Executive dysfunction is a deficiency in skills of planning and problem solving that characterizes many neuropsychiatric disorders. The Towers Task is a commonly used measure of planning and problem solving for assessing executive function. Towers Task data are usually zero-inflated and right-censored, and ignoring these features can result in biased inference for the disease characterization of executive dysfunction. In this manuscript, a mixed-effects model for longitudinal censored semicontinuous data is developed for analyzing longitudinal Towers Task data from the PREDICT-HD study. The model is contrasted with current practice, and implications for general use are discussed.
CulbertsonWZillmerE. Tower of London, Drexel University (TOL DX), Chicago, IL: Multi-Health System, 2001, 2005.
2.
KirkUKempSKorkmanM. NEPSY: A development neuropsychological assessment subtest administration, San Antonio, TX: The Psychological Corporation, 1998.
3.
SahakianBMorrisREvendenJ, et al.A comparative study of visuospatial memory and learning in Alzheimer-type dementia and Parkinson’s disease. Brain1998; 111: 695–718.
4.
GuevaraMMartinezLAguirreF. Prefrontal-parietal correlation during performance of the towers of Hanoi task in male children, adolescents and young adults. Dev Cogn Neurosi2012; 2: 129–138.
5.
Ruiz-DiazMHernandez-GonzalezMGuervaraM, et al.Prefrontal EEG correlation between EEG during Tower of Hanoi and WCST (Wisconsin Card Sorting Test): effect of emotional and visual stimuli. J Sex Med2012; 9: 2631–2640.
6.
ZookNDavalosDDeloshE, et al.Working memory, inhibition and fluid intelligence as predictors of performance on Tower of Hanoi and London tasks. Brain Cogn2004; 56: 286–292.
7.
SchulzeCSimmermannRGschwandtnerU, et al.Can cognitive deficits facilitate differential diagnosis between at-risk mental state for psychosis and depressive disorders?Early Interv Psychiatry7; 4: 381–390.
8.
BeaunieuxHEustacheFBussonP, et al.Cognitive procedural learning in early Alzheimer’s disease: imparied processes and compensatory mechanisms. J Neuropsychol2012; 6: 31–42.
9.
The Huntington’s Disease Collaborative Research Group. A novel gene containing a trinucleotide repeat that is expanded and unstable on Huntington’s disease chromosomes. Cell1993; 72: 971–983.
PennyJJVonsattelJMacDonaldE, et al.CAG repeat number governs the development rate of pathology in Huntington’s disease. Ann Neurol1997; 41: 689–692.
14.
OlsenMSchaferJ. A two-part random effects model for semicontinuous longitudinal data. J Am Stat Assoc2001; 96: 730–745.
15.
BerkKLachenbruchP. Repeated measures with zeros. Stat Methods Med Res2002; 11: 303–316.
16.
HallDZhangZ. Marginal models for zero inflated clustered data. Stat Model2004; 4: 161–180.
17.
LachenbruchP. Analysis of data with excess zeros. Stat Methods Med Res2002; 11: 297–302.
18.
LiuHChanK. Generalized additive models for zero-inflated data with partial constraints. Scand J Stat2011; 38: 650–665.
19.
TianL. Inferences on the mean of zero-inflated lognormal data: the generalized variable approach. Stat Med2005; 24: 3223–3232.
20.
TianLWuJ. Confidence intervals for the mean of lognormal data with excess zeros. Biomed J2006; 48: 149–156.
21.
ToozeJGrunwaldGJonesR. Analysis of repeated measures data with clumping at zero. Stat Methods Med Res2002; 11: 341–355.
22.
YauKLeeANgA. A zero-augmented gamma mixed model for longitudinal data with many zeros. Aust N Z J Stat2002; 44: 177–183.
23.
LawNTaylorJSandlerH. The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of a cure. Biostatistics2002; 3: 547–563.
24.
YuMLawNTaylorJ, et al.Joint longitudinal-survival-cure models and their application to prostate cancer. Stat Sinica2004; 14: 835–862.
25.
WeiL. The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. Stat Med1992; 11: 1871–1879.
26.
BuckleyJJamesI. Linear regression with censored data. Biometrika1979; 66: 429–436.
27.
AkaikeHInformation theory and an extension of the maximum likelihood principle. In: PetrovBNCsakiF (eds). Second international symposium on information theory, 1st ed. Budapest: Academiai Kiado, 1973, pp. 267–281.
28.
ZhangYLongJMillsJ, et al.Indexing disease progression at study entry with individual at-risk for Huntington disease. Am J Med Genet B: Neuropsychiatr Genet2011; 156: 751–763.
29.
SimonH. The functional equivalence of problem-solving skills. Cogn Psychol1975; 7: 268–288.
30.
ShalliceT. Specific impairments in planning. Philos Trans R Soc Lond Biol Sci1982; 298: 199–209.
31.
PappKSnyderPMillsJ, et al.Measuring executive dysfunction longitudinally and in relation to genetic burden, brain volumetrics, and depression in prodromal Huntington disease. Arch Clin Neuropsychol2013; 28: 156–158.
32.
TsengYHseihFWangJ. Joint modeling of accelerated failure time and longitudinal data. Biometrika2005; 92: 587–603.
