Disorders are often conceptualized as the extreme end of continuous traits, eg in ADHD (1). However, many scales used to capture the traits focuses only on one part of the distribution –the negative symptoms. Thus, the distribution of the resulting scale contains a lot of “non-endorsers”, ie zeros – sometimes this is referred as the scale being zero-inflated. However, given the plausible belief that the scale is not capturing the entire variation of the trait, calling it left-censored is more appropriate. When analyzing this data, under assumption of a missing part of the distribution, and normality assumption, a so-called tobit transformation may be used (2). Another option is the polychoric correlation, or ordered probit model when referring to single outcomes, but has costs with regards to precision of estimates (2). To our knowledge, no description of straight-forward and easily implemented approaches to incorporate censored variables in a likelihood setting in structural equation models has been published. Thus, we suggest a general method to incorporate censored variables in quantitative genetic analyses in a likelihood setting, by deriving a re-statement of the likelihood through conditional probabilities. The re-statement of likelihood can be used for any type of structural equation model, including univariate and multivariate heritability models, where variables analyzed may be continuous, ordered categorical, or censored, or any combination thereof. Further, we will address the best normalizing transform in censored data within the Box-Cox-family of transformations. We will investigate the properties (ie, bias, precision, and power) in a series of simulations, and apply the method to estimate heritability of ADHD using the A-TAC questionnaire assessed in Swedish twins. We will also highlight the symmetric problem of right-censored data, such as survival data (i.e., time of an event happening), via a heritability analysis of time to cause-specific death in prostate cancer (3).
References:
1. Larsson H, Anckarsater H, Rastam M, Chang Z, Lichtenstein P. Childhood attention-deficit hyperactivity disorder as an extreme of a continuous trait: a quantitative genetic study of 8,500 twin pairs. Journal of child psychology and psychiatry, and allied disciplines. 2012;53(1):73-80.
2. van den Oord EJ, Simonoff E, Eaves LJ, Pickles A, Silberg J, Maes H. An evaluation of different approaches for behavior genetic analyses with psychiatric symptom scores. Behavior genetics. 2000;30(1):1-18.
3. Szulkin R, Clements MS, Magnusson PKE, Wiklund FE, Kuja-Halkola R. Estimating Heritability of Prostate Cancer-Specific Survival Using Population-Based Registers. Prostate. 2017;77(8):900-7.
