or sports teams), odds are the preferred way of expressing how much more likely one event is over another.  We can always derive the associated probability.  But since odds are unconstrained,  there is no issue with saying the Los Angeles Dodgers are 11 times as likely (as of May 31, 2021) to win the World Series in 2021 than the Chicago Cubs.

So, the next time someone tells you the odds of rain during your camping trip this weekend are 5 to 2, you might want to sleep in a tent.

[1] As of May 31, 2021, the reported odds of the Dodgers repeating are 3 to 1 or 3/1.  In the betting world, this is referred to as fractional odds. The number on the left or numerator is typically the number of times the team is expected to lose. 3/1 yields an implied probably of losing 3 times out of 4 or 75%.  Thus, the probability of the Dodgers repeating are (1 – 0.750) or 25%.  Expressing as odds yields 1/3.

[2] In the limit, if the odds = infinity, then probability = 1.

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