Methods for longitudinal studies with multiple outcomes, informative drop-out and censoring: a study in cognitive decline
The proposed work aims to develop statistical methodology for longitudinal studies which simultaneously involve informative drop-out, censored observations (floors, ceilings or interval-censored) and multiple outcomes of different types (survival times, discrete or continuous repeated measures). The new statistical methods will be illustrated by undertaking analysis of the University of Manchester Longitudinal Study of Cognition, a longitudinal study that was established with the scope of examining the nature, time course, extent and aetiology of changes in cognitive function in old age. This will provide answers to a number of important substantive questions in the field of cognitive decline, depression and Alzheimer’s disease in elderly people. In particular, the project will model the causal/temporal relationship between cognitive decline and depression in older age and will elucidate the relation over time between cognitive decline or depression and onset of Alzheimer’s disease. The new methodology will be implemented into a statistical program which is freely downloadable from the internet.
Duration of the project
1 July 2008 - 31 July 2009
Economic and Social Research Council (ESRC)
Members of the project
|Dr Milena Falcaro||Principal investigator|
|Professor Andrew Pickles||Co-investigator|
|Professor Neil Pendleton||Collaborator|
Aims of the project
The research project will focus on methodology but will deliver substantive results as a valuable by-product. More specifically, the broad objectives of the grant are the following.
• To generalise the Falcaro and Pickles’ method (Statistics in Medicine, 2007) to a range of multivariate problems involving longitudinal data with multiple outcomes, as well as selective drop-out and complex censoring patterns.
• To implement the new statistical methods into the freely available structural equations modelling program Mx. The possibility to implement the methodology in the commercial software Mplus will also be examined.
• To apply the new methodology to model the causal/temporal relationship between cognitive decline and depression in older age and to elucidate the relation over time between cognitive decline or depression and onset of pathological cognitive impairment.
Falcaro, M. and Pickles, A. (2007). A flexible model for multivariate interval-censored survival times with complex correlation structure. Statistics in Medicine 26, 663-680.
Muthén, L.K. and Muthén, B.O. (1998). Mplus User’s Guide. Fifth Edition. Muthén & Muthén, Los Angeles, CA.
Neale, M.C. et al. (2002). Mx: Statistical Modeling, 6th ed. Dept. of Psychiatry, Richmond, Virginia.
Rabbitt, P., Diggle, P., Horan et al. (2004). The University of Manchester longitudinal study of cognition in normal healthy old age, 1983 through 2003. Aging Neuropsychology and Cognition 11, 245-279.
• Analysing ordinal or censored longitudinal data with non-ignorable dropout. 7th Int. Amsterdam Multilevel Conference, 9-10 April 2009.
• Modelling censoring and non-ignorable missing data in Mplus. Mplus UK users meeting, Bristol, 8-9 June 2009. [mplus2009.ppt]
• Interval and non-ignorable censored observation of longitudinal cognitive data: Inferring abnormality in a context of developmental delay. 16th International Meeting of the Psychometric Society, Cambridge, 20-24 July 2009.
• Analysing censored longitudinal data with non-ignorable dropout (poster presentation). 16th International Meeting of the Psychometric Society, Cambridge, 20-24 July 2009. [Poster.ppt]
• Advanced methods of analysis for developmental data. Workshop presented at the Cognitive and Behavioural Development Centre, Birkbeck College, London, 21-25 September 2009.
Falcaro M., Pendleton N. and Pickles A. (2009). Analysing censored longitudinal data with non-ignorable missing values and individually-varying observation schedule: depression in older age. To be submitted to Journal of the Royal Statistical Society, series A.
Falcaro M. and Pickles A. (2009). Riskplot: a graphical aid to investigate the effect of multiple categorical risk factors. The Stata Journal, in Press.
Software to download
Mplus code (second-order latent growth models):
• Model for longitudinal data with non-ignorable missing values, individually-varying times of observation and floor effects (left censoring) [Second-order_LGM (floor).inp]
• Model for longitudinal data with non-ignorable missing values, individually-varying times of observation and ceiling effects (right censoring) [Second-order_LGM (ceiling).inp]
Mx code (second-order quadratic latent growth models):
• Model for longitudinal data with non-ignorable missing values, floor effects and individually-varying times of observation (see Falcaro et al., 2009) [QLGMfloor.mx]
• Model for longitudinal data with non-ignorable missing values, interval-censored observations, individually-varying time points and practice effects [QLGM_intcens_practice.mx]