Biometrics 63, 398–404 June 2007 DOI: 10.1111/j.1541-0420.2006.00723.x Regression Models for the Mean of the Quality-of-Life-Adjusted Restricted Survival Time Using Pseudo-Observations Adin-Cristian Andrei Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, K6/428 CSC 600 Highland Avenue, Madison, Wisconsin 53792-4675, U.S.A. email: andrei@biostat.wisc.edu and Susan Murray Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, Michigan 48109, U.S.A. Summary. In this research we develop generalized linear regression models for the mean of a quality- of-life-adjusted restricted survival time. Parameter and standard error estimates could be obtained from generalized estimating equations applied to pseudo-observations. Simulation studies with moderate sample sizes are conducted and an example from the International Breast Cancer Study Group Ludwig Trial V is used to illustrate the newly developed methodology. Key words: Gap time; Inverse weighting; Nonparametric; Quality-of-life; Successive events. 1. Introduction In clinical trials, the length of specific disease or treatment stages and the quality-of-life (QOL) are of high interest to the practitioner. For instance, in the initial phase (TOX) of the International Breast Cancer Study Group (IBCSG) Ludwig Trial V (see Gelber et al., 1992), patients experience moderate or increased toxicity, according to treatment arm assignment (short- versus long-duration chemotherapy). Unless precluded by death, TOX is followed by a disease-free period known as time without symptoms or toxicity (TWiST), and then by a period of cancer relapse (REL). The amount of chemotherapy received during TOX impacts patient well-being thereafter; hence, the need for tools summarizing the quantitative and qualitative health aspects in a unitary and meaningful way. When data are not censored, the quality-adjusted-life-year (QALY) method is one such simple and easily interpretable measure (see Torrance and Feeny, 1989). Essentially, the pa- tient’s well-being is classified into a discrete number of health states, each having a utility value. QALY is the sum of the utility-weighted time periods spent in each health state. As mentioned in Glasziou et al. (1998), sensitivity analyses of the utility weights in QALY provide insight into the nature of the quantity versus QOL tradeoff. Examples and practical considerations involving QALY are presented, for instance, in Goldhirsch et al. (1989), Glasziou, Simes, and Gelber (1990), or Gelber et al. (1995). When censoring is present, QALY may only be identifiable in restricted or truncated form and quality-of-life-adjusted lifetime (QAL) tests, which are based on integrated weighted areas under the survival curve, could be used instead. This class of tests has been studied by Gelber, Gelman, and Goldhirsch (1989) and Huang and Louis (1999), among oth- ers. A particular QAL test, attractive in its simplicity, Q- TWiST has been introduced by Glasziou et al. (1990) and successfully used as an inferential tool in various AIDS or can- cer clinical trials, as presented in Gelber et al. (1992), Cole et al. (1996), and Gelber et al. (1996). Its closed-form asymp- totic variance has been given by Murray and Cole (2000). The survival distribution of QAL is also of clinical interest. Gelber et al. (1989) pointed out that, in this case, the Kaplan–Meier estimator is biased due to the induced dependent censoring. To correct for the bias, Zhao and Tsiatis (1997, 1999) have proposed estimators involving inverse probability-of-censoring weighting techniques, as in Robins and Rotnitzky (1992). Zhao and Tsiatis (2001) have developed testing methods for detecting differences between survival functions of QALs. As a way to incorporate prognostic covariates, Cole, Gelber, and Goldhirsch (1993) have proposed and studied Cox regres- sion models for the QOL-adjusted survival analysis. Another regression method involving Cox models has been proposed by van der Laan and Hubbard (1999). However, because these methods usually model the QALs indirectly via their hazard functions, the coefficient estimates thus obtained lack a clin- ically meaningful interpretation. Although meritorious, this approach to modeling has moved away from the simple and intuitive characteristics of mean QAL. Alternatively, we propose a much simplified approach to multiple regression of QALs, by using the so-called 398 C  2006, The International Biometric Society