Analyzing Health-Related Quality of Life Data to Estimate Parameters for Cost-Effectiveness Models: An Example Using Longitudinal EQ-5D Data from the SHIFT Randomized Controlled Trial

Heart failure is a chronic condition which can result in substantial morbidity, reduced HRQoL, and premature death [6, 7]. SHIFT was a multicenter RCT conducted in 6505 HF patients with New York Heart Association (NYHA) class II, III, or IV HF, in sinus rhythm, and with left ventricular ejection fraction (LVEF) ≤35% and baseline resting heart rate ≥70 bpm. SHIFT demonstrated that ivabradine, a heart rate lowering therapy, in combination with standard therapy, including beta-blockade, was associated with a significant reduction in cardiovascular (CV) death or hospitalization for worsening HF (hazard ratio 0.82; 95% confidence interval 0.75, 0.90, p < 0.0001) and improved patient HRQoL [8]. SHIFT was a robust, well-conducted study and provides one of the largest samples of EQ-5D HRQoL data from an RCT in HF patients.

SHIFT EQ-5D HRQoL data were collected in a substudy at baseline, 4 months, and annually until study close providing up to five HRQoL assessments for each patient over the observed trial period (median follow-up 22 months) [9]. The EQ-5D is a generic instrument designed to capture patient-reported outcomes across five health domains (self-care, mobility, usual activities, pain/discomfort, anxiety/depression) [2]. HRQoL weights (utility values) may be derived from the EQ-5D using country-specific values for different health profiles. All patients randomized in SHIFT were included in the EQ-5D substudy (n = 5313/6505 patients) providing a validated EQ-5D instrument was available for the country of interest (i.e., an approved country-specific EQ-5D questionnaire). The SHIFT cost-effectiveness analysis was undertaken from a UK National Health Service and Personal and Social Services (PSS) perspective [1]; hence in our analysis, HRQoL weights values were based on EQ-5D index scores using UK population preference-weights [10].

A de novo analysis of SHIFT HRQoL data was required to provide suitable parameter estimates for the SHIFT cost-effectiveness analysis. There are a number of approaches that can be used to analyze longitudinal HRQoL data for a cost-effectiveness analysis from RCTs such as SHIFT. Simple summary measures may be used to estimate the effect of treatment on HRQoL outcomes directly, e.g., based on the mean difference in HRQoL between treatments at one or more intervals over the trial period. Summary estimates from observed data, however, may not capture the full impact of clinical events that result in temporary fluctuations in HRQoL, such as hospitalizations, as some such events occur outside of data collection. Summary estimates equally do not take into account correlation between repeated observations from the same individual. Measurements from the same individual are much more likely to be correlated than measurements from different individuals and it is important to take into account such correlation when analyzing data with repeated measures to avoid misrepresenting uncertainty in estimates and drawing incorrect inferences. Furthermore, from an economic modelling perspective, simple summary measures do not provide estimates over a sufficient time horizon nor provide adequate explanation of the variation in HRQoL to populate a cost-effectiveness analysis [11].

In addition to summary measures, a variety of regression approaches can be applied to analyze longitudinal HRQoL data. These include general linear models (GLM) and generalized estimating equations (GEE).

A GLM framework attempts to explain variation in HRQoL according to known factors including, e.g., treatment allocation, patient baseline characteristics, and key clinical outcomes. Whilst this approach can be used to explain potential variation in HRQoL outcomes, it is also not designed to explicitly take into account the longitudinal structure of the data (repeated observations for individuals over time) [12].

A GEE framework (also known as marginal or population averaged model) is an extension to GLM which takes into account the correlation associated with repeated sampling from the same individual by adjusting standard errors using an imposed (predefined) correlation structure [13].

Multilevel modelling techniques, in particular mixed models (also known as variance components modelling, hierarchical modelling, or panel data modelling) can also be used to analyze longitudinal HRQoL. There are two ways of measuring effects in multilevel modelling: fixed effects and random effects. A fixed effects model assumes that the intercept for each patient is fixed. This substantially increases the number of parameters in the model and consequently a fixed effects model can be inefficient in terms of degrees of freedom; furthermore time-invariant variables will be dropped because of the correlation between regressors and unobserved individual heterogeneity. A fixed effects model is likely to be preferable if the purpose of the model is only to provide predictions on the sample of data itself [12‐14].

