Affiliation of authors: Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD.
Correspondence to: Sholom Wacholder, Ph.D., National Institutes of Health, EPS 8046, 6120 Executive Blvd., Bethesda, MD 20892-7244 (e-mail: Wacholder{at}nih.gov).
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ABSTRACT |
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INTRODUCTION |
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This phenomenon is called population stratification in epidemiologic studies investigating the effect of a genetic factor on disease. Concerns about population stratification have raised doubts about the credibility of reported findings (2) and have led to calls for routine use of related controls in casecontrol studies of genetic factors (3) to eliminate the possibility of population stratification. The editors of Nature Genetics stated recently, "Population stratification (or admixture) errors are clearly a problem for casecontrol studies" (4). The textbook by Strachan and Read (5) includes the statement that association studies "became discredited because of statistical problems," particularly population stratification.
In fact, population stratification is a manifestation of confounding (Fig. 1). Classically, confounding is the distortion of the relationship between the exposure of interest and disease due to the effect of a true risk factor that is related to the exposure. Similarly, population stratification is the distortion of the relationship between a genotype of interest and disease due to the effect of a true risk factor that is related to the genotype. In population stratification, ethnicity acts as a surrogate for the true risk factor, which may be environmental or genetic; as such, controlling for ethnicity can reduce the confounding bias. For example, the misleading association in the chopsticks example presented above, where both the genotype and the phenotype are distributed differently in Americans of Chinese origin than in those of European origin, would be greatly reduced by controlling for ethnicity.
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METHODS |
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Properties of the CRR
The CRR can be used to determine whether E, the genotype of interest, is related to risk of disease without bias from a confounder C. CRR is defined as the ratio of the risk ratio RRp obtained from pooling over (i.e., by ignoring) the confounder C to the risk ratio RR obtained after adjusting for the confounder C. Thus, the CRR is equal to 1 when there is no bias, including specifically the situations where the genotype is unrelated to the true risk factor. A CRR of 0.9 or 1.1 means that the pooled estimate of the risk ratio from the genotype is 10% lower or 10% higher than the adjusted risk ratio, respectively. In general, the CRR can be expressed [p. 96 in (10)], as in equation 1:
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where C has K levels k = 1 through K, E of 1 or 0 indicates the presence or absence of the genotype, respectively, and RRk, is the ratio of Rk, the risk of disease in ethnic group k, relative to R1, the risk in ethnic group 1 when E = 0. Equation 1 defines the expression of CRR as the ratio of the crude and adjusted estimates; equation 2
, below, shows that the CRR is a ratio of weighted averages of the rate ratios specific to each level of C (8).
Equation 2 applies generally to the bias from confounding by any factor. To estimate the confounding bias from population stratification due to ethnicity in an analytic study of a genotype and cancer, we re-express CRR in terms of data parameters that we are able to obtain, particularly, Pr (E|C = k), the proportions of population with an allele of interest, and Rk, the disease incidence rates in level k. In particular, we obtain equation 2
below from equation 1
by replacing RRk with Rk/R1 (justified by the definition of rate ratio) and Pr (C = k|E= i) (i can be equal to 0 or 1) with Pr (E = i|C = k)Pr (C = k)/Pr (E = i) (justified by Bayes theorem):
![]() | (2) |
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That is, the CRR is again expressed as a ratio of two weighted averages of level-specific rates. The weights in the numerator Pr(E = 1) and denominator Pr(E = 0) of CRR are complements of one another, i.e., the proportions of the population with and without the genotype of interest and in level k of C, respectively.
Equation 2 shows clearly that the extent of the bias measured by CRR depends on the variability of both the disease rates Rk and the genotype frequencies across the K levels of the confounder C. Remarkably, however, no measure of the strength of the genotypedisease relationship appears in equation 2
; indeed, the CRR is not affected by whether or not the genotype itself is related to disease. Although incidence rates of a disease with a genotype that is a major determinant of risk might track with the prevalence of the genotype across levels of the confounder, the amount of confounding (and the CRR) is based on the cancer rates of those without the genotype of interest and is, therefore, unaffected by the risk associated with the genotype. For simplicity, our empirical investigation uses the readily available national cancer-incidence rates, which are weighted averages of the cancer rates in individuals with and without the genotype (11).
