Human mtDNA codes for 13 essential polypeptide components of the mitochondrial respiratory chain that generates the principal source of intracellular energy, ATP (DiMauro and Schon 2003). mtDNA is inherited almost exclusively through the maternal line and is highly polymorphic. Human populations can be divided into several mtDNA haplogroups on the basis of specific SNPs scattered throughout the mitochondrial genome, reflecting mutations accumulated by a discrete maternal lineage. Each mtDNA haplogroup forms a mutually exclusive category (Torroni and Wallace 1994). Among Europeans, 95% of the population belongs to 1 of 10 haplogroups: H, I, J, K, M, T, U, V, W, and X (Torroni et al. 1996). Given the fundamental role of the mitochondrial genome in cellular metabolism, there have been a number of studies investigating the association between mtDNA lineages and multifactorial diseases and aging (e.g., De Benedictis et al. 1999; Ruiz-Pesini et al. 2000; Carrieri et al. 2001; Niemi et al. 2003; Mancuso et al. 2004; van der Walt et al. 2004). Despite initially promising results, often reaching high levels of statistical significance (α), it has rarely been possible to replicate the findings of the original reports. There are a number of explanations for the inconsistency, including difficulties in matching cases and controls and when there is a genuine variation in the size of a genetic effect in different populations. However, the consistent inability to reproduce the original result brings into question the power of individual studies.

The standard statistical method for analyzing haplogroup distributions is to use a 2×N_H contingency table and the χ² test, where N_H is the number of haplogroups. However, low counts in the less common haplogroups will tend to inflate the χ² value and lead to a false-positive result (Roff and Bentzen 1989). This can been tackled in one of two ways, either by performing Fisher’s exact test for each haplogroup in turn, with an appropriate correction for multiple significance testing, or by grouping the less frequent haplogroups. Both approaches potentially mask a real difference between two haplotypes, particularly if they are uncommon in the general population. In addition, correcting for multiple significance testing is not straightforward, since each haplogroup frequency is dependent on the others. To address this problem, we developed a Monte Carlo permutation test to determine the exact type I error (false-positive rate) associated with a specific data set under study. (See the “Methods” section in appendix A.) This Monte Carlo permutation test has the advantage that it is not dependent on any prior assumptions about the distribution of the data or the number of haplogroups under study. We then compared the results of the Monte Carlo simulations with the results of a number of published studies.

In most cases, direct simulation generated a level of significance (α) that was greater than the theoretical value based on an assumed null χ² distribution (table 1). For some studies, the simulated result was not significant by conventional criteria. As expected, these studies were thorough in determining the frequency of rare haplogroups (defined as <5% of controls). However, because of the limited study size, a number of haplotype groups contained fewer than five individuals. The simulations confirmed that, under these circumstances, the χ² value is artificially elevated, and tabulated values of χ² should not be used to determine statistical significance. This problem can be avoided by applying Cochran’s “rule of thumb” that no expected frequency be <1 and that ⩽20% of the expected frequencies be <5 (Cochran 1954). If the results of a study do not comply with this rule, then direct simulation provides an unbiased and reliable alternative. This is often the case for mtDNA association studies, in which 6 of the 10 European haplogroups are each found in <10% of the population but account for 17% of the total (Torroni et al. 1996).

We used a Monte Carlo simulation to determine the power to detect a difference between cases and controls at different levels of significance, on the basis of the known distribution of the 10 major European haplogroups (Torroni et al. 1996) (see fig. 1 for examples). We simulated both increases and decreases in the frequency of a each haplogroup, with the difference distributed proportionally between the remaining haplogroups, thus simulating a typical exploratory mtDNA haplogroup study for which there is no a priori assumption of an association with any one specific haplogroup. Figure 2A shows simulated data for five haplogroups, at α=.05. As this plot shows, the power values do not have a simple relationship with the raw number of cases and controls. In figure 2B, we normalize the X-axis, using a relationship derived from standard binomial theory (Armitage et al. 2002), and show that there is a simple relationship between the power and the normalized number of cases and controls. These results were compared with the theoretical curve for two haplogroups (fig. 2B for α=.05; fig. A1 for α=.01 and α=.001). The curve described by the simulation data for the 10 European haplogroups was similar in shape to the theoretical 2×2 curve (corresponding to 2 haplogroups) but was displaced to the right. To explore the effect of different numbers of haplogroups on the position power curve, we then simulated other theoretical haplogroup distributions within the population (2, 5, or 20 discrete categories). These subdivisions could correspond to superhaplogroups, haplogroup clusters, or any mutually exclusive sequence variants in any population. The entire data set collapsed to a single universal curve when the X-axis was normalized by the number of haplogroups, N_H, raised to the power 0.37, by use of the expression

where N_c is the number of cases with a disease (assumed to be equal to the number of controls), p₀ is the frequency of the haplogroup in the control population, and p₁ is the frequency of the haplogroup in the disease group (fig. 2C for α=.05; fig. A2 for α=.01 and α=.001). The power ± SD (0.37±0.01) was determined by the standard approach of curve fitting. For the European haplogroup data studied here, N_H=11, reflecting additional category “other” for individuals not belonging to the 10 major haplogroups.

