Sample3 SRC Proposal for AMS Conferences

Sample3 Proposal for a
Joint Summer Research Conference

1. Proposal submitted by:

Jane-Ling Wang
Department of Statistics
University of California
Davis, CA 95616
Tel. (530)752-7624
Fax: (530)752-7099
e-mail: wang@wald.ucdavis.edu

2. Title of proposed conference: Emerging Issues in Longitudinal Data Analysis

3. Organizing committee:

Marie Davidian (co-chair), North Carolina State University
Xihong Lin (co-chair), University of Michigan

4. Program information:

4.1. Proposed Program Motivation and Summary

With mounting advances in modern technology, more and more data are being recorded over a period of time on the same subject (or other experimental unit), leading to a data structure in which several observations are available on each of a number of subjects. Such data arise commonly in health sciences research and engineering research. Different terms have been applied to describe such data, e.g. they are often referred to as "longitudinal data" by statisticians in biomedical applications, where a small number of repeated measures over time per subject are often obtained, and as "functional data" in engineering and computational applications, where a large number of repeated measures over time per subject are available. Statistical approaches to analyze such data are also intrinsically different in the longitudinal and functional data research communities. One goal of this conference is to bring the two communities together to promote advances in both areas by allowing each to explore the alternative approaches of the other and by providing an opportunity for brainstorming on challenging problems of common interest.

Analysis of longitudinal data in the last decade has focused mainly on parametric GEE-based marginal models and random effects models, but recently the field has been challenged by new issues that require more complex and exible frameworks. Emerging new areas include nonparametric and semiparametric regression, joint modeling longitudinal and survival outcomes, methods for handling missing data, and approaches to making causal inference. These issues are of substantial importance in biological, biomedical, environmental and engineering studies. Although these four areas have enjoyed some significant developments in the past several years, there remain numerous open questions that are subject to debate and controversy.
Although the approaches and emphases may be different in each area, they share many related features. A second goal of this conference is to provide a forum for researchers in each of the four areas to debate the merits of various approaches and exploit insights from other areas to stimulate new ideas for addressing controversial issues.
Overall, it is hoped that the conference will provide a unique opportunity for researchers to be exposed to new ideas from different, but related, areas, stimulating new advances and new collaborations.
4.2 Scientific Narrative on the Four Research Areas
4.2.1 Nonparametric and Semiparametric Regression in Longitudinal Data
Nonparametric smoothing techniques such as kernels, local polynomial and splines are well-developed for independent data (Fan and Gijbels, 1996; Green and Silverman; 1994, Simono, 1996; and Wand and Jones, 1995), and have been implemented in standard software such as Splus. However, nonparametric smoothing/regression methods for longitudinal data are rather sparse, and have begun to emerge as practical and important tools with many challenges (Brumback and Rice, 1998; Hall et al., 2001; Hoover et. al, 1998; M*uller and Wang, 1998; Staniswalis and Lee, 1998; Rice and Wu, 2001). It was through a nonparametric approach that a mid-growth spur was first detected at age 7 for boys (Gasser et. al, 1984). Standard nonparametric methods often need to be adjusted for longitudinal data, e.g.. Rice and Silverman (1991) showed how cross validation should be applied properly to longitudinal/functional data.

