Modelling and estimation of health-related quality of life after hip fracture: A re-analysis of data from a prospective cohort study.

OBJECTIVES: This study investigates the reporting of health-related quality of life (HRQoL) in patients following hip fracture. We compare the relative merits and make recommendations for the use for two methods of measuring HRQoL; (i) including patients who died during follow-up and (ii) including survivors only.
METHODS: The World Hip Trauma Evaluation has previously reported changes in HRQoL using EuroQol-5D for patients with hip fractures. We performed additional analysis to investigate the effect of including or excluding those patients who died during the first four months of the follow-up period.
RESULTS: The dataset included 503 patients, 25 of whom died between 30 days and four months of injury. There was a statistically significant difference in 30-day HRQoL between those alive (mean 0.331 and standard deviation (sd) 0.360) and those dead (mean 0.156 and sd 0.421) by four months (independent-samples t-test; p 0.022). The estimated difference of 0.175 in HRQoL (95% confidence interval 0.025 to 0.325) was also highly clinically significant.
CONCLUSION: When reporting HRQoL for patients after a hip fracture, excluding patients who die during follow-up leads to an overestimate of the effects of the intervention or treatment pathway. We would recommend that death-adjusted estimates should be used routinely when reporting HRQoL in this population.Cite this article: N. Parsons, X. L. Griffin, J. Achten, T. J. Chesser, S. E. Lamb, M. L. Costa. Modelling and estimation of health-related quality of life after hip fracture: A re-analysis of data from a prospective cohort study. Bone Joint Res 2018;7:1-5.

Analysis of health-related quality of life (HRQoL) after hip fracture including patients who died during follow-up versus survivors only.

When reporting HRQoL using EuroQol-5D for patients after a hip fracture, excluding patients who die during follow-up leads to overly-optimistic estimates of patient outcomes and the effects of the treatment pathway.

We would recommend that ‘death-adjusted’ estimates should be used routinely when reporting HRQoL in this population.

This is a large study that reports highly significant differences between HRQoL outcomes in this population.

The main limitation is that all of the data were reported from a single trauma centre.

Introduction

Health-related quality of life (HRQoL) is now the most widely used primary outcome measure for studies reporting outcomes for patients after hip fracture.[1-5] The EuroQol-5 Dimensions (EQ-5D) has become the preferred measure to determine HRQoL in the United Kingdom and in many other countries.[1,2,6-9] EQ-5D at four months after the fracture is part of the UK Core Outcome Set for hip fracture studies,[10] which has been adopted by the National Institute for Health and Care in its most recent Hip Fracture Guidelines.[11]

Hip fracture affects an older and often frail population. Griffin et al[2] report conservative estimates of mortality in the United Kingdom population of approximately 12% at four months and 20% at one year for patients aged > 80 years. In many areas of healthcare, patients who die before completing a study are often excluded from the primary analysis. This is, in general, not a particularly important issue if the number of patients who die is low. However, since the number of patients who die in the months following a hip fracture is relatively high, this approach inevitably leads to a loss of data and therefore a loss of precision when estimating outcomes. It also potentially leads to biased analyses, as by excluding those patients who die early we are likely to produce unduly optimistic estimates of HRQoL. One potential advantage of EQ-5D is that it provides, through the associated health utilities, a natural value for study participants who died prior to an outcome assessment; EQ-5D is anchored at 1 for full health and 0 for death. By including the important sub-group of patients who die in the months following hip fracture in the primary analysis of outcomes, we could therefore increase the precision of hip fracture studies. Hereafter, we refer to the inclusion of patients who died during follow-up as a ‘death-adjusted’ EQ-5D estimate, as opposed to a ‘complete-case’ estimate, which is based on only those patients alive at the index assessment occasion (four months). However, if the patients who die early had high HRQoL before their death, then assuming that their EQ-5D score was zero risks underestimating the potential benefits of an intervention, even if the patient subsequently dies before reaching their four-month assessment.

In this study, we investigate the use of a death-adjusted EQ-5D score in the analysis of outcomes following hip fracture. We undertake additional analysis of the data available from the World Hip Trauma Evaluation (WHiTE),[1,2,4] which provided routine EQ-5D at four weeks, in addition to the four-month timepoint. These early outcome data allow us to model temporal changes in EQ-5D during the recovery phase, and to compare the relative merit of a death-adjusted versus a complete-case EQ-5D estimation and make recommendations about which to use.