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Figure 1

Examples of mtDNA haplogroup power curves determined by simulation—haplogroup H (A), haplogroup J (B), and haplogroup I (C)—on the basis of control data for the European population. The abscissa shows the number of cases and controls simulated (e.g., 400 = 400 cases and 400 controls). Black squares/solid line = .05 significance level; green circles/dashed line = .01 significance level; red triangles/dotted line = .001 significance level. The figures on the graph describe the percentage change in haplogroup frequency associated with a particular group of curves; for example, 100%↑ = haplogroup increases by 100%, with the remaining cases distributed evenly over the remaining nine haplogroups. For clarity, only the .05 level data is shown for haplogroup I.

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Figure 2

The power to detect an association between mtDNA haplogroups and disease. In all situations, the number of disease cases is assumed to be equal to the number of control subjects. A, Monte Carlo simulation data for the European haplogroups H, I, J, K, and U. Data from the individual simulations, including those shown in figure 1, are shown on the same graph for different changes in the percentage level of a particular haplogroup at the α=.05 significance level. This demonstrates the scatter of the data points. B, These data collapse onto a simple sigmoid curve, with the X-axis scaling based on standard binomial theory. N_c is the number of disease cases (equal to the number of controls), p₀ is the frequency of the haplogroup in the control population, and p₁ is the frequency of the haplogroup in the cases. Data are shown for the significance level α=.05 (for α=.01 and α=.001, see fig. A1). Both the data and the theoretical curve describe the same sigmoidal shape, with the European haplogroup simulation data (with the 10 major European haplogroups plus “others” being equivalent to a 2×11 table) shifted to the right. C, Simulations (symbols) and theoretical 2×2 curve (red line) for populations with different numbers of mutually exclusive haplogroups. The simulated subdivisions could correspond to superhaplogroups, haplogroup clusters, or any mutually exclusive sequence variants in any population. All of the data collapse onto a single curve when the X-axis is normalized by the number of haplogroups, N_H, raised to the power 0.37 (eq. [1]). Data are shown for the significance level α=.05 (for α=.01 and α=.001, see figure A2). D, Example showing the number of cases and controls required to generate 90% power at the .05 significance level for a study of the 10 major European haplogroups (N_H=11 to account for the <5% that do not fall into these 10 groups and are considered “others”). Haplogroup proportions in the control group are based on published values (haplogroup H=0.41 in controls [black line]; I=.02 in controls [blue line]; J=.11 in controls [red line]) (Torroni et al. 1996).

Equation (1) can be used to determine the minimum number of disease cases (N_Cmin) and control subjects required for a specific level of power,

by use of the scaling value, N_scaled, derived from the universal curves at each significance level α (table 2). Ninety percent power is achieved when N_scaled is 8.5 for α=.05, 11 for α=.01, and 14 for α=.001, as derived from figure 2C (table 3). This approach can be used for any number of mutually exclusive genotypes in any population (fig. 3). Resolving equation (2) in terms of the odds ratio (OR) is complex, but equation (2) can be used by determining the proportion of cases that correspond to a specific OR for a given haplogroup, by use of the standard equation

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Figure 3

Algorithm to determine the power of an mtDNA haplogroup association study at a given level of statistical significance. The algorithm is based on the assumption that no specific haplogroup is suspected of being associated with a disease. α = statistical significance; N_H = the number of haplogroups (mutually exclusive genotypes) in a given study; p₀ = the frequency of the allele in control subjects; p₁ = the frequency of the allele in individuals with the disease; N_Cmin = the minimum number of cases to generate a given power.

The ORs, based on one published control data set (Torroni et al. 1996), corresponding to percentage changes in haplogroup frequency for the 10 European haplogroups are shown in tables ​tablesA1A1 and ​andA2.A2. An example of this approach is given in figure 2D, with use of the European haplogroup distribution for 90% power at α=.05. These results also show the limited power of moderate study sizes. With no prior reason to suspect an association with haplogroup H, ∼6,000 cases and ∼6,000 controls are required to form a study with 90% power to detect a 10% change in the frequency of haplogroup H in European populations (corresponding to an OR >1.18). Studies with only 500 cases and 500 controls would have only 90% power to detect >35% increase in the frequency of haplogroup H, corresponding to an OR >1.75. For less common haplogroups or more-subtle changes in haplogroup frequency, even greater sample sizes will be required (fig. 2D).

mtDNA is inherited almost exclusively down the maternal line and undergoes little, if any, intermolecular recombination. This makes the haplotype distribution in a given sample exquisitely sensitive to minor population genetic bottlenecks, which lead to differences in haplogroup frequency over short geographical distances. These factors increase the chance of detecting a spurious difference between cases and controls (false-positive or type I error). The standard approach to this problem is to consider the first study result as preliminary and to then generate a hypothesis that should be tested on an independent cohort. Here, we present a single equation that can be applied to mtDNA haplogroup studies around the globe, enabling a priori power calculations for exploratory or confirmatory studies. However, subtle changes in haplogroup frequency will require massive cohorts. In some populations, the frequency of mtDNA haplogroups in controls varies considerably over short geographic differences (Ghezzi et al. 2005), which makes it impossible to collect an adequately sized homogeneous study cohort, particularly for uncommon diseases. The same applies to population-genetics studies based on haplogroup comparisons between control populations across the globe, which have been used to deduce patterns of population migration (Mishmar et al. 2003; Ruiz-Pesini et al. 2004). These studies are equally likely to suffer from type I error, and they often show subtle differences in haplogroup frequency but require adequate sample sizes to demonstrate and confirm geographic differences in haplogroup distribution. An inability to reproduce the result with an adequately powered study would question the validity of the original result.