HLTH 4200 Week 5 Two-by-Two Table Example

Indoor Tanning and Melanoma in a Composite Case-Control Study: Filling the Two-by-Two Table, Reading the Odds Ratio and Explaining Why the Same Four Cells Cannot Give a Risk

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Walden University

HLTH 4200: Principles of Epidemiology

Instructor Name

Month Day, Year

Indoor Tanning and Melanoma in a Composite Case-Control Study: Filling the Two-by-Two Table, Reading the Odds Ratio and Explaining Why the Same Four Cells Cannot Give a Risk

The Study

This exercise uses a composite case-control study with round, invented counts. Investigators identified 400 adults aged 18 to 49 with a new diagnosis of cutaneous melanoma at hospitals in one region (cases) and 800 adults of similar age from the same region without melanoma (controls). Each participant was asked whether they had ever used an indoor tanning bed or booth. A case-control study selects people by their outcome and then looks back at their exposure (Schulz & Grimes, 2002), and that order of selection determines what the table can show.

The Table

Among cases, 120 of 400, or 30%, had ever used indoor tanning. Among controls, 160 of 800, or 20%, had.

Table 1

Ever Use of Indoor Tanning Among Cases and Controls

Column totals were fixed by the investigators when they chose 400 cases and 800 controls; only the split within each column was observed.

The Odds Ratio

The measure of association for a case-control study is the odds ratio. The odds of exposure among cases are a ÷ c = 120 ÷ 280 = 0.429. The odds of exposure among controls are b ÷ d = 160 ÷ 640 = 0.250. The odds ratio is the ratio of these odds:

Odds ratio = (a × d) ÷ (b × c) = (120 × 640) ÷ (160 × 280) = 76,800 ÷ 44,800 = 1.71.

In words: the odds of having ever used indoor tanning were about 1.7 times as high among people with melanoma as among people without it. Because the odds ratio is symmetric, this also equals the odds of melanoma among the ever-exposed divided by the odds of melanoma among the never-exposed, within the study population.

For comparison, a systematic review and meta-analysis of 27 studies found a summary relative risk of 1.20 for melanoma among people who had ever used sunbeds, and 1.87 among those who first used them before age 35 (Boniol et al., 2012). The composite study's estimate of 1.71 falls between these, which is plausible for a study restricted to adults under 50, though its counts are invented for illustration.

Why the Same Cells Cannot Give a Risk

It is tempting to read the table across its rows: of 280 people who ever tanned indoors, 120 had melanoma, so the "risk" of melanoma among tanners is 120 ÷ 280, or 43%; among never-tanners it is 280 ÷ 920, or 30%. Both numbers are meaningless as risks, and the reason lies in how the table was built.

A risk is the proportion of people in a group who develop the outcome over a period. To calculate it, the investigator must start with a defined group, count everyone in it and see who becomes ill. In a cohort study, that is what happens (Grimes & Schulz, 2002): the row totals are people who were followed, and the number who developed melanoma in each row is observed. In this case-control study, the investigators did not follow anyone. They decided in advance to study 400 people with melanoma and 800 without. The ratio of cases to controls, one to two, was their choice. Had they chosen 400 cases and 1,600 controls, the "risk" read across the exposed row would fall sharply, though nothing about melanoma or tanning had changed. In the real population, melanoma is uncommon among young adults, nowhere near the one-in-three proportion the table shows.

The odds ratio survives this problem because it compares exposure within the cases with exposure within the controls. Doubling the number of controls doubles both b and d, leaving their ratio, and the odds ratio, unchanged. The risks and the risk ratio do not survive, because they depend on the ratio of cases to controls, which the investigators set.

When the Odds Ratio Approximates the Risk Ratio

Although the table cannot give a risk, the odds ratio can approximate the risk ratio under certain conditions. When the outcome is rare in the population, as melanoma is among adults under 50, the odds of disease and the risk of disease are nearly equal, and so the odds ratio from a well-conducted case-control study approximates the risk ratio that a cohort study would have found. This is why case-control studies of rare diseases are often reported as if they estimated relative risk. The approximation requires that controls represent the exposure distribution of the population that gave rise to the cases.

What Could Distort the Odds Ratio

Two problems common to case-control studies apply here (Schulz & Grimes, 2002). First, recall bias: people diagnosed with melanoma may think harder about past sun exposure and be more likely to remember or report indoor tanning than controls, inflating the odds ratio. Second, control selection: if controls were drawn from a group that tans less or more than the population from which cases came, the comparison would be distorted. A third issue, confounding, arises if a factor such as natural sun exposure or skin type is linked to both indoor tanning and melanoma; the crude odds ratio above makes no adjustment for it.

Reporting the Result

A complete report of this table would give the odds ratio with a confidence interval, the number of cases and controls and a plain statement of what the measure means. For these counts, a standard calculation gives a 95% confidence interval of roughly 1.3 to 2.3, which excludes 1.0. The report should not translate the odds ratio into a statement such as "tanners are 71% more likely to get melanoma" without noting that this reading depends on melanoma being rare and on the controls representing the population the cases came from.

Conclusion

The two-by-two table yields one valid measure: an odds ratio of 1.71, meaning the odds of past indoor tanning were about 1.7 times higher among people with melanoma than among those without. The same four cells cannot give the risk of melanoma among tanners or non-tanners, because the investigators fixed the number of cases and controls, and any proportion read across a row depends on that choice. Only because melanoma is rare in this age group can the odds ratio be read as an approximate risk ratio.

References

Boniol, M., Autier, P., Boyle, P., & Gandini, S. (2012). Cutaneous melanoma attributable to sunbed use: Systematic review and meta-analysis. BMJ, 345, Article e4757. https://doi.org/10.1136/bmj.e4757

Grimes, D. A., & Schulz, K. F. (2002). Cohort studies: Marching towards outcomes. The Lancet, 359(9303), 341-345. https://doi.org/10.1016/S0140-6736(02)07500-1

Schulz, K. F., & Grimes, D. A. (2002). Case-control studies: Research in reverse. The Lancet, 359(9304), 431-434. https://doi.org/10.1016/S0140-6736(02)07605-5