Materials and Methods

Data

We conducted a prospective longitudinal cohort study to assess HRQoL at four weeks, four months and one year after hip fracture,[4] referred to as the WHiTE study. In addition, a small convenience sample of the WHiTE study participants provided HRQoL assessments immediately post-injury. All patients, or proxy respondents where appropriate, provided informed consent or agreement, respectively. The study is registered with Current Controlled Trials (ISRCTN63982700) and full protocols have previously been published.[4,12] The data in this study comes from participants who presented with a hip fracture at a single major trauma centre in England between January 2012 and March 2014; those who were aged less than 60 years or who were managed nonoperatively were excluded from the study. A full description of the totality of data collected is available elsewhere.[2] Here we focus exclusively on the primary outcome measure, which was the EQ-5D score (EQ-5D-3L),[6,7] a generic health utility instrument used to measure HRQoL. EQ-5D is a validated, cross-disciplinary standardized instrument that is widely used to assess HRQoL after hip fracture. It has two parts: a visual analogue scale (VAS), which measures self-rated health and a health status instrument consisting of a three-level response (no problems, some problems and extreme problems) for five health domains related to daily activities. These health domains are mobility, self-care, usual activities, pain and discomfort and anxiety and depression. More recent data collected as part of the WHiTE study uses the 5L version of EQ-5D that provides greater sensitivity than the 3L. Responses from the EQ-5D health classifications were converted into an overall score using a published utility algorithm for the population of the United Kingdom.[13]

Statistical analysis

Study data were summarized using means and standard deviations (sd), and visualized by box plots and strip plots to show variation in outcomes. Independent-samples t-tests were used to draw inferences on mean differences between selected sub-populations. The complexity of the setting we describe here is that early death of study participants postoperatively caused dropout (loss to follow-up), since no EQ-5D measurements were available after the terminal event for the four-month timepoint. If this dropout is non-random, then this is likely to cause bias in any analysis that ignores the dropout process. To obtain valid inferences, we use methods that allow fitting of joint models of longitudinal and time-to-event (survival) data.[14] The longitudinal model for the temporal changes in EQ-5D postoperatively was a mixed-effects model that had a random additive participant effect, fixed effects for the baseline (pre-injury) EQ-5D and a quadratic (second-order polynomial) model for the log-transformed postoperative time. The survival data was summarized using a proportional-hazards (Cox) model,[15] adjusting for the baseline EQ-5D score. Joint models were fitted in the R package, JM (R Foundation, Vienna, Austria),[16,17] using a piecewise-constant baseline risk function and the Gauss-Hermite method for integral approximation.

Results

The totality of data available (n = 741) has been described previously and in full by Griffin et al;[2] there were 118 deaths reported during the course of study, with age, gender, American Society of Anesthesiologists (ASA) grade,[18] and preoperative Abbreviated Mental Health Score (AMTS)[19] all being statistically significant predictors of survival.[2] Postoperative trends in EQ-5D varied by AMTS score (⩽ 8 and > 8) and age-group (⩽ 80 years and > 80 years); in summary, recovery was generally worse for those in the older group and those with lower AMTS.[2] EQ-5D scores did not recover to baseline (pre-injury) levels but followed a characteristic trajectory up to 12 months, with little or no improvements after four months.[2]. Therefore, we focus our modelling work on this four-month period.

Population characteristics

The full (baseline, four weeks, and four months) or partial (one or more of the values present) time courses of EQ-5D data were available from 503 of the WHiTE study participants. The age distribution, gender split and baseline EQ-5D for this group was comparable with the full study population (Table I).

Table I.

Age, gender split and baseline EuroQol 5 Dimensions (EQ-5D) for participants from the full World Hip Trauma Evaluation population (n = 741) and for those available for this study (n = 503)

	Full population(n = 741)	Study population (n = 503)
Mean age, yrs (sd)	83.1 (8.7)	82.8 (8.3)
Gender, female:male (% F)	503:186 (73.0)	362:117 (75.6)
Mean baseline EQ-5D (sd)	0.559 (0.348)	0.574 (0.337)

SD, standard deviation

The study population consisted of 478 participants who survived to four months, and 25 who died after providing four-week EQ-5D data but before reaching the four-month follow-up timepoint. Table II shows the characteristics of these two groups.

