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The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 57:B129-B133 (2002)
© 2002 The Gerontological Society of America

A Case-Only Approach for Assessing Gene by Sex Interaction in Human Longevity

Qihua Tana, Anatoli I. Yashina, Else M. Bladbjergb, Moniek P.M. de Maatb, Karen Andersen-Ranbergc, Bernard Jeunec, Kaare Christensenc and James W. Vaupela

a Max Planck Institute for Demographic Research, Rostock, Germany
b Department of Thrombosis Research, University of Southern Denmark–Odense University and Department of Clinical Biochemistry, Ribe County Hospital, Esbjerg, Denmark
c Department of Epidemiology, Institute of Public Health, and Aging Research Center, University of Southern Denmark–Odense University

Anatoli I. Yashin, Max Planck Institute for Demographic Research, Doberaner Strasse 114, 18057 Rostock, Germany E-mail: Yashin{at}demogr.mpg.de.

Decision Editor: John A. Faulkner, PhD


   Abstract
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 Abstract
Methods
 Examples
 Discussion
 Appendix
 References
 
As one aspect of the complex feature of longevity, gene by sex interaction plays an important role in influencing human life span. With advances in molecular genetics, more studies aimed at assessing gene by sex interaction are expected. New and valid statistical methods are needed. In this article, we introduce a nontraditional approach, the case-only design, which was originally proposed for assessing gene and disease associations, to detect gene by sex interaction in human longevity. Applications of this method to data collected from centenarian studies show that it can produce consistent results as compared with results obtained from case-control and other approaches. The method cannot be used as a substitute for traditional case-control studies since it is limited to the detection of interactions only. However, the easily applicable case-only approach can be an important tool for screening many potential genes that contribute to human longevity.

AGREAT deal of interest has been generated in the study of genetic influences on human longevity because of rapid developments in molecular genetics (1). In recent literature, the gene by sex interaction arises as an important phenomenon in the genetic modulation of human life span. For example, Ivanova and colleagues (2) reported on the correlation between HLA-DR7 and longevity, with an elevated frequency of DR7 in long-lived men. De Benedictis and colleagues (3) observed a significant decrease in the frequency of the tyrosine hydroxylase (THO) large allele group (alleles 9, 10-1, 10) in male Italian centenarians, but not in females. As concerning statistical analysis, a conventional gene frequency method based on the case-control design has been used (2)(3)(4). A relative risk approach that combines sex-specific population survival distributions has been proposed and applied to data from cross-sectional studies to detect the risk of gene alone as well as the risk of gene by sex interaction that potentially contribute to human life-span heterogeneity (5)(6). Comparisons between the two approaches have been made (5)(7)(8) that reveal a better performance for the latter, because it makes full use of individual genetic as well as survival information. However, both approaches have difficulty in dealing with crucial issues that originate from the cross-sectional design. Spurious conclusions could be made when improper control is chosen. In this article, we introduce a nontraditional approach, the case-only method, which was originally designed for analyzing gene by environment (9)(10)(11) and gene by gene (12) interactions in disease etiology to detect gene by sex interaction in human longevity when centenarians were treated as cases. This approach appears to have greater precision and requires fewer case subjects than the traditional case-control study when the primary interest is in gene by sex interaction (9)(11)(13). We show that the same method is also a valid approach that gives consistent results on reported gene by sex interactions from previous gene longevity association studies. Special issues that come up when the model is applied to the longevity studies are discussed, with advantages of the application highlighted.


   Methods
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 Abstract
 Methods
Examples
 Discussion
 Appendix
 References
 
Suppose that we are interested in analyzing the genetic influence on longevity that is sex dependent by using case-control design. We can display our data in a 2 x 4 table (Table 1 ). In Table 1 , we classify the genotype as presence (1 or 2 alleles) or absence (0 allele) of the susceptible gene. We also assign 1 for males and 0 for females. Using females without the susceptible allele as the reference group, we can calculate the odds ratio for the other groups with different sex and genotype compositions. In Table 1 , OR01 is the odds ratio for female carriers as compared with female noncarriers of the allele or, in other words, the effect of the gene alone; OR10 is the odds ratio for sex; OR11 is the odds ratio for the combined effect for both sex and genotype. The case-only odds ratio (Table 2 ) can be calculated as the cross-product

