After a brief review of the use of latent variables to accommodate the correlation among multiple outcomes of mixed types, through theoretical and numerical calculation, the consequences of such a construction are quantified. The effects of including latent variables on marginal inference in these models are contrasted with the situation for jointly normal outcomes. A simulation study illustrates the efficiency and reduction in bias gains possible in using joint models, and analysis of an example from the field of osteoarthritis illustrates potential practical differences.
McCulloch CE, Searle SRGeneralized, linear and mixed models. Wiley, 2000.
3.
Ritz J., Spiegelman D.A note about the equivalence of conditional and marginal regression models . Statistical Methods in Medical Research2004; 13: 309—23.
4.
Arminger G., Kusters U.Latent trait models with indicators of mixed measurement level. In Langeheine R, Rost J eds. Latent trait and latent class models. Plenum, 1988: 51—73.
5.
Wu MC, Carroll RJEstimation and comparison of changes in the presence of informative right censoring by modeling the censoring process (Corr: V45 P1347; V47 P357) . Biometrics1988; 44: 175—88.
6.
Pawitan Y., Self S.Modeling disease marker processes in AIDS. Journal of the American Statistical Association1993; 88: 719—26.
7.
Tsiatis AA, DeGruttola V., Wulfsohn MSModeling the relationship of survival to longitudinal data measured with error. Applications to survival and CD4 counts in patients with AIDS . Journal of the American Statistical Association1995; 90: 27—37.
8.
Wulfsohn MS, Tsiatis AAA joint model for survival and longitudinal data measured with error . Biometrics1997; 53: 330—9.
9.
Wang Y., Taylor JMG.Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association2001; 96(455): 895—905.
10.
Lin H., Turnbull B., McCulloch C., Slate E.Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. Journal of the American Statistical Association2002; 93: 1124—9.
11.
Catalano PJ , Scharfstein DO, Ryan LM, Kimmel CA, Kimmel GLStatistical model for fetal death, fetal weight, and malformation in developmental toxicity studies. Teratology1993; 47: 281—90.
12.
Regan MM, Catalano PJLikelihood models for clustered binary and continuous outcomes: application to developmental toxicology. Biometrics1999 ; 55: 760—8.
13.
Geys H., Regan MM, Catalano PJ, Molenberghs G.Two latent variable risk assessment approaches for mixed continuous and discrete outcomes from developmental toxicity data. Journal of Agricultural, Biological, and Environmental Statistics2001; 6(3): 340—55.
14.
Yu ZF, Catalano PJQuantitative risk assessment for multivariate continuous outcomes with application to neurotoxicology: the bivariate case. Biometrics2005; 61(3): 757—66.
15.
Fitzmaurice G., Laird N.Regression models for a bivariate discrete and continuous outcome with clustering. Journal of the American Statistical Association1995; 90: 845—52.
16.
Dunson D.Bayesian latent variable models for clustered mixed outcomes. Journal of the Royal Statistical Society, Series B2000; 62: 355—66.
17.
Dunson D., Herring A.Bayesian latent variable models for mixed discrete outcomes. Biostatistics2005; 6: 11—25.
18.
Catalano P.Bivariate modelling of clustered continuous and ordered categorical outcomes. Statistics in Medicine1997; 16: 883—900.
19.
Speiss M.Estimation of a two-equation panel model with mixed continuous and ordered categorical outcomes and missing data. Applied Statistics2006; 55: 525—38.
20.
Sorensen J. , Dilley J., London J., Okin R., Delucchi K., Phibbs C.Case management for substance abusers with HIV/AIDS: a randomized clinical trial. The American Journal of Drug and Alcohol Abuse2003; 29(1): 133—50.
21.
Masson C., Sorensen J., Phibbs C., Okin R.Predictors of medical service utilization among individuals with co-occurring HIV infection and substance abuse disorders. AIDS Care2004; 16(6): 744—55.
22.
Beck A., Steer R.Manual for the revised Beck Depression Inventory. Psychological Corporation, 1987.
23.
Bellamy N.WOMAC osteoarthritis user's guide. Victoria Hospital , 1995.
24.
Link TM, Steinbach L., Ghosh S., Ries M., Lane N., Majumdar S.Osteoarthritis: MR imaging findings in different stages of disease and correlation with clinical findings. Radiology2003; 226: 373—81.
25.
Little R., Rubin D.Statistical analysis with missing data. Wiley, 2002.
26.
Johnson NL, Kotz S., Balakrishnan N.Continuous univariate distributions, second edition. Wiley, 1995.
27.
Qu Y., Williams GW, Beck GJ, Medendorp SVLatent variable models for clustered dichotomous data with multiple subclusters . Biometrics1992; 48: 1095—102.
28.
Chan KS, Ledolter J.Monte Carlo EM estimation for time series models involving counts . Journal of the American Statistical Association1995; 90: 242—52.
29.
McCulloch C. , Lin H., Slate E., Turnbull B.Discovering subpopulation structure with latent class models. Statistics in Medicine2002; 21: 417—29.
30.
Laird NMMissing data in longitudinal studies. Statistics in Medicine1988; 7: 305—15.
31.
Rabe-Hesketh S., Skrondal A., Pickles A.Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects . Journal of Econometrics2005; 128: 301—23.
32.
Lesaffre E. , Molenberghs G.Multivariate probit analysis: a neglected procedure in medical statistics. Statistics in Medicine1991; 10: 1391—403.
33.
Fitzmaurice G., Laird N.Regression models for a mixed discrete and continuous responses with potentially missing values. Biometrics1997; 53: 110—222.
34.
Gueorguieva R., Agresti A.A correlated probit model for joint modeling of clustered binary and continuous responses. Journal of the American Statistical Association2001; 96(455): 1102—12.
35.
Gueorguieva R., Sanacora G.Joint analysis of repeatedly observed continuous and ordinal measures of disease severity. Statistics in Medicine2006; 25: 1307—22.