A random effects model is designed to estimate subject-specific effects and, hence, provides distilled estimates of the specified covariates (i.e., a fixed component of the model), plus estimates of random variation according to clusters (i.e., a random component of the model). For longitudinal HRQoL data the individual patient represents the cluster in which multiple observations over time are nested. A mixed model may include fixed or random coefficients for time-varying variables. A mixed model which includes fixed coefficients is termed a random intercept model, whilst a model which includes random coefficients for any time varying variable is a random coefficient model. Mixed models provide a flexible framework compared to GLM or GEE approaches; however, these models are not as parsimonious and require a large sample size to generate reliable results [12‐14].

We evaluated HRQoL outcomes based on SHIFT EQ-5D data for the SHIFT cost-effectiveness analysis. We considered estimates of the intraclass correlation (ICC) to determine whether a multilevel model would be preferable to a GLM. The ICC estimates the proportion of variance in a regression model due to clustering and is calculated as the ratio of between cluster variance and the total variance. Intraclass correlation takes values from 0 to 1; if there is little or no difference between cluster means the ICC will be close to zero (i.e., simple linear regression model may be appropriate), whilst a value of 0.5 would be considered a large ICC [15], suggesting a multilevel model would be preferred.

Patient characteristics considered for selection in the regression model were based on the clinical study protocol, a previous regression equation in HF [10], and clinical advice and included baseline sociodemographic and clinical characteristics [age, sex, NYHA class, HF duration, LVEF, smoking status, alcohol use, diabetes, race, body mass index (BMI)], baseline use of HF medications [beta-blockers, angiotensin-converting enzyme inhibitors, aldosterone antagonists, loop diuretics (dose/kg/day), angiotensin II receptor antagonists, cardiac glycosides, allopurinol], baseline use of other cardiac therapies (cardiac resynchronization, implantable cardiac device, conventional bradycardia-indicated pacemaker), medical history, i.e., prior CV event (myocardial infarction, stroke, coronary artery disease, atrial fibrillation, renal disease, hypertension), and biological characteristics (serum sodium, potassium, creatinine clearance, cholesterol systolic blood pressure). Two time-varying variables were used to capture key clinical outcomes: hospitalization within a 2-month interval (hospitalizations were flagged if they occurred ±30 days from EQ-5D visit date; a 60-day window) and NYHA class. Each hospitalization was assumed to be associated with a change in HRQoL weights over a 2-month period. It is assumed that patients’ HRQoL would be affected up to 30 days before an admission (i.e., due to onset of illness) and up to 30 days after an admission (i.e., recovery). We recognize that this may or may not represent the exact duration of a hospitalization’s impact on a patient’s HRQoL; acute admissions may occur suddenly and recovery may be shorter or longer than the window considered. This time interval was chosen on the basis of clinical advice and according to practical constraints (number of observations available for analysis and a time period which would be consistent with the model cycle length and viable for the cost-effectiveness analysis).

Ivabradine exhibited greater efficacy in patients with higher baseline heart rates in SHIFT [15]; hence, the European license for ivabradine was granted for a subgroup of the trial population—patients with a baseline heart rate ≥75 bpm (SHIFT n = 4154/6505 patients). In our analysis the HRQoL regression model was developed using data from the entire SHIFT substudy cohort (n = 5313 patients). The difference in outcomes for ivabradine associated with baseline heart rate, identified in previous clinical analyses [8, 15], is captured in the HRQoL regression equation using a treatment interaction term (treatment × baseline heart rate). In order to match the population reflected in the license indication, the HRQoL estimates used in the cost-effectiveness analysis and reported in this manuscript reflect estimates for patients with a baseline heart rate ≥75 bpm (predicted from our regression equation) [5].

An initial set of variables were identified using backwards stepwise elimination and cross validated using forwards stepwise selection. The regression model was fitted with and without the variable of interest, the direction and magnitude of effect of other variables was reviewed, and a likelihood ratio test undertaken to test the significance of the nested model. The variables included in the regression model were those variables that demonstrated evidence of an important association with HRQoL outcomes based on magnitude and significance of effect (p < 0.05). The correlation matrix for the initial regression model was reviewed and those variables which appeared strongly correlated were further analyzed for evidence of collinearity. All variables included in the final HRQoL regression model were reviewed by a clinical expert to ascertain whether any spurious or unexpected results had been obtained and whether the direction and magnitude of effect for included variables was consistent with clinical expectations based on a knowledge of the published literature and clinical practice. Data were analyzed using the Stata xtmixed command in Stata Statistical Software: Release 11 (College Station, Texas, United States, StataCorp LP 2009 [16]).

This article is based on previously conducted studies and does not involve any new studies of human or animal subjects performed by any of the authors.