Empirical Study of N-Acetyltransferase 2 Gene Slow Acetylators and Male Bladder Cancer and Female Breast Cancer
We use the CRR to estimate the bias from population stratification in a study of a genotype and cancer in the United States that did not account for ethnicity at all. With the use of equation 2, we estimate the CRR, the ratio of the rate ratios obtained by dividing the rate ratio for cancer obtained from a hypothetic analytic study that pooled immigrants from different countries and their descendants by the rate ratio adjusted for the country of ancestry. We make two simplifying and conservative assumptions to quantify the bias from population stratification in studies in the United States: 1) that there is no intermarriage across ethnic groups among Americans of European descent and 2) that the genotype frequencies and the cancer rates among these groups are the same as in their country of ancestry.
For our empirical study, we focus on the effect of being a slow acetylator due to mutations in the NAT2 gene on cancer risk. The NAT2 genotype is characterized phenotypically (by measuring the extent of acetylation of a drug by this enzyme) or by direct analysis of DNA. Below, we refer to "NAT2 slow acetylators," regardless of how the determination was made. We chose to study NAT2 acetylation because there is some evidence that slow acetylators may be at elevated risk of developing cancer (12) and because of the availability in the literature of extensive international data on the frequency of this genotype. We chose to study bladder cancer incidence in men and breast cancer incidence in women; NAT2 slow acetylators are believed to be at increased risk of bladder cancer (12) but not of breast cancer (13). For determining the proportion of the population with confounder level k, i.e., Pr (C = k), we use information on "first ancestry" based on the first ethnicity reported to the U.S. census (14) (also available from URL http://venus.census.gov/cdrom/lookup/922371159) to determine the numbers of American descendants of immigrants from the eight European countries. These ancestries were chosen because they represent the top eight fractions of non-Hispanics of European origin in the United States. We obtained cancer incidence rates, Rk, from a registry for each country included in Cancer in Five Continents (11) and frequency of NAT2 slow acetylators from a published study from each of these countries: Germany (15), Ireland (16), England (17), Italy (18), France (19), Scotland (20), Poland (21), and Sweden (22). We used published data on frequency of slow acetylators in the eight countries to determine Pr (E = 1|C = k) for our calculations (Table 2), with C being the confounder with eight levels corresponding to K = 8 countries and E = 1 indicating an NAT2 slow acetylator.
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Theoretical Study of Bias From Population Stratification
We also performed some theoretic calculations using equation 2 to estimate the bias from population stratification when a genotype is unrelated to cancer risk. We investigate the CRR over a wide variety of ranges of genotype frequencies and of rates of disease. We first focus on ranges that are representative of those found in European populations from which most non-Hispanic Americans descend and then expand to values that represent populations that are even more diverse. For this analysis, we assume that there are eight strata of equal size in the population, with a specified range of allele frequencies and relative rates of disease, spaced to be equidistant on a logistic and logarithmic scale, respectively.
Of the five genotype frequency ranges (GFRs) we studied, four (0.0010.10, 0.010.20, 0.100.40, and 0.300.60) are broadly representative of the range of frequencies of different alleles for a large number of genes reported by Cavalli-Sforza et al. (23) in Europe (excluding ethnicities not found in the United States in substantial numbers, such as Lapps and Basques). The other GFR (0.010.99) is more extreme. Of the range of six rate ratio ranges (RRRs) that we studied, RRRs of 11.5, 12, and 13 represent realistic values for the range of cancer rates among European countries (11); a relative rate of 3 is probably a very conservative upper bound in any two European-American ethnic groups present in the United States for several generations. To demonstrate what can happen in an extreme case, perhaps for an outcome other than cancer, we also considered RRRs of 1 : 10 and 1 : 100.
