Data came from the ongoing Complementary Comfort Care randomized trial of complementary and alternative medicine at the end of life, sponsored by the National Cancer Institute (William Lafferty, PI). Enrollees are randomized to receive massage, guided meditation, or a friendly visit. For this paper, we ignored treatment group assignment and considered all persons enrolled to date as a single group.
2.1 Study Participants
Study participants were recruited from four Seattle-area hospice organizations and other medical care sites that were likely to see persons with advanced medical conditions who were near the end of life, as well as through support groups and personal networks. Persons who were 18 years of age or older, English speaking, able to report reasonably accurately on symptoms and quality of life for the previous 7 days, willing to accept assignment to any of the three treatment arms, and who had a family member or friend who would act as their “study partner” to provide ancillary data to the study were eligible to participate, regardless of specific diagnosis. Enrollees and their study partners were paid $25 after completing baseline interviews. Longitudinal information on quality of life and symptom status was collected either in person or by telephone after every two intervention visits. The goal was to provide up to two intervention visits per week, and persons were allowed to reschedule or to drop out of the study at any time.
2.2 Outcome Measures
Although there are many instruments for measuring QOL, this study needed to minimize subject burden. We collected only 6 items from the Perceived Quality of Life survey, [2
] and for this paper report on only a single item. Patients were asked “How would you rate your over-all quality of life during the last 7 days?” from 0 for no quality of life to 10 for perfect quality of life. Here, QOL is defined as the person's rating, which was collected after every 2 intervention visits (approximately every week). Participants also rated their health status, at baseline only, on the same 0–10 scale. A 6-point rating of the presence and severity of pain was also obtained at each interview. There is no recommended way to code “dead” on any of these measures, which is a potential problem in studies where some persons die.
To estimate the reliability of the QOL measure in a stable population, we compared QOL values made one week apart for persons whose pain rating did not change in that week. The intraclass correlation coefficient (test-retest reliability) was 0.73, which is acceptable for our purposes. We arbitrarily defined a value of 7–10 as “good QOL”. The intervention providers were also asked to estimate the prognosis in terms of QOL for about 30 persons who stopped providing data substantially before death or the analysis date, to help inform our later sensitivity analysis of the imputation model.
2.3 Study sample for the current paper
This paper deals with the subset of data available in February, 2007 (referred to as the analysis date). We eliminated 15 persons whose vital status was not then known (not known to be dead, but had provided no data in the most recent 45 days). The prospective sample included all persons who enrolled 12 or more months before the analysis date. The retrospective sample included all persons who died 10 weeks or more after enrollment. Persons could be in both samples.
2.4 Accounting for Death and Missing Data
Longitudinal data at the end of life are often difficult to collect and interpret because of varying lengths of follow-up, different dying trajectories, and missing observations. Some persons had no QOL data at, say, 52 weeks, because they were recruited less than 1 year before the analysis date, had died, were not scheduled to provide data that week, or had missing data for some other reason. The average of all available QOL value at 52 weeks is thus meaningless. We needed to account for death and for other missing data.
One way to account for death is to transform the original variable that has no value for death into a new variable that does have such a value. [13
] Here we transformed QOL to the probability that a person will have good QOL next week (have QOL ≥ 7 next week), estimated from his QOL this week. We used all transition pairs (two values of QOL for the same person 1 week apart) in the longitudinal data, and estimated the transformation parameters from a logistic regression (using data from the first 148 enrollees) of a binary variable “Good QOL 1 week later” on “QOL now”. The regression results were as follows:
logit (Good QOL 1 week later) = -4.180 + .680*QOL now.
The estimated probability of having good QOL 1 week later as a function of current QOL is then:
(where QOLt refers to QOL-transformed). For example, a QOL of 10 corresponded to a QOLt of .932, and a QOL of 0 corresponds to a QOLt of 0.015. The probability that a dead person will have good QOL a week later is clearly 0, which provides a value after death. We set the values of QOLt for the weeks after a person died to zero, with the new variable referred to as QOLtd (QOL transformed with deaths added).
