tables of death counts per calendar year and per year of birth and of birth counts per year, as reported for Italy in the Human Mortality Database (www.mortality.org). To take into account the dramatic changes in mortality that the cohorts under study experienced we used a synthetic survival function S(x) computed from the cohort survival functions as described in (29). In the text that follows, the term ‘‘synthetic’’ will be dropped for brevity. Because data are available both for male and female subpopulations, distinct survival functions were computed for the two genders. If we regard the population (whole, male, or female) as consisting of carriers of A allele (AA and AG genotypes) and noncarriers of A allele (GG genotypes), we can define the survival functions S (x) and S (x) of carriers A B and noncarriers, respectively. The relationships between S (x), S (x), S(x), and the age-related frequencies of A B carriers and noncarriers can be found in (29). The marginal survival functions S (x) and S (x) were estimated from the A B genotypes and ages of the individuals in the sample by maximizing an appropriate likelihood (29). The null hypothesis S (x) ¼ S (x) ¼ S(x), which means that the A B TNF(A/G)-308 polymorphism does not affect survival, was tested by using the likelihood ratio. Because in this case the probability distribution of the ratio is not known, it was empirically built up by Monte Carlo simulation (29) (1000 virtual samples). A Matlab (MathWorks, Natick, MA) code described in (29) was used for all the above analyses.

R ESULTS

GD Analysis of Survival Functions

categorized according to the presence or absence in the genotype of the A allele at the TNF(A/G)–308 locus. In particular, we estimated the survival function of carriers (AA plus AG) and noncarriers (GG) of the A allele, thus assuming that AA and AG genotypes have a comparable effect on the survival phenotype (dominance of the A allele). This consideration came from literature data that report a functional role of the allele A associated with a higher expression of TNF-a (11–13). Furthermore, as the survival function is sex-specific, the analysis was carried out in men and women separately. Figure 1 shows the maximum likelihood estimates of the survival functions in male carriers and noncarriers of allele A (AA plus AG genotypes and GG genotype, respectively). At all ages, the survival function estimated in the A carriers (S (x)) was A lower than that in the noncarriers (S (x)); furthermore, the B null hypothesis S (x) ¼ S (x) ¼ S(x), where S(x) is the A B survival function estimated in the whole male population, was rejected with an empirical probability level of p ¼ .044. In women, the survival functions of Aþ and A– participants were not significantly different from that of the population (p ¼ .16; data not shown). Therefore, the data indicated a dominant, detrimental effect of allele A on survival, present in men but not in women.

To compare gene and/or haplotype frequencies between age classes, we defined three sex-specific age classes: for men [women], the first class consists of individuals ,66 years old [,73 years old], the second class of individuals 66–88 years old [73–91 years old], the third class of individuals .88 years old [.91 years old]. These classes have been introduced in (30), where the rationale of the choice is widely discussed. In brief, considering the shape of the survival function S(x) (both in women and men) we can observe that it is characterized by changes of the curvature. Therefore, the limit between the youngest class and the intermediate class can be chosen as the age at which the curvature of the graph is negative and has the largest abso- lute value (formally, the age corresponding to the minimum value of the second derivative S99(x) of the survival function). Equivalently, the limit between the intermediate class and the oldest class was chosen as the age at which the curvature of the graph is positive and has the largest absolute value (formally, the age at which the second derivative S99(x) of the survival function attains the maxi- mum value). Note that the age classes defined according to this criterion are gender-specific and account for the dif- ferent survival of men and women in the Italian population.

Three age classes were defined on the basis of demo- graphic information as described in Methods, and the allele and genotype frequency distributions of the TNF(A/G)-308 polymorphism were compared among the classes (Table 2). A significant frequency variation was observed in men, with a progressive tendency to a decrease of Aþ participants in the older classes (from 27.7% in class 1, to 22.2% in class 2, to 10.7% in class 3, p ¼ .019); similarly, a decrease of the A allele in classes of increasing age was also observed (p¼.028). No significant difference was observed in women (p . .05 for both genotypes and alleles).

Allele and genotype frequencies were estimated within each age class by allele and/or genotype count. An expec- tation maximization (EM) algorithm, implemented in the Arlequin software package (35), was used to obtain maxi- mum likelihood estimation of multilocus haplotype fre- quencies the standard deviations of which were calculated by bootstrap resampling (1000 replications). Pairwise link- age disequilibrium was tested by using a likelihood ratio test

Haplotype Analysis

To check if the detrimental effect of the A allele observed in men did involve a particular haplotype, three microsatellites (TNFa, TNFc, TNFe) located in the TNF genomic region were analyzed in addition to the TNF(A/G)-308 marker. First, Hardy–Weinberg equilibrium was verified for each single microsatellite (TNFa: p¼.18; TNFc: p¼.62; TNFe: p¼.26).

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