For each hypothesized pair of values of GFR and RRR, we calculate the lowest and the highest possible CRR using any two genotype frequencies and any two rate ratios from the set of eight. These represent the worst-case scenarios for a study of two ethnic groups, with the most extreme differences in genotype frequencies and disease rates from each set of GFRs and RRRs. We also consider the 8! = 40 320 CRRs from each possible permutation of the genotype frequencies in the eight groups. We calculate the geometric mean and the largest and smallest of the 40 320 CRRs as well as the 10th, 50th, and 90th percentiles. (See Table 4 for results.)
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RESULTS |
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We present the CRRs calculated for a study of NAT2 slow acetylation phenotype/genotype and male bladder cancer or female breast cancer in Table 3. The qualitative impressions of bias are almost the same for male bladder cancer or female breast cancer throughout. When the actual acetylation frequencies are used, the CRRs (ratios of the rate ratios from a study that ignored ethnicity to one that adjusted for ethnicity under our assumptions) are very close to unity (Table 3
). When the range of the acetylation frequency is stretched or expanded artificially (Fig. 2
, B), the CRRs are slightly higher but still too small to affect the qualitative conclusions of a study in a major way. The CRR was also close to 1 (0.978) when allele frequencies calculated by subtracting 45% from the actual ones were used (resulting in a range of 6%20%; see Table 2
). None of the 40 320 possible permutations, or pairings of acetylation frequency and cancer rates, lead to appreciable bias; with census weights, the range of the CRR is 0.951.06 for male bladder cancer and 0.981.02 for female breast cancer (data not shown). When no weighting is used, the bias is most extreme (data not shown) for the permutations where the relationship between acetylation frequency and cancer rate has the most extreme rank associations (Fig. 3
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Effect of Number of Ethnicities
Fig. 4 shows the maximum and minimum bias, as measured by the CRR, over all subsets of sizes k = 18 among the K = 8 ethnicities by use of census weights. Note that the most extreme bias is for k = 2 and k = 3 and that the bias becomes closer to 1 as the number of ethnic groups in the populations increases.
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Table 4 shows the effect of the variability of genotype frequencies and cancer rates over a wider range of scenarios than the empirical example. As before, we consider the range of possible CRRs when a population is a mixture of eight distinct populations; we also assume that the cancer rates and genotype frequencies are spaced equidistantly within a specified range on the logarithmic and logistic scales. For example, in Table 4
, the CRR ranges between 0.89 and 1.12, where the ratio of the highest to the lowest rate of disease is 2 and the genotype frequencies range from 0.1 to 0.4. Table 4
demonstrates that, when cancer rates are the same across ethnic groups (i.e., RRR = 1.01.0), the CRR is 1.0 and there is no bias, regardless of the difference in genotype frequencies. As observed previously, the worst bias for two-ethnic group comparisons is always greater than when eight ethnic groups are compared. The CRRs for the GFRs and RRRs that might exist in a population of non-Hispanic American Caucasians descended from different European countries is almost always usually under 10%. The most extreme CRRs that are realistic for European-Americans are only 0.78 and 1.22 (see Table 4
), corresponding to RRR of 1.003.00 and GFR of 0.0010.10. Furthermore, these extremes always occur when there was maximum rank correlation (monotonicity) between genotype frequency and the RR. Even this is tempered by the observation that the CRR is 1.00 when the genotype frequencies and relative rates are independent and that the median and geometric mean of the CRR over all possible orderings are always 1.00. While the extreme values of CRR are somewhat larger for GFRs and RRRs that are unrealistic for Americans of European origin, the geometric means and medians remain at 1.00. Furthermore, the vast majority of the simulations show CRRs to be much closer to 1.00 than the extreme values. Changing the spacing of genotype frequencies to a linear scale does not alter the impression of Table 4
(data not shown).