Statistical properties of the nonparametric regression methods for longitudinal data also differ from those for independent data and those for parametric longitudinal models (Fan and Zhang, 2000; Hart and Wehrley, 1986, Lin and Carroll, 2000).
For marginal models, nonparametric regression using kernel methods has been investigated within the GEE framework (Wild and Yee, 1996; Wu et al., 1998). Spline methods have also been proposed using penalized likelihood methods (Berhane and Tibshirani, 1998; Welsh et al.2001). Most authors ignore the within-subject correlation when calculating kernel estimators.
Lin and Carroll (2000) provided theoretical evidence in support of this working independence method, showing that the most efficient kernel estimator of the nonparametric function is obtained by entirely ignoring the within-subject correlation. This is rather surprising as the most efficient estimators of parametric regression coefficients are obtained by accounting for the true within-subject correlation (Liang and Zeger, 1986).
An alternative framework for analyzing longitudinal data is random (mixed) effects models. Nonparametric regression methods have been investigated within this class of models (Chiou et al., 2000; Lin and Zhang, 1999; Rice and Wu, 2000; Wang, 1998; Zhang et al., 1998). A key computational advantage of using smoothing splines, variable knot splines or orthogonal series methods in random effects models is that these estimators can be written as a linear combination of fixed effects and random effects. As a consequence, a nonparametric mixed effects model can be formulated as an augmented parametric mixed effects model allowing implementation using the existing software for fitting standard mixed models, such as SASPROC MIXED and SAS GLIMMIX. However, the theoretical properties of these methods are more elusive than those based on kernel or local polynomial methods, and have not been investigated.
A common feature of longitudinal data is that the number of observations per subject is small while the number of subjects is large. By contrast, in functional data analysis (FDA), the number of observations per subject is often large. Nonparametric smoothing techniques are thus commonly used in functional data analysis to analyze such longitudinal data (Muller 1988; Ramsay and Silverman, 1997). However, large sample properties of the nonparametric procedures are still not well understood, and many issues remain open. One open issue is the time transformations (either as warping function or as stochastic latent time transformation), which are often necessary to register the data to retain landmark features of the structure (Gasser and Kneip, 1995; Capra and Muller, 1997; Muller et. al; 1997, Ramsay and Li, 1998). While the need to register data is now commonly known within the FDA community, it received less attention within the longitudinal data community. Conversely, methods to handle missing data are better understood by the longitudinal data community than the FDA community.
Many relevant statistical developments taking place in the two communities seem to be disconnected. Hence, the conference will serve to bring the two communities together to exchange ideas, explore each other's approaches, debate the merits of various approaches, and stimulate new research.
Compared to that on parametric and nonparametric regression, statistical research on semiparametric regression for longitudinal data is even less developed. Semiparametric regression models specify main covariate effects of interest (e.g., treatment) parametrically and some nuisance covariate effects (e.g., time) nonparametrically. Such approaches have emerged as promising alternatives to analyze longitudinal data by complementing fully parametric models
and fully nonparametric models. They provide robust inference on the covariate effects of major interest by making minimal assumptions on the effects of the nuisance covariates. However, statistical methods for fitting semiparametric longitudinal models are not well developed. Severini and Staniswalis (1994) considered profile-kernel GEE methods. Zeger and Diggle (1994) used the kernel method to estimate the nonparametric function by assuming working independence and then estimated the parametric covariate effects using the weighted least squares.
Their models was further explored by Lin and Ying (2001) by ignoring the within-subject correlation. Survival analysis techniques based on counting-process framework were employed to obtain theoretical results for semi-parametric longitudinal regression, opening the possibility of yet another approach. Recently, Lin and Carroll (2001) showed that if the profile-kernel GEE method is used, consistent estimators of the parametric covariate effects require ignoring the within-subject correlation or artificially undersmoothing the nonparametric function if the true correlation matrix is used. They derived the semiparametric efficient scores of the finite dimensional parameters. However, construction of the semiparametric efficient estimators of the finite-dimensional parameters is still an open question. A goal of the conference is to stimulate more research on statistical methods for semiparametric regression.
4.2.2 Joint Modeling of Longitudinal and Time-to-event Data

In many biomedical studies, a time to event, often a survival time, is observed along with other longitudinal data for each subject; e.g. a biomarker such as viral load is measured longitudinally for HIV patients along with survival status. A challenging problem is joint modeling of these data to elucidate the association between the two types of responses and to evaluate whether the longitudinal outcome is a good surrogate marker for survival. A common approach to such modeling is to assume that longitudinal and time-to-event outcomes are related to a latent process. Tsiatis et al. (1995) assumed a linear mixed model for the longitudinal outcome and regressed time-to-event on the random effects and other covariates (e.g., treatment) in the Cox model. Follmann and Wu (1995) and Henderson et al. (2000) assumed different but correlated random effects in the survival and longitudinal models.