Table II.

Age, gender split and baseline EuroQol 5 Dimensions (EQ-5D) for participants who were alive (n = 478) and for those dead (n = 25) by the four-month timepoint

	Alive at 4 mths (n = 478)	Dead at 4 mths (n = 25)	p-value
Mean age, yrs (sd)	82.7 (8.2)	85.8 (8.5)	0.062[*]
Gender, female:male (% F)	346:110 (75.9)	16:7 (69.6)	0.464[†]
Mean baseline EQ-5D (sd)	0.581 (0.339)	0.434 (0.254)	0.034[*]

independent-samples t-test

Fisher’s exact test

A t-test indicated that the baseline EQ-5D was statistically significantly lower for those participants who were dead at four months than for those who were alive at this timepoint (p = 0.034); estimated difference 0.146 (95% CI 0.01 to 0.282).

Figure 1 shows strip plots and box plots of four-week EQ-5D data; medians and interquartile ranges (IQRs) for the two groups are 0.290 (IQR 0.055 to 0.640) and -0.040 (IQR -0.170 to 0.625). Evidence from previous analyses is that Gaussian approximations for EQ-5D are reasonable for this population;[1,2] focusing on means and sds, a t-test shows that there was a statistically significant difference in four-week EQ-5D between those alive (mean 0.331 and sd 0.360) and those dead (mean 0 .156 and sd 0.421) by four months (t-test; p 0.022). The estimated difference 0.175 (95% CI 0.025 to 0.325) was also highly clinically significant (the minimum clinically important difference for EQ-5D is 0.074),[20] and indicated (together with the significant difference in baseline EQ-5D) that low EQ-5D was strongly associated with postoperative death.

Fig. 1

Strip plots and box plots of four-week EuroQol 5 Dimensions (EQ-5D) data. For those World Hip Trauma Evaluation study participants alive (n = 478) and those who died (n = 25) at four months postoperatively. Stacked bars show numbers of participants for each EQ-5D score and box plots show interquartile range (IQR; box), median (solid line) and whiskers at 1.5 times the IQR.

Complete-case analysis

The most widely used and recommended endpoint for EQ-5D in this population is at four months.[2] When reporting results of this outcome for a randomized controlled trial (RCT), one approach to analysis is to simply report summary statistics (e.g. means and sds) based on the population of patients who are alive at the four-month timepoint. If we are willing to accept that withdrawals and losses due to participant deaths are not related to the interventions, then comparing, for instance, group means at four months should provide an appropriate analysis, all else being equal.

Using EQ-5D data from only those participants alive at the four-month timepoint (n = 478) provides an estimate of the mean EQ-5D at four months of 0.454 (95% CI 0.414 to 0.495).

Model-based prediction

It is clear from Figure 1 and Table I that the characteristics of those participants who die early (before four months) are different from those who survive to provide EQ-5D assessments. Therefore, we proceed to fit joint models that enable us to explicitly allow for the effects of the underlying longitudinal EQ-5D outcome on the risk of death. In these models, we implicitly make the assumption that the complete EQ-5D longitudinal response (to the study endpoint at four months) is meaningful for all participants, including EQ-5D observations that would have been collected after death for those participants who died early.

One could argue that in this setting, as the terminating event is death, it makes no sense at all to consider the value of EQ-5D after death. However, for the purposes of exposition we proceed to fit models to the observed data and make predictions on future trends in EQ-5D scores for those study participants who died early. Figure 2 shows observed data and model fits for the full population, for participants alive at four months, and for participants who were dead at four months. The projected EQ-5D for the population of early deaths (under the assumption that they did not die but progressed to the four month timepoint) (Fig. 2c) indicates that, for this group, EQ-5D was likely to remain lower than that of those patients who we know survived to four months. The predicted EQ-5D score at four months for the dead group (n = 25) was 0.349 (95% CI 0.260 to 0.438) and for the alive group was 0.445 (95% CI 0.425 to 0.464); there was a statistically significant difference between groups based on an independent-samples t-test of predictions at four months (p-value = 0.034).