(1)
where ORco is the control-only odds ratio, b11b00/b10b01. Assuming that the susceptible genotype and sex are independent and that the event (longevity) the interaction is associated with is rare, then ORco becomes unity (see the A), and we can rewrite 1 as

(2)


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  		Table 1. Gene by Sex Interaction Based on Case-Control Design

 

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  		Table 2. Case-Only 2 x 2 Table Classified by Genotype and Sex

 
Here 2 means that the case-only odds ratio measures the departure from multiplicative joint effect of the genotype and sex or, in other words, the effect of gene by sex interaction. The null hypothesis for this approach is H0:ORca = 1. Any statistically significant deviation of ORca from unity indicates that there is a gene by sex interaction that contributes to and modifies the probability of achieving longevity. By comparing variances of the maximum likelihood estimate of the logarithm of 1 and 2, Piegorsch and colleagues (9) concluded that the case-only study has increased precision in estimating interactions because the variance corresponding to 1 involves an extra component for ORco, the control-only odds ratio.

A statistical test for the null hypothesis can be conducted by using the log likelihood ratio (LLR) test by calculating twice the difference between the log likelihoods at ORca = 1 and at ORca estimated. When the sample size is large, the LLR is approximately distributed as {chi}2 on one degree of freedom. Alternatively, we can apply the standard {chi}2 statistic to test the null hypothesis (Table 2 ), that is, {chi}2 = [n..(a11a00 - a10a01)2]/(n1.n2.n.1n.2) with one degree of freedom. Here n1., n2., n.1, n.2 is the marginal sum of the observations by sex and by genotype, n.. is the total sum of the observations (cases). The {chi}2 statistic with continuity correction can also be applied but is not recommended (14). For a significant ORca, confidence intervals can be constructed. The procedure is first to construct a confidence interval for the natural log of ORca and then to exponentiate the boundaries to get the confidence intervals for ORca. The standard error of ln(ORca) is given by

Because the natural log of the odds ratio is more normally distributed than the odds ratio itself, we can use the critical values of the standard normal distribution for calculating the intervals.


   Examples
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Discussion
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Cardiovascular Disease Associated Genes and Longevity
In order to explore if genes involved in the etiology of cardiovascular disease are also associated with human longevity, a cross-sectional investigation was conducted in Denmark with blood samples taken from controls (healthy young subjects) and centenarians (15). Results from the data analysis show that there is no significant influence on longevity from each of the genes alone (6)(15). However, a reanalysis of the data with consideration of gene by sex interaction has revealed that three genetic polymorphisms, angiotensinogen M/T235, FVII R/Q353, and FVII–323ins10, manifest significant sex-dependent effects that are favorable to the longevity of males (6). When the risk of female carriers was set to 1, the relative risks for male carriers of angiotensinogen M235, FVII Q353, and FVII–323p10 alleles were estimated as 0.67, 0.68, and 0.69, respectively. All are highly significant. Applying the case-only approach to centenarian data on the three alleles, we got consistent results as shown in Table 3 . The odds ratios for the 3 alleles are 2.519 for angiotensinogen M235 (p = .013), 2.353 for FVII Q353 (p = .038), 2.305 for FVII–323p10 (p = 0.037). All are significantly different from unity, which means that male centenarians are more likely to carry these mutants than female centenarians. The results suggest that these mutant alleles might convey gene by sex interactions that are beneficial to male survival. We also tried to do the same calculation on other genes tested in the study but no further gene by sex interaction was found.


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  		Table 3. Case-Only Approach for Assessing Gene by Sex Interactions in the Danish Centenarian Study

 
Although the results are compatible, the previous analysis by Tan and colleagues (6) relies on the proportional hazard assumption, which may not be an appropriate approach because it ignores the possible antagonistic genetic effect in the process of aging. This problem is avoided in the case-only study because we are drawing our conclusions only from the centenarians.