Several approaches to estimation are possible. A two-step, "regression calibration" approach, in which one fits a mixed model at each risk set and substitutes best linear unbiased predictors for true random effects in the Cox model, is simple to implement but may lead to bias. Wulfsohn and Tsiatis (1997) used nonparametric maximum likelihood assuming normal random effects, jointly fitting the two models, where the baseline hazard is estimated by a step function with jumps at the distinct failure times. Bayesian methods for fitting these models were considered by Lin et al. (2000).
Research on joint modeling continues to present new challenges. Theoretical properties arestill unresolved. As longitudinal markers are rarely perfect surrogates as in Prentice (1988), interest often focuses on assessing the degree of surrogacy. Such measures have been proposed, e.g. proportion of treatment effect explained (Freedman, et al. 1992) and the relative effect (Buyse and Molenberghs, 1998), but whether these can be adapted within a joint model is an open question. A potential drawback of latent process modeling is the routine strong parametric assumptions made on the process; whether inference is sensitive to misspecification of this assumption is unknown. Semiparametric approaches that relax these assumptionshave been proposed recently (Tsiatis and Davidian, 2001; Song et al., 2001) but have not been compared or evaluated theoretically. Additional challenges include developing alternatives to latent variable models and new joint models in the presence of informative censoring, which is closely related to developments on modeling informatively missing longitudinal data, viewing the dropout time as survival. Some longitudinal processes are not well-modeled parametrically, so incorporation of more exible nonparametric random effects representations in joint models is called for. All these issues will be explored at the conference.
4.2.3 Modeling of Informatively Missing Data
A common problem in analyzing longitudinal data is that complete history of the data may not be available, e.g. because subjects drop out of studies or are not available to provide responses when required. Dropouts and other missing data such as missing covariates pose a great complication, as the pattern of missing data often carries useful information, and ignoring or mishandling this information may lead to biased inferences on quantities of interest. This is especially diifficult when the missingness may depend on the unobserved outcomes; i.e., the data are missing informatively. Valid statistical inference requires appropriate modeling of the missingness or dropout process.
Two classes of approaches have been proposed to model informatively missing longitudinal data: selection models (Diggle and Kenward, 1994) and pattern mixture models (Little, 1995). They differ in how the likelihood is factorized. Selection models specify the marginal distribu-tion of the longitudinal outcome and the conditional distribution of the dropout process giventhe longitudinal outcome. Hence, the regression coefficients have attractive interpretations.
However, inference in selection models is sensitive to modeling assumptions. Sensitivity analysis is often recommended (Verbeke, et al. 2001). Pattern mixture models, on the other hand, specify the conditional distributions of the longitudinal outcomes within each dropoutpattern. They make less modeling assumptions than selection models, but the interpretations of regression coefficients are less direct, since they are defined conditional on the dropout patterns. In addition to these parametric methods, semiparametric approaches have been developed. Robins and colleagues used estimating equations with inverse probability weights (Robins et al., 1995; Rotnitzky et al., 1995; Scharfstein et al., 1999) to model informatively missing dropouts. The conference will feature sessions discussing these approaches and directions for future research.
4.2.4 Causal Inference for Longitudinal Data
Many longitudinal studies are observational studies, where treatments of interest are not ran-domly assigned. Consequently, the regression coefficients in standard longitudinal regression models, such as GEEs or random effects models, often do not have causal interpretations; however, the objective of analysis is often to make inferences with a causal interpretation. Thus,causal inference for longitudinal data is an important, emerging area of research, and only very limited work has been done. It is of substantial interest to elucidate conditions under which causal inference may be made from longitudinal observational data and develop associated statistical methods.
