Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Applied Statistics Unit (ASU-Kolkata)


Dewanji, Anup (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

Quality Adjusted Lifetime (QAL)Normally, overall survival time is considered as the end point for many clinical trials to study the effectiveness of different treatments. If the survival time passes through different health states, which differ in their quality of life, then other endpoints are also considered for treatment comparison, which incorporates both quality and duration of life. It is, therefore, necessary to provide a composite measure for comparison of different treatment choices, specially in the context of clinical trials, after taking into account both quality and duration of life. This issue has been first addressed by Gelber and coauthors in a series of papers (Gelber and Goldhirsch 1986; Gelber et al., 1987; Gelber et al., 1989) by introducing an endpoint called Time Without Symptoms of disease and Toxicity due to treatment (TWiST) in the context of breast cancer patients (Ludwig Breast Cancer Study Group, Trial III). Time with toxic side effects of treatment and time with unpleasant symptoms of disease are subtracted from overall survival time to calculate TWiST for each patient (Gelber et al., 1989). See also Gelber et al. (1991, 1992a, 1992b, 1995, 1996), Murray (2000) and Cole et al. (2004) for TWiST as a composite measure for comparing treatments in the context of cancer patients.The endpoint TWiST has been generalized by Goldhirsch et al. (1989) and Glasziou et al. (1990) to incorporate the concept of quality of life, termed as QTWiST which stands for ‘Quality-Adjusted Time Without Symptoms of disease and Toxicity due to treatment’. The concept of quality adjusted lifetime (QAL), thus developed, has been made popular by many subsequent work and commonly used in the context where patients may experience several intermediate health states before ending in death. Quality of life associated with these states is measured by a utility coefficient ranging from zero to one. For each unit of time spent in the state, the utility coefficient reflects its value against perfect health (utility 1). Death has utility zero. This leads to a utility function over time which takes the value of the utility coefficient of the state occupied at that time. Then, QAL is formally defined asQ = Z T 0 W(u)du,where Q denotes the QAL, T the lifetime and W(u) the utility function at time u. The number of health states is usually assumed finite. Then, the QAL reduces to a weighted sum of the time spent in each health state, where the weights are the utility coefficients. For example, as shown in Figure 1.1, if a patient experience k health states 1,... ,k, which differ in their quality of life, before ending in death (D) with the corresponding sojourn times T1,... ,Tk and utility coefficientsw1,... ,wk, then the QAL is given byQ = X k i=1 wiTi .In HIV/AIDS research, for example, in a cohort of HIV positive patients, appearance of AIDS symptoms can be equated with intermediate health state before death (D). In this example, one would be interested in quality adjusted life of HIV patients. If THIV denotes the time till AIDS symptoms appear (since time of infection) and TAIDS denotes the time till death (since onset of AIDS symptoms) with utility coefficients w1 and w2, respectively, then this QAL is defined as w1THIV +w2TAIDS. In International Breast Cancer Study Group (IBCSG) Trial V data for cancer patients (Gelber et al. 1992a), the individuals, after going through the chemotherapy which induces a period of toxicity, start in the state of ‘Toxicity’ (state 1); at the end of this toxicity period they enter the state of ‘No symptoms of disease and toxicity of treatment’ (state 2), followed by ‘Relapse of the disease’ (state 3) and finally the death (absorbing state D). Here, the three periods (time spent in the health states) corresponding to the three health states are denoted by TOX, TWiST and REL. If w1, w2 and w3 are the utility coefficients, then the QAL is defined as w1TOX + w2TWiST + w3REL. A similar concept can be considered in the context of reliability. For example, in a parallel system with k components, the failure of successive components may be equated with successive illness states. The system fails when all the components fail. Also, while dealing with life or service times of items, the QAL may be interpreted as the quality adjusted service time as the items may be able to provide service, in its lifetime, with different levels of satisfaction or utility.


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