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DISCUSSION |
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The results presented here indicate that the following set of conditions must be met to have important bias from population stratification when there is truly no effect of the allele. 1) The frequency of the genotype of interest varies substantially by ethnicity. 2) The cancer rate varies substantially by ethnicity. 3) The cancer rates and genotype frequencies vary together; this can only happen in a study of multiple ethnic groups when the genotype is related to a true risk factor with attributable risk so high as to explain much of the international variability. When there is little or no association, the bias is clearly small on average (Table 4). 4) The risk factors truly responsible for the variation in cancer rates across ethnicity are unknown or information about it is unavailable; if data on these risk factors were available, they could be used in the analysis, thereby reducing or eliminating the bias. 5) The investigators are unable to distinguish among ethnic groups with different genotype frequencies and cancer rates, even crudely. Even if all of these conditions are met in a single study and, in fact, produce substantial bias, the results will probably not be replicated in a distinctly different study population because the same conditions are unlikely to exist.
A genotype may not cause cancer, yet it may still be strongly related to cancer rate across ethnicities (point 3 above) if the genotype frequency varies with a true risk factor across populations. For example, an allele with a strong NorthSouth frequency gradient in Europe would be associated with drinking beer instead of wine or with the amount of olive oil consumed; if one of these is an important risk factor for the cancer under study, there could be some bias, even if the allele is not causally related to beer or olive oil consumption. This is the scenario, as shown in Fig. 1, of a risk factor for disease noncausally related to the allele frequency, leading to bias in assessment of the allelecancer relationship. The bias in these examples can be reduced, however, by the standard epidemiologic tools for controlling confounding, such as adjustment for wine or olive oil consumption.
In our quantification of bias, the true impact of population stratification is exaggerated rather than underestimated by the conservative assumptions we made. We assumed that the American descendants of Europeans have the same cancer rates as current residents of their country of ancestry. In fact, cancer rates of the descendants of migrants approach those of their new country of residence in subsequent generations as their lifestyles become more similar to those of their neighbors (25). For example, some of the difference in bladder cancer rates among European countries could be because of smoking black versus blond tobacco. Since there is almost no smoking of black tobacco in the United States, it could not be an important cause of interethnic differences in the United States. In addition, we did not allow for any adjustment of international differences in cancer rates by known risk factors, which would be controlled for in a well-conducted epidemiolgic study. Finally, we assumed no intermarriage across descendants from different European ethnic groups. The cancer rates and the allele frequencies in those of mixed ancestry will lie between those of their parents, leading to less variability and, therefore, less bias.
One important and previously unrecognized conclusion from our study is that ethnic diversity actually reduces the bias from population stratification. With homogeneity (K = 1 ethnic group), there is no opportunity for confounding; K = 2 and K = 3 are the worst situations, and then with K = 48, the CRR moves closer to 1 as the number of ethnic groups increases further. Why is this so? We know that the direction for confounding bias from any group is positive when the genotype frequency and cancer rates are both above or both below the overall frequencies and rates; it is negative when one is above and the other is below. When there are only two ethnic groups, there is only one direction of bias. As the number of groups increases, however, the relationship between genotype frequency and cancer rate will not be monotonic or even be associated in many situations; in these instances, confounding from each group will tend to cancel as some groups contribute positive confounding and others contribute negative confounding; thus, overall, the effect of the additional ethnic groups is likely to dampen the bias. Since equation 2 applies within each ethnicity as well as among ethnicities, it is unlikely that microstratification, or residual confounding from further stratification within ethnic groups, will have a major effect.