Current approaches for causal inference in longitudinal studies are a matter of much debate and controversy. Causal inference is commonly based on the concept of counterfactuals (Rubin, 1978; Holland, 1986). However, their use has been recently challenged by Pearl (2000) and Dawid (2000). Compared to cross-sectional studies, causal inference in longitud inal studies is also subject to additional complications. In order for the model parameters to have causal interpretations, one needs to carefully formulate the models by appropriately conditioning on the whole past histories of the covariates and the outcomes (Robins et al., 1999). Structural nested models and marginal structural models have been proposed (Hern'an et al.,1999; Robins,1999). Another challenging problem in making causal inference in longitudinal studies is how to handle censoring by death (Rubin, 2000). In some longitudinal studies, the current treatment assignment depends on the past history of the outcome. It is of recent interest to investigate how to make causal inference in such dynamic regimen trials (Murphy et al., 2001). This conference will allow researchers in this field to exchange ideas and debate the merits of various approaches, and will hopefully expose other researchers to the area and stimulate new ideas.
4.3 Conference Description
The above four areas of research in longitudinal data are in an early or ongoing stage of development. They present researchers with many challenges and opportunities. Although some phenomenal work has been carried out in the past few years, many open questions still remain and controversial issues need to be resolved. The conference will provide a platform forresearchers to explore these areas in depth, discuss pros and cons of the existing methods, identify new research directions, and gain inspiration for new ideas. Moreover, it will serve as an effective educational opportunity for junior researchers who work in one of these areas, serving to introduce them to current developments and challenges in other areas and to provide a forum for them to interact with leading senior researchers.
We prefer a conference format that stimulates discussion and inspires ideas. The conference is planned to last for five days, with two days focusing on nonparametric and semiparametric regression and one day each on each of the other three topics. Each day will start with a one-hour expository lecture delivered by a keynote speaker, targeting graduate students and nonspecialists. The keynote speakers will provide an introduction to the topic area and discuss current status, challenges, and future directions. Keynote speakers for the four areas have been identified: (Note: The keynote speakers' name were included in the origonal proposal, but has been deleted from this sample for reasons of confidentiality.) A 20-25 minute discussion will then be provided by a panel of experts. The rest of the day will be devoted to 5 to 6
30-40-minute talks, with long breaks between sessions to allow for interaction and discussion among the participants. Some of these sessions may include a discussant.
On some evenings, there will be a presentation of a case study, with a description of the data-analytic challenges and of preliminary or ad hoc approaches taken so far. Floor discussion will follow the presentation to generate ideas to overcome these difficulties, which may in turn lead to new avenues of statistical research. Additional possibilities for the evening program include a round table discussion led by a panel of experts on a theme topic. We will also solicit data from conference participants and make them available to all participants in advance.
4.4 Partial list of Speakers
The following speakers have been invited. Those marked with an asterisk have already agreed to attend. (Note: This list, while included in the original proposal, has been delete from this sample for reasons of confidentiality.)
4.5 List of Other Participants:
About 30 people from the following list will be invited to participate in the conference. A largeportion of the following potential participants are junior researchers and graduate students. (Note: This list, while included in the original proposal, has been deleted from the sample for reasons of confidentiality.)
4.6 Recent Conferences in Related Areas