QOL for weeks when persons were alive but had no QOL data were imputed from the regression of QOLtd on the logarithm of time from death (or time from the analysis date if still alive), as explained in detail in Appendix 1 and considered further in the discussion section. An example of the missing data is given in the following section.
2.5 Data Organization
The plan was for persons to receive up to two treatment interventions per week, but some persons preferred to receive one intervention per week, and so were scheduled to provide QOL data every two weeks. Some persons skipped weeks and/or dropped out of the intervention. As a result, each person had a unique data collection schedule. The steps required in preparing this complex dataset for analysis (transform, account for death, impute missing data – “tdi”) are explained by example here, and in more detail in Appendix 1. An assessment of the sensitivity of results to imputation of missing data, is described below in section 3.4 and in more detail in Appendix 2.
The data for one participant, “Mr. Smith”, are shown in Table . This gentleman was enrolled in the study 137 weeks before the analysis date, but survived for only 18 weeks. He provided eleven QOL assessments between week 0 (his enrollment week) and week 15 (shown in column 3).QOLt is the transformed QOL value (the estimated probability of having good QOL in the following week conditional on his current QOL), which is in column 4. [16
] As noted above, a person with a QOL of 10 has probability 0.93 of having good quality of life one week later (or, put another way, about 93% of persons with a QOL of 10 had QOL ≥ 7 one week later). The probability that a dead person will have good QOL a week later is zero, and so column 5 includes a zero for each week after he died (QOLtd). In column 6 the remaining missing values were imputed from a regression of Mr. Smith's data on the log of time from death, as explained in Appendix 1 (QOLtdi). Note that Mr. Smith had no real QOL data in the three weeks before death, and is set to missing from weeks 138 to 150 because his potential follow-up was only 137 weeks. Figure shows Mr. Smith's data in the first 52 weeks; a circle is observed data, an x represents imputed data, and a square represents the zeroes after death.
Longitudinal Data for “Mr. Smith” (WQL = 12.63 prospective, = 5.10 retrospective)
Quality of Life over time for "Mr. Smith".
For column 7, the QOLtdi data were transformed back to the original scale, and the values of “QOLback” are shown. There are more values in column 7 than in column 3, and not all of them are integers, because of the re-transformation of the imputed QOLtdi data. There are no numerical values after death, but “d” flags are included to indicate weeks when he was dead. More detail is given in Appendix 1.
If we plotted the QOLtdi values in column 6 from week 0 to week 52 against time, as in Figure , the area under this curve would be the estimated number of weeks of good-quality life in the year after enrollment. This area was calculated, using the trapezoidal method, as the sum of those 53 QOLtdi values, minus half of the first and last values. [17
] Mr. Smith had the equivalent of 12.63 weeks of good-quality life (WQL). Weeks of good-quality life in the 10 weeks before death are the sum of QOLtdi from week -9 to the first zero QOLtdi minus half of the first and last values. Mr. Smith experienced the equivalent of 5.10 weeks of good-quality life in the 10 weeks before his death.
We used several graphical methods to describe QOL in the 52 weeks after enrollment and in the 10 weeks before death. We estimated the area under the curve of QOLtdi over time, which is interpreted as (expected) weeks of good-quality life, or WQL. (WQL is conceptually similar to quality-adjusted life years (QALY) except that it is measured in weeks, and is based on QOLtdi, which is not a preference-rated measure). We regressed WQL on age, log age, sex, age*sex, log age * sex, education, cancer, and the baseline values of QOL, Pain, and Health status, using backward elimination to obtain a parsimonious model. For the retrospective regression analysis we also added length of survival as a potential covariate, because the baseline values were likely to be less salient for a person with lengthy survival. Interactions between survival and baseline values were also included.