The Calculation of Target Height Reconsidered

Objective: To correct the calculation of target height (TH) for assortative mating and parent-offspring correlations. Methods: Define the standard deviation score (SDS) of TH as the mean parental height SDS: TH SDS = (Father SDS + Mother SDS)2. This needs correcting for assortative mating and regression bias, using r(P,P) the parent-parent correlation and r(P,O) the parent-offspring correlation. Together they give the conditional target height (cTH SDS):cTH SDS=TH SDS x r(P,O) x 2/(1+ +r(P,P))+ error where the error term has mean 0 and standard deviation 1 - r(P,O) 2 . Results: We assume r(P,P) = 0.27 and r(P,O) = 0.57, based on the Swedish data of Luo et al. Pediatr Res 1998;44:563-571, so that: cTH SDS = TH SDS x 0.57 x √2/(1 + 0.27) = TH SDS x 0.72 with a 95% confidence interval of ′1.6 SDS units. The formula is independent of sex, and if parental height SDS is obtained from growth charts dating back one generation, the formula is also independent of secular height changes. Conclusions: cTH SDS is equal to only 0.72 times the average of father's and mother's height SDS. Current practice ignores this scaling factor, so that the children of short parents are ascribed a TH which is as much as 4 cm too low. This will tend to exaggerate the benefits of growth-promoting therapies.