1. Modeling Longitudinal and Spatially Correlated Data: Methods, Applications and Future Directions. Nantucket, MA, 1996.

2. Conference on Models for Multilevel data. Chicago, IL, 1999.
3. Conference on Generalized Linear Mixed Models and Related Topics. University of Florida, Gainesville, FL, 1999.
4. Statistical Issues in PSA Modeling. Ann Arbor, MI, 1999.
5. Conference on Analyzing Longitudinal Data. University of Missouri, Columbia, MO 1998.
6. Conference on Modeling Informatively Missing Data. Texas A&M University, College Station, TX 1999.
7. Second Seattle Symposium in Biostatistics: Analysis of Correlated Data, Seattle, WA, 2000.
4.7 Budget and Estimated Attendance

We propose to cover a large portion of the local expenses for most of the approximately 60 to 75 invited participants. Participants with difficulties supporting their transportation expenses may receive additional support.

Bibliography

Berhane, K. and Tibshirani, R. J. (1998). Generalized additive models for longitudinal data. Canadian Journal of Statistics, 26, 517-535.

Brumback, B. A. and Rice, J. A. (1998). Smoothing Spline Models for the Analysis of Nested
and Crossed Samples of Curves (with discussion). Journal of the American Statistical Association, 93, 961-994.
Buyse, M. and Molenberghs, G. (1998). The Validation of Surrogate Endpoints in Randomized Experiments. Biometrics , 54, 1014-1029.
W.B. Capra, H.G. Muller (1997), An accelerated time model for response curves. J. American Statistical Association 92, 72-83.
Carroll, R. J., Ruppert, D. and Welsh, A. (1998). Local Estimating Equations. Journal of the American Statistical Association, 93, 214{227.
Chiou, J.M., Muller, H.G. and Wang, J.L. (2000). Functional quasi-likelihood regression models with smooth random effects. Preprint.
Dafni, U.G. and Tsiatis, A.A. (1998). Evaluating Surrogate Markers of Clinical Outcome When Measured with Error. Biometrics, 54, 1445-1462.
Daniels, M.J. and Hughes, M.D. (1997). Meta-analysis for the Evaluation of Surrogate Markers.Statistics in Medicine, 16, 1965-1982.
Dawid, A. P. (2000). Causal Inference Without Counterfactuals (with discussion). Journal of the American Statistical Association, 95, 407-444.
Diggle, P., and Kenward, M. G. (1994). Informative Dropout in Longitudinal Data Analysis (with discussion), Applied Statistics, 43, 49-94.
Diggle, P. J., Liang, K. Y. and Zeger, S. L. (1994). Analysis of Longitudinal Data, Oxford:Oxford University Press.
Diggle, P. J., and Hutchison, M. F. (1989). On Spline Smoothing with Autocorrelated Errors. Australian Journal of Statistics, 31, 166-168.
Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B{splines and penalties (with discussion). Statistical Science, 11, 89-121.
Fan, J. and Gijbels, I. (1996). Local Polynomial Modeling and its Applications. London: Chapman and Hall.
Fan, J. and Zhang, J.T. (2000). Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society, Series B, 62,303-322.
Faucett, C.J. and Thomas, D.C. (1996). Simultaneously Modeling Censored Survival Data and Repeated Measured Covariates: A Gibbs Sampling Approach. Statistics in Medicine, 15,1663-1685.
Follmann, D. and Wu, M. (1995). An Approximate Generalized Linear Model With Random Effects for Informative Missing Data. Biometrics , 51, 151-168.
Freedman, L. S., Graubard, B. I. and Schatzkin, A. (1992). Statistical Validation of Intermediate Endpoints for Chronic Diseases. Statistics in Medicine, 11, 167-178.
Frangakis, C. E. and Rubin, D. B. (1999). Addressing Complications of Intention-to-treat Analysis in the Combined Presence of All-or-none Treatment-noncompliance and Subsequent Missing Outcomes. Biometrika , 86, 365-379.
Gasser, T. and Kneip, A. (1995). Search for Structure in Curve Samples. Journal of the American Statistical Association, 90, 1179-1188.
Gasser, T., M*uller, H. G., K*ohler, W., Molinari, L. and Prader, A. (1984). Nonparametric Regression Analysis of Growth Curves. Annals of Statistics, 12, 210-229.
Green, P.J. and B.W. Silverman (1994). Nonparametric Regression and Generalized Linera Models: a roughness penalty approach. London:Chapman and Hall.
Greenland, S., Robins, J. M., and Pearl, J. (1999). Confounding and Collapsibility in Causal Inference, Statistical Science, 14, 29-46.
Hall, P., Poskitt, D.S. and Presnell, B. (2001) A functional data-analytical approach to signal discrimination. Technometrics, 43, 1-9.
