Sex Ratio and Proportion of Affected Sons in Sibships with X-Chromosomal Recessive Traits: Maximum Likelihood Estimation in Truncated Multinomial Distributions

Abstract

If mothers are carriers of a recessive male sex-linked disorder, their children may include females, healthy males and affected males. The composition of the possible sibships follows a multinomial distribution. If the mothers are diagnosed as carriers independently of their offspring, then the distributions are not truncated, but if they are classified as carriers after the birth of at least one affected son, the distributions are truncated. In order to avoid ascertainment bias, the statistical analyses of the corresponding data must differ. We present procedures for estimation in both the untruncated and the truncated case. The formulae obtained are applied to family data for X-chromosomal recessive retinoschisis (RS) from the region of Satakunta in southwestern Finland. Earlier studies indicated that, among the offspring of RS carriers, the sex ratio was increased. In our model, therefore, we include both the proportion of males and the proportion of affected individuals among the males. The sex ratio was significantly increased (131.0), but the proportion of affected males was slightly lower than expected (42.5%). RS seems to be the only known genetic disorder in which the offspring of carriers of the mutation include a statistically significant surplus of males.

Sex Ratio in Sibships With Twins

“…The SEs of mean proportions obtained for heterogeneous groups are less than the SEs for homogeneous ones (Fellman & Eriksson, 2002). Consequently, in our study, the CIs are too long, and the strengths of the significance are less than if heterogeneity had been considered.…”

“…With the methods used in the 1960s, we noted a marked excess of males within families with X-linked retinoschisis, but normal sex ratios in the X-linked recessive disorders haemophilia and colour blindness (Eriksson et al, 1967). However, with the exception of the X-linked recessive retinoschisis data expanded and tested with more advanced statistical methods (Fellman et al, , 2002Huopaniemi et al, 1999), there are no unequivocal examples of genes in man that affect the sex ratio. Summing up, to the best of our knowledge, the only genetic characteristic observed to have a marked influence on the sex ratio within families is X-linked retinoschisis.…”

Secondary Sex Ratio in Multiple Births

“…In this study, we present alternative CIs and a new χ 2 test. Variations in the SR that have been reliably identified in family data have in general been slight and without notable influence on national birth registers (for references, see Fellman et al, 2002;Fellman & Eriksson, 2008).…”

Temporal Trends in the Secondary Sex Ratio in Nordic Countries

“…We noted a marked excess of males but, in contrast, normal SRs in other X-linked recessive disorders such as hemophilia and color blindness (Eriksson et al 1967). However, with the exception of the X-linked recessive retinoschisis confirmed by us with expanded data and more advanced statistical methods (Fellman et al , 2002Huopaniemi et al, 1999), no unequivocal examples of genes in man that affect the SR exist.…”

“…Garenne's findings of rather high SR levels differ slightly from the findings presented by Visaria (1967) and Chahnazarian (1988Chahnazarian ( , 1990), but the heterogeneity observed supported Visaria's statement. Sieff (1990) presented an extensive review, including references, concerning factors influencing the SR. Variations in the SR that have been reliably identified in family data have generally been slight and without a notable influence on national birth registers (for references, see Fellman, Eriksson, and Forsius 2002;Eriksson 2008, 2010).…”