HLA-DR7 and Human Longevity
In an effort to examine the contribution of HLA-DRB1 polymorphisms to human longevity, a case-control study was set up in France (2). A total of 533 centenarians (89 males and 444 females) were pooled for the study (Table 4 ). The allele frequency of HLA-DR7 was observed at 14% in the control group but at 21.9% in male and 14% in female centenarians. When allele frequency differences were compared between centenarians and the control group, the HLA-DR7 allele frequency was found to be significantly increased in male but not in female centenarians; OR = 1.72, 95% confidence interval (CI) 1.19–2.5, p = .004 for males. The conclusion was that the DR7 allele has a beneficial effect on male longevity (2). Here we examine the sex-dependent influence of HLA-DR7 by applying the case-only approach. Table 4 is arranged in complete conformity with Table 2 , with numbers calculated according to the allele frequency and total number of centenarians available from the article (2). The case-only odds ratio is estimated as 1.816 (p = .013) with a 95% CI from 1.129 to 2.923. This result again indicates that the HLA-DR7 allele favors male longevity, which is compatible with the conclusion drawn from the case-control approach.


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  		Table 4. Case-Only Approach for Assessing Gene by Sex Interactions for the HLA-DR7 Allele in French Centenarians

 

   Discussion
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 Abstract
 Methods
 Examples
 Discussion
Appendix
 References
 
As one aspect of the complex feature of human longevity, the gene by sex interaction is an important phenomenon that should be addressed. The rapid advance in molecular technology is leading to the relative ease of searching for a large number of DNA markers at several candidate gene loci. With large amounts of individual genetic information available, new and efficient statistical methods are needed to help search for important genes that play crucial roles in the various pathways constituting the network of human longevity. In this regard, the easily applicable case-only approach can serve as a valid and useful way for screening gene by sex interactions in human longevity. Because the case-only approach does not use control subjects, crucial issues in the choice of an appropriate control group that have been perplexing with regard to case-control study are avoided (10). This is important because the improper choice of a control group could lead to spurious conclusions that distort the study. In addition, this approach has greater precision in estimating interactions than the traditional case-control design (9)(11)(13). However, there are important assumptions that underlie the application of the model (9)(10)(16)(17).

First, in order to apply this method, researchers must assume that sex and the genotype are independent. This assumption holds for any autosomal genes because their segregation does not depend on sex. However, one must note that for sex-linked genes, such an application definitely violates the basic assumption. When our primary interest is gene by sex interaction, such a valid assumption is much preferable to the weak assumptions underlining the traditional case-control study, such as no population stratification (for example, cases and controls are ethnically different), no cohort effects, and so on.

Second, the event (longevity) associated with gene by sex interaction should be rare. The study of longevity fits into this assumption because longevity by definition is always a rare event. It was estimated that there were approximately 44 centenarians per million population in the developed countries in 1990 (18). Although the number is increasing very rapidly (19), according to a United Nations' prediction, in the year 2050 centenarians will comprise approximately 1% of the total population in Japan, which has the highest number of centenarians in the world. Schmidt and Schaid (20) showed that the cross-product computed from case-only data may be substantially smaller than the odds ratio calculated from a case-control study. This would underestimate the true effect when the risk of event associated with the gene is relatively high. Fortunately, we do not have to worry about the problem in a longevity study because we are always dealing with the small proportion in the population who managed to achieve extraordinarily long lives.

Because the context of the centenarian study fits into the case-only approach for assessing gene by sex interaction, we believe that the method is valid and should be promoted. However, one has to keep in mind that the case-only approach makes sense only when the primary interest is in estimating the possible sex-dependent effect from the susceptible gene. The odds ratio estimated from the case-only approach measures only the departure of the overall effect of both the gene in question and sex from the multiplicative effect. Because no effect of gene or sex alone is estimated in this approach, it does not provide any definite information on the survival of particular genotype carriers. Thus, although the case-only approach for assessing gene by sex interaction in longevity can be used as a tool for preliminary screening of many candidate genes, it cannot be used as a substitute for the traditional case-control studies. A better strategy could be that after screening the candidate genes for gene by sex interaction, we can then fit survival models to the data and estimate survival functions for males and for females separately (5)(6). In this way, application of this easily applicable method can help to rapidly increase efficiency for future longevity studies. Also, it is necessary to point out that, like other association studies, the case-only approach also has difficulty in the situation when linkage disequilibrium exists (10)(16). The detected interaction could be due to the fact that the marker is in linkage disequilibrium with the real gene that is relevant to longevity. Nevertheless, such an association approach can complement future research aimed at localizing the specific gene loci. At this point, one also has to be aware that, by longevity relevant genes, we only mean those genes whose action increases physiological capacity or reserve and thus indirectly increases the potential of longevity (21)(22), because there is no gene that is solely responsible for longevity.