We have focused primarily on bias from population stratification in studies of descendants of Europeans who immigrated to the United States. In studies that include, but fail to distinguish among, descendants of immigrants from Africa, Asia, and Europe, we would expect larger differences in allele frequency but a dampening of differences in cancer rates from the country of origin to prevailing U.S. rates. As Table 4 shows, even with a threefold difference in cancer rates across eight groups, the amount of bias would be modest in most circumstances, even for a range of genotype frequency of 1%99%. Even a crude adjustment for region of origin would reduce bias further. When there is admixture within these groups, the amount of bias is likely to be even less; however, the precise quantification of the bias is difficult because of the paucity of data.
If bias from population stratification is so small, why has the issue been so controversial? Concern for population stratification seems to have originated in part with the Pima Indian example (6). However, there the frequency of the genetic variant is 75% and the disease rate 15% in those of pure tribal descent in contrast to 1% and 60% in those with no tribal ancestry (Table 1); these are extreme differences in disease rate and in allele frequency. Also, only two ethnic groups are considered. Even so, the bias factor from population stratification is only 0.64. In any case, if the rate of disease varies strongly by ethnicity, standard practice in epidemiology would be to focus not on the crude association but instead on the estimate of effect adjusted for ethnicity. Furthermore, there has also been speculation that the inconsistent association between the D2 dopamine receptor locus DRD2 and alcoholism (26), which has rates of disease that may vary more than cancer by ethnic group, is a consequence of population stratification (27); however, a design flaw in the original study or chance is probably a more likely explanation than population stratification for the failure of subsequent studies to confirm the association (27).
In addition, theoretical arguments have overstated the evidence for important bias from population stratification. One attempt to assess bias considered scenarios with mixtures of only two groups and with differences in genotype frequencies and disease rates that are unlikely to be applicable to studies of common variants in the cancer setting (3). Furthermore, it is tempting to infer that any bias that exists in a study of two ethnic groups will be amplified when additional distinct groups are included; we show that, in fact, the bias tends to become smaller. Also, some argue that ethnic groups can be difficult to distinguish; we think that major bias from population stratification is unlikely when this is the case because only ethnic groups that maintain their individual identities are likely to remain endogamous and retain any important differences in genotype frequencies and cancer rates. Finally, Ewens and Spielman (28) assert that the usual chi-square association statistic is "not an appropriate test" of the hypothesis of no association in subdivided populations. But, in fact, the bias in the test statistic will not be large when the CRR is small. Just as the success of epidemiology in identifying environmental causes of cancer has been achieved without perfectly valid models, so too can epidemiologic studies that incorporate genetic as well as environmental factors tolerate some slightly biased test statistics.
Some (3) have raised population stratification as a threat to the study of geneenvironment interaction. The interaction between a genotype and a dichotomous factor on a multiplicative scale is the ratio of the odds ratios in the levels. If the CRRs in the strata are all near 1 or all of similar magnitudes, the distortion of the estimate of interaction will be small. When the magnitudes of the bias are large and in opposite directions for some strata, the distortion in the estimate of the interaction may be larger; it is difficult, however, to conceive a realistic situation for this scenario.
We have focused on the bias in estimation, not on hypothesis testing. The CRR is a way to evaluate theoretically the possible direction and extent of bias in a given study of an allele and disease; for example, it can be used to argue that population stratification should not be a concern when the magnitude of the alleledisease effect is greater than the worst-case CRR. The probability of a resulting false-positive finding (i.e., type I error) does depend on the magnitude of the bias, the prevalence of the genotype of interest, and the sample size. With a large enough sample size, any positive bias will lead to statistical significance. However, assessment of causality requires consideration of the estimate of effect as well as significance.
Our results suggest that bias from population stratification is unlikely to be substantial when an epidemiologic study of common genetic polymorphisms and cancer is properly designed, conducted, and analyzed. In general, cancer researchers choosing the best setting and most appropriate design for a study of the effect of a common specific genotype on risk of cancer should be more concerned about ascertainment of case patients, selection of control subjects, response rates, power, cost, and statistical efficiency than about population stratification.
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NOTES |
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Manuscript received October 15, 1999; revised May 12, 2000; accepted May 16, 2000.
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