represent heritability in the narrow sense when considering full siblings because one has to take into account dominance variance, as well. See Hartl and Clark (1997) for a more thorough discussion of using the covariance between two relatives to estimate heritability.
Rice and colleagues (1997) extended this approach to incorporate correlations from multiple relative pairs (rsib, siblings; rp‐o, parent–offspring; rsp, spousal):
Example Using Correlation Coefficients to Calculate Heritability
In a large study that assessed the genetic contribution to normal variation of pulmonary function, Wilk and colleagues (2000) calculated familial correlations for spouses, parent–offspring pairs, and siblings from 455 Caucasian families for forced expiratory volume (FEV1; a measure of airflow), forced vital capacity (FVC; a measure of lung volume), and the ratio of FEV/FVC and using formula 3.6, obtained heritability estimates for the three traits (Table 3.4).
Correlations for a trait among monozygotic and dizygotic twins can also be used to calculate heritability:
(3.7)
Heritability estimates can be quite useful for data mining of a phenotype prior to initiating a genome scan. For example, if several phenotypic measures for a condition have been collected, heritability estimates may provide guidance as to which of those measures will be most useful for genetic analysis. That is, those phenotypes with the highest h2 values should be prioritized for analysis.
Table 3.4 Familial correlation and heritability estimates of pulmonary function.
Source: Wilk et al. (2000, table II).
| Trait | r sib | r p‐o | r sp | h 2 |
|---|---|---|---|---|
| FEV1 | 0.259 | 0.239 | −0.067 | 0.52 |
| FVC | 0.257 | 0.242 | −0.135 | 0.54 |
| FEV1/FVC ratio | 0.27 | 0.19 | 0.071 | 0.45 |
With the advent of Genome‐Wide Association Study (GWAS), the concept of “missing heritability” was coined to describe the difference between the estimated heritability and the amount of heritability attributable to genome‐wide significant loci detected through GWAS (Manolio et al. 2009). From this observation, methods to estimate heritability using genome‐wide SNP data emerged such that one could calculate the “SNP heritability,” suggesting that additional SNP loci not meeting genome‐wide significance contribute to the missing heritability. The most widely used of these methods include genomic‐relatedness‐matrix restricted maximum likelihood (GREML) (Yang et al. 2010) which is implemented in GCTA software (Yang et al. 2011), linkage disequilibrium score regression (LDSR) (Bulik‐Sullivan et al. 2015), and LD‐adjusted kinships (LDAK) (Speed et al. 2017). A good review of genome‐wide heritability estimation can be found in Hall and Bush (2016).
Segregation Analysis
Segregation analysis is a modeling tool that is used to examine the patterns of disease in families and determine if the patterns are indicative of traditional genetic inheritance models (such as autosomal dominant, autosomal recessive, and polygenic) or are more consistent with nongenetic (environmental) models (Elston 1981; Morton 1982; Lalouel 1984). The likelihood of the data to fit a particular inheritance model is computed. By comparing the likelihood of several models, one can determine which model provides the “best fit” to the data. Segregation analysis does not prove that a particular inheritance model is correct but will determine if the data are consistent with that inheritance model.
The advantage of segregation analysis is that it can provide an inheritance model and parameters that may be used in parametric linkage analysis. However, generally segregation analysis can only model 1–2 loci, which may not be very useful for most complex diseases. That is, if none of the inheritance models examined in the segregation analysis can adequately accommodate the complexities of the underlying inheritance model of the disorder, even the “best‐fitting” model will not provide much information.
Additionally, this approach is extremely sensitive to ascertainment bias. In genetic analysis, families are often collected based on the presence of many affected individuals. Thus, for segregation analysis, there may be a high proportion of families with numerous affected individuals that are used in the analysis, when in reality these types of families only make up a small percentage of the disease population and most cases may be observed in families with only one or two affected individuals. For example, the probability that an affected individual will be ascertained as a proband is π, and when π = 1, all the individuals in the study population who have the condition have been ascertained. This is referred to as “complete ascertainment.” When the probability that an affected individual is a proband is very low (π approaches 0), each sibship is expected to have only a single proband. This is called “single ascertainment.” With this latter ascertainment approach, the probability that a family will come to the investigator’s attention, and be included in the study, is related to the number of affected individuals in the family. That is, the more affected the individuals in the family, the higher the likelihood that this particular family will be ascertained, thus introducing a biased distribution of family types in the analysis.
If one does not correct for the method in which the families were ascertained, the estimate of the segregation probability of the disease allele can be biased, which can affect the “best‐fitting” genetic model. In some cases, the ascertainment bias may be so great that it causes the investigator to incorrectly conclude that the disorder is consistent with a single‐gene model (Greenberg 1986). For a discussion on approaches for correcting ascertainment bias, see Khoury et al. (1993).
There are several analytic approaches to segregation analysis, each with its strengths and weaknesses. The most commonly used methods include the mixed model (Morton and MacLean 1974; Lalouel and Morton 1981; MacLean et al. 1984), the transmission probability model (Elston and Stewart 1971), the unified model (Lalouel et al. 1983) which draws on the strengths of both the mixed and transmission probability models, and the regressive model (Bonney 1984). All of these approaches are computationally intensive but are available for use in several software packages such as POINTER (Lalouel and Morton 1981), SAGE (http://darwin.cwru.edu/sage/) and PAP (Hasstedt 1993).
Segregation analysis is not widely used in the evaluation of complex diseases because it is susceptible to the presence of genetic heterogeneity, phenocopies, gene–gene and gene–environment interactions, which are quite difficult to model. Consequently, segregation analysis results that support the