The importance of independence between exposure (sex in our context) and genotype in applying this method has been addressed by previous researchers (10)(17). Recently, Albert and colleagues (23) showed that inferences from the case-only design can be highly distorted when there is departure from the independence assumption. Although in the context of gene by sex interaction, such an assumption holds provided the genes of interest are autosomal, caution has to be paid when we want to apply the same approach to study gene by environment interactions (Table 5 ). In the latter situation, especially when the environment relates to the geographical allocation, it is important to check the ethnic origin of the populations to make sure that the assumption is satisfied. The choice of subject in the case-only study should follow the usual rules of case selection for any case-control study (16)(24). However, given the importance of centenarian studies, the case-only approach is a promising tool for finding important genes that contribute to human health and longevity.


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  		Table 5. Case-Only Approach for Assessing Gene by Environment Interaction for Simulated Data

 


   Acknowledgments
 
We are thankful to G. De Benedictis from the Cell Biology Department, University of Calabria, Rende, Italy and to Jinhua Zhao from the Department of Psychological Medicine, Institute of Psychiatry, St. Bartholomew's and Royal London School of Medicine and Dentistry for useful discussions. We also thank Dr. Karl Brehmer for help in preparing the manuscript.

Received April 17, 2001

Accepted November 8, 2001


   Appendix
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 Abstract
 Methods
 Examples
 Discussion
 Appendix
References
 
In accordance with Table 1 , let S = 1 stand for males and S = 0 for females, and let G = 1 stand for carriers of the susceptible genotype and G = 0 for noncarriers of the genotype. Let L stand for cases (longevity) and for controls. By treating sex as an outcome and following Piegorsch and colleagues (9), we find that the control-only odds ratio is

(3)

The independence between genotype and sex means

(4)

In 4, P(S =1| G = 1) = P(S = 1| , G = 1)P(| G = 1) + P(S = 1| L, G = 1)P(L| G = 1). Because longevity is a rare event, P(L| G = 1) {approx} 0 and P(| G = 1) {approx} 1. Then we have P(S = 1| G = 1) {approx} P(S = 1| , G = 0). Do the same for the rest in 4 and substitute to yield


   References
Top
 Abstract
 Methods
 Examples
 Discussion
 Appendix
 References
 

  1. De Benedictis G, Tan Q, Jeune B, et al. 2001. Recent advances in human gene-longevity association studies. Mech Ageing Dev. 122:909-920. [Medline]
  2. Ivanova R, Henon N, Lepage V, Charron D, Vicaut E, Schachter F, 1998. HLA-DR alleles display sex-dependent effects on survival and discriminate between individual and familial longevity. Hum Mol Genet. 7:187-194. [Abstract/Free Full Text]
  3. De Benedictis G, Carotenuto L, Carrieri G, et al. 1998. Gene/longevity association studies at four autosomal loci (REN, THO, PARP, SOD2). Eur J Hum Genet. 6:534-541. [Medline]
  4. Heijmans BT, Gussekloo J, Kluft C, et al. 1999. Mortality risk in men is associated with a common mutation in the methylene-tetrahydrofolate reductase gene (MTHFR). Eur J Hum Genet. 7: (2) 197-204. [Medline]
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  7. Yashin AI, De Benedictis G, Vaupel JW, et al. 1999. Genes, demography, and life span: the contribution of demographic data in genetic studies on aging and longevity. Am J Hum Genet. 65:1178-1193. [Medline]
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  9. Piegorsch WW, Weinberg CR, Taylor JA, 1994. Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies. Stat Med. 13: (2) 153-162. [Medline]
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