Longitudinal models for postoperative EuroQol 5 Dimensions (EQ-5D) from the full World Hip Trauma Evaluation study population (n = 503) (a), for participants alive at four months (n = 478) (b) and for participants who had died at four months (n = 25) (c). Observed means are plotted, with 95% confidence intervals (bars) and also fitted curves with 50% confidence regions.

Using EQ-5D data from the full population (n = 503), then building a model to predict and project how those participants who died early may have progressed if they did not die, provides an estimate of the mean EQ-5D at four months of 0.440 (95% CI 0.421 to 0.459).

Death-adjusted analysis

Rather than attempt to model and project changes in EQ-5D scores from months one to four for those patients who did not survive to the study endpoint (the dashed line in Fig. 2c), a simpler approach is to assume that EQ-5D becomes zero at death, and then carry this observation forward to subsequent assessment occasions. We call this ‘death-adjusted’ EQ-5D.[2]

Undertaking this analysis for the WHiTE study population provides an estimate of the mean EQ-5D at four months of 0.424 (95% CI 0.384 to 0.464).

Discussion

Three methods of summarising EQ-5D at four months postoperatively have been presented for patients after hip fracture. The first method (complete-case analysis) summarizes outcomes at four months using data only for those patients who were alive at this timepoint. Estimates of mean EQ-5D using this method (0.454; 95% CI 0.414 to 0.495) were larger than the other two methods discussed. This is not an unexpected result, as we show that those patients who died before four months had significantly lower EQ-5D at the early four-week assessment. By modelling the observed temporal changes in EQ-5D, we attempt to predict what the EQ-5D would have been for these participants who died early, if they had survived to four months. This model-based prediction provided an estimate of mean EQ-5D at four months (0.440; 95% CI 0.421 to 0.459) that was lower than the complete-case method. Even if we assume that, for those who died, the cause of death was not directly related to the intervention, we conclude that the complete-case method provides positively biased estimates of EQ-5D (i.e. it tends to overestimate the measure). Therefore, we would not generally recommend the complete-case analysis unless the focus of a study is purely on outcomes for those participants who survived to the study endpoint. If this is the case, then some inflation to the sample size should be made to allow for postoperative losses due to death.

The death-adjusted analysis method provided estimates of EQ-5D (0.424; 95% CI 0.384 to 0.464) that were lower still than the model-based prediction method. Again, this is not unexpected, as we have replaced the missing four-month data for individuals who died prior to the four month assessment (n = 25) with values of zero, which were always lower than the model-based predictions. A paired t-test indicated that death-adjusted EQ-5D estimates were statistically significantly smaller than corresponding model-based predictions (p-value = 0.037), although the difference (paired mean difference in EQ-5D is 0.027) was such as to be clinically unimportant.[20]

Due to the lack of clinically important difference between these methods of estimation, because the death-adjusted analysis method is considerably simpler than the model-base method, and because the assumptions required for the model-based method are unlikely to be met (i.e. that participants could have survived to provide observations at the index four-month timepoint), we recommend that death-adjusted estimates should be routinely used for reporting HRQoL in this population.

One could argue that, for comparative analyses (i.e. comparing groups A and B in a RCT), in principle it is not necessarily important whether estimates of EQ-5D are biased, as we are only interested in differences between groups. This is a weak argument, as if one knows that estimates of EQ-5D are likely to be positively biased, then it is difficult to justify not attempting a correction. Reporting death-adjusted EQ-5D also provides the additional benefit of increasing the sample size, as we no longer need to discard participants who have died prior to the study endpoint. However, experience suggests that the death-adjusted estimator has a larger variance than the complete-case estimator, due to the inclusion of the zero scores, which are not typically located at the mean of the distribution. Therefore, some inflation of the sd, relative to previously reported values based on complete-cases,[5] should be considered when calculating study sample sizes. It should be noted that the model-based approach provided tighter confidence intervals than either of the other methods discussed, as it uses full information for estimation and it imposes constraints on the form of the longitudinal model for EQ-5D.

In conclusion, when reporting HRQoL for patients after a hip fracture, excluding patients who die during follow-up leads to an overly optimistic estimation of the effects of the intervention or treatment pathway. We would recommend that death-adjusted estimates should be routinely used for reporting HRQoL in this population.