Hart, J.P. andWehrley, T.E. (1986). Kernel regression estimation using repeated measurements data Journal of the American Statistical Association, 81, 1080-1088..
Henderson, R., Diggle, P. and Dobson, A. (2000). Joint Modeling Longitudinal Measures and event time data. Biostatistics , 4, 465-480.
Hernan, M., Brumback, B., and Robins, J.M. (2000). Marginal Structural Models to Estimate the Causal Effect of Zidovudine on the Survival of HIV-Positive Men. Epidemiology 11(5):561-570.
Holland, P. W. (1986). Statistics and Causal Inference (with discussion). Journal of the American Statistical Association, 81, 945-970.
Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, Y. (1998). Nonparametric Smoothing Estimates of Time{Varying CoeÆcient Models with Longitudinal Data. Biometrika, 85, 809-822.
Ibrahim, J.G., Chen, M. H., and Sinha, D. (2001). Bayesian Methods for Joint Modeling of Longitudinal and Survival Data With Applications to Cancer Vaccine Studies. Preprint
Liang, K. Y. and Zeger, S. L. (1986). Longitudinal Data Analysis Using Generalized Linear Models. Biometrika, 73, 13-22.
Lin, D.Y., Fleming, T.R., and DeGruttola, V. (1997). Estimating the Proportion of Treatment Effect Explained by a Surrogate Marker. Statistics in Medicine, 16, 1515-1527.
Lin, D.Y. and Ying, Z. (2001). Semiparametric and nonparametric analysis of longitudinal data. Journal of the American Statistical Association, 96, 103-126.
Lin, H., McCulloch, C.E., Turnbull, B.W., Slate, E.H., and Clark, L.C. (2000) A Latent class mixed model for analyzing biomarker trajectories with irregularly scheduled observations. Statistics in Medicine 19, 1308-1318.
Lin, X. and Carroll, R. J. (2000). Nonparametric Function Estimation for Clustered Data When the Predictor is Measured Without/With Error. Journal of the American Statistical Association, 95, 520-534.
Lin, X. and Carroll, R. J. (2001). Semiparametric Regression For Clustered Data Using Generalized Estimating Equations. Journal of the American Statistical Association, in press.
Lin, X. and Zhang, D. (1999). Inference in Generalized Additive Mixed Models Using Smoothing Splines. Journal of the Royal Statistical Society, Series B, 61, 381-400.
Little, R.J.A. (1995). Modeling the Drop-Out Mechanism in Repeated Measures Studies. Journal of the American Statistical Association, 90, 1112-1121.
Little, R. J. A., and Rubin, D. B. (1987). Statistical Analysis with Missing Data, New York: John Wiley.
Murphy S. A., van der Laan, M. J., Robins J. and CPPRG (2000), Marginal Mean Models for Dynamic Regimes. preprint.
Muller, H. G. (1988). Nonparametric Regression Analysis of Longitudinal Data. Springer-Verlag.
Muller, H.G. and Wang, J.L. (1998). Statistical tools for the analysis of nutrition effects on the survival of cohorts. Mathematical Modeling in Experimental Nutrition. Ed. A. Clifford and H.G. Muller, Advances in Experimental Medicine and Biology, 445, 191-203, Plenum Press.
Muller, H.G. Wang, J.L., Capra, W.B., Liedo, P. and Carey, J.R. (1997). Early morality surge in protein-deprived females causes reversal of sex differential of life expectancy in
Mediterranean fruit flies. Proceedings of the National Academy of Sciences of the USA, 94, 2762-2765.
Pearl, J. (2000) Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press.
Prentice, R. L. (1989). Surrogate Endpoints in Clinical Trials: Definition and Operational Criteria Statistics in Medicine, 8, 431-440.
Ramsay, J. O. and Dalzell, C. J. (1991). Some Tools for Functional Data Analysis (with discussions). Journal of the Royal Statistical Society, Series B, 53, 539-572.
Ramsay, J. O. and Silverman, B. W. (1997). Functional Data Analysis. New York: Springer-Verlag.
Ramsay, J.O. and Li, X. (1998). Curve registration. Journal of the Royal Statistical Society,
Series B, 60, 351-363.
Rice, J. A. and Silverman, B. W. (1991). Estimating the Mean and Covariance Structure Nonparametrically When the Data are Curves. Journal of the Royal Statistical Society, Series B, 53,
233-243.
Rice, J.A. and Wu, C. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics, to appear.
Robins, J.M. (1999). Marginal Structural Models versus Structural Nested Models as Tools for Causal Inference. Statistical Models in Epidemiology: The Environment and Clinical Trials. M.E. Halloran and D. Berry, Editors, IMA Volume 116, NY: Springer-Verlag, pp. 95-134.
