ISOQOL 2004 Symposium
"Stating the Art: Advancing Outcomes Research Methodology and Clinical Applications"
June 27-29, 2004
Boston Park Plaza Hotel
Boston, MA, USA

Tuesday, June 29, 2004

Session 5: Advanced Statistical Analysis II
Presenters: Hebert Thijs and Dennis Fryback
Chair: Diane Fairclough

Sensitivity Analysis for Longitudinal Clinical Trials
Herbert Thijs, PhD
Center for Statistics, Limburgs University, Diepenbeek, Belguim

In a longitudinal study or experiment, each unit is measured on several occasions. It is not unusual in practice for some sequences of measurement to terminate early for reasons outside the control of the investigator, and any unit so affected is often called a dropout. Furthermore Rubin (1976) and Little and Rubin (1987, Ch. 6) make important distinctions between different missing values processes. A dropout is independent of both unobserved and observed data and random (MAR) if, conditional on the observed data, the dropout is independent of the unobserved measurements; otherwise the dropout process is termed non-random (MNAR). Currently in clinical trials standard methodology used to analyze longitudinal data subject to non-response is mostly based on the MCAR assumption and includes Last Observation Carried Forward (LOCF), Complete Case analysis, etc. This is often done without questioning possible influence of these assumptions on the final results. On the other hand if a dropout process is random then a valid analysis, can be obtained through a likelihood-based analysis that ignores the dropout mechanism, provided the parameters describing the measurement process are functionally independent of the parameters describing the dropout process, the so-called parameter distinctness condition. This situation is termed ignorable by Rubin (1976) and Little and Rubin (1987). This leads to considerable simplification in the analysis. In many examples, however, the reasons for dropout are many and varied and it is therefore difficult to justify on a priori grounds the assumption of random dropout. Arguable, in the presence of non-random dropout, a wholly satisfactory analysis of the data is not feasible. One approach is to estimate from the available data the parameters of a model representing a non-random dropout mechanism. Is may be difficult to justify the particular choice of dropout model, and it does not necessarily follow that the data contain information on the parameters of the particular model chosen, but where such information exists the fitted model may provide some insight into the nature of the dropout process and of the sensitivity of the analysis to assumptions about this process. This is the route taken by Diggle and Kenward (1994) in the context of continuos longitudinal data; see also Diggle, Liang and Zeger (1994, Ch. 11). Further approaches are proposed by Laird, Lange, and Stram (1982), Wu and Bailey (1988, 1989), Wu and Carroll (1988), and Greenlees, Reece, and Zieschang (1982). An overview of the different modeling approaches is given by Little (1995). Also the case of categorical outcomes has received considerable attention. See for example Baker and Laird (1988), Stasny (1986), Baker, Rosenberger, and Dersimonian (1992), Conaway (1992, 1993) Park and Brown (1994) and Molenberghs, Kenward and Lesaffre (1997). With the volume of literature on non-random missing data increasing, there has been growing concern about the fact that models often rest on strong assumptions and relatively little evidence from the data themselves. This point was already raised by Glynn, Laird and Rubin (1986) who indicate that this is typical for so-called selection models, where the joint distribution of the measurement and missingness processes is factorized into the marginal distribution of the measurement process and the conditional process of the missingness process given the measurements, while it is much less so for a pattern-mixture model (Little 1993, 1994, Hogan and Laird 1997), where the reverse factorization is used. Since the model of Diggle and Kenward (1994) fits within the class of selection models, it is fair to say that it raised, at first, too high expectations. This was made clear by many discussants of their paper. This implies that, for example, formal tests for the null hypothesis of random missingness, while technically possible, should be approached with caution. In response, there is a growing awareness of the need for methods that investigate the sensitivity of the results with respect to the model assumptions. See for example Nordheim (1984), Little (1994), Rubin (1994), Laird (1994), Fitzmaurice, Molenberghs and Lipsitz (1995), and Molenberghs, Goetghebeur and Lipsitz (1998). Still, only a few actual proposals have been made. Moreover, many of these are to be considered as useful but ad hoc approaches. In our view, a more formal approach to sensitivity analyses should be fruitful as well. Taking this into account and based on a case study from he clinical industry we would like to stress the major drawbacks of a simple LOCF analysis or CC analysis. We will show the discrepancies of both the results from the these analyses and we will also compare both analyses with a stronger MAR analysis with regard to the results. Futhermore we will expand our investigation of sensitivity towards MAR and MNAR models, combining a measurement model with a dropout model as done by Diggle and Kenward (1994), allowing the investigator to make prior conclusions with regard to the missingness process. At last, we will also apply some advanced sensitivity tools, such as local and global influence as they are introduced by Verbeke et al (2001) and further discussed by Molenbergs et al (2001) and Thijs, Molenberghs and Verbeke (2003). Using these tools may lead to the detection of influential subjects. In addition, it will be shown that a pattern mixture approach (Thijs et al 2002) is a viable alternative to gain insight in the specific problems regarding missing data.

 

Bayesian Analysis of Health Status and Quality of Life Data
Dennis Fryback, PhD
Professor, Dept. of Population Health Studies, University of Wisconsin-Madison, Madison, WI

The past 15 years has seen large advances in applied Bayesian methodology and the wide distribution of the relatively accessible BUGS and WinBUGS software for Bayesian data analysis. In this talk we present illustrate Bayesian analysis capabilities using SF-36 data (including SF-6D utility scoring) from the Beaver Dam Health Outcomes Study along with long term longitudinal follow-up of this cohort.