Robins, J. M., Greenland, S. and Hu, F. (1999). Estimation of the Causal Effect of a Time-varying Exposure on the Marginal Mean of a Repeated Binary Outcome (with discussion). Journal of the American Statistical Association, 94, 687-700.
Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1995). Analysis of Semiparametric Regression
Models for Repeated Outcomes in the Presence of Missing Data. Journal of the American Statistical Association, 90, 106-121.
Rotnitzky, A., Robins, J. and Scarfstein, D. (1998). Semiparametric Regression for Repeated Outcomes With Nonignorable Nonresponse. Journal of the American Statistical Association, 93, 1321-1339.
Rubin, D. B. (1978). Bayesian Inference for Causal Effects: The Role of Randomization. The Annals of Statistics, 6, 34-58.
Rubin, D. B. (2000). Discussion of "Causal Inference with Counterfactuals" by A. P. Dawid. Journal of the American Statistical Association, 95, 435-437.
Ruppert, D. and Carroll, R. J. (2000). Spatially{adaptive Penalties for Spline Smoothing. Australian and New Zealand Journal of Statistics, 2, 205-224.
Scharfstein, D., Rotnitzky, A. and Robins, J. M. (1999). Adjusting for Nonignorable Drop-out Using Semiparametric Nonresponse Models. Journal of the American Statistical Association, 94, 1096-1120.
Severini, T. A. and Staniswalis, J. G. (1994). Quasilikelihood Estimation in Semiparametric Models. Journal of the American Statistical Association, 89, 501-511.
Simonoff, J.S. (1996). Smoothing Methods in Statistics, Springer.
Song, X., Tsiatis, A.A., and Davidian, M. (2001). A Semiparametric Likelihood Approach for Joint Modeling of Longitudinal and Time-to-event Data. Preprint.
Staniswalis, J.G. and Lee, J.J. (1998). Nonparametric regression analysis of longitudinal data. Journal of the American Statistical Association. 93, 1403-1418.
Taylor, M. G., Cumberland, W. G. and Sy, J. P. (1994) A Stochastic Model for Analysis of Longitudinal AIDS Data. Journal of the American Statistical Association, 89, 727-736.
Ten Have, T.R., Kunselman, A.R., Pulksteins, E.P., and Landis, J.R. (1998). Mixed Effects Logistic Regression Models for Longitudinal Binary Response Data With Informative Drop-out. Biometrics , 54, 367-383.
Tsiatis, A. A., Degruttola, V. and Wulfsohn, M. S. (1995). Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS. Journal of American Statistics Association 90, 27-37.
Tsiatis, A. A. and Davidian, M. (2001). A Semiparametric Estimator for the Proportional Hazard Model with Longitudinal Covariates Measured with Error. Biometrika , in press.
Verbyla, A. P., Cullis, B. R., Kenward, M. G. and Welham, S. J. (1999). The Analysis of Designed Experiments and Longitudinal Data Using Smoothing Splines (with discussion). Applied Statistics, 48, 269-311.
Verbeke, G., Mollenbergh, G., Thijs, H., Lesaffre, E. and Kenward, M. G. (2001). Sensitivity Analysis for Nonrandom Dropout: A Local In uence Approach. Biometrics , 7-14.
Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. London: Chapman and Hall.
Wang Y. (1998). Mixed-Effects Smoothing Spline ANOVA. Journal of the Royal Statistical Society B, 60, 159-174.
Welsh, A. H., Lin, X. and Carroll, R. J. (2001). Marginal Longitudinal Nonparametric Regression: Locality and Efficiency of Spline and Kernel Methods. Journal of the American Statistical Association, tentatively accepted.
Wild, C. J. and Yee, T. W. (1996) Additive Extensions to Generalized Estimating Equation Methods. Journal of the Royal Statistical Society, Series B, 58, 711-725.
Wu, C. O., Chiang, C. T. and Hoover, D. R. (1998). Asymptotic Confidence Regions for Kernel
Smoothing of a Varying Coefficient Model with Longitudinal Data, Journal of the American Statistical Association, 93, 1388{1402.
Wulfsohn, M. S. and Tsiatis, A. A. (1997), A Joint Model for Survival and Longitudinal Data Measured with Error. Biometrics , 53, 330-339.
Zeger, S. L. and Diggle, P. J. (1994), Semi-parametric Models for Longitudinal Data With Application to CD4 Cell Numbers in HIV Seroconverters. Biometrics, 50, 689-699.
Zhang, D., Lin, X., Raz, J. and Sowers, M. (1998), Semi-parametric Stochastic Mixed Models for Longitudinal Data. Journal of the American Statistical Association, 93, 710-719.

20-Aug-2001
Comments: pop@ams.org
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