Addressing Ceiling Effects in Health Status Measures: A Comparison of Techniques Applied to Measures for People with HIV Disease

Health-related quality of life (HRQoL) is increasingly used to measure health status. Health profile and preference-based approaches are two types of methods frequently used to measure HRQoL. Health profiles tap multiple dimensions of health. Preference-based approaches quantify the extent to which an individual prefers specific health states using a single index from 0 (death) to 1 (full health). The MOS-HIV Health Survey (Wu et al. 1997) and EQ-5D (The EuroQol Group 1990) are typical health profile and preference-based instruments, respectively. The availability of preference-based HRQoL data is limited because direct assessment is not always feasible. Therefore, researchers have attempted to predict preference-based scores from health profiles, generally using ordinary least squares (OLS) regression (Fryback et al. 1997; Franks et al. 2004). A common phenomenon observed in both health profile and preference-based measures is that the score distribution tends to be skewed to the left. This is called the “ceiling effect.” When data have pronounced ceiling effects, the use of OLS regression violates the statistical requirement for linearity of conditional expectation, leading to inaccurate predictions of preference-based scores and inaccurate identification of predictor variables (Kennedy 1998). Several methods have been proposed to address ceiling effects, such as Tobit models, the censored least absolute deviation (CLAD) approach, two-part models (TPM), and latent class models (LCM) (Greene 2003). The Tobit and CLAD models are preferable to OLS in the presence of a ceiling effect or censored dependent variable. The Tobit model assumes that there is a true unobservable dependent variable that depends linearly on independent variables. The observable dependent variable is defined to be equal to the unobserved variable whenever the true unobserved variable is greater than or equal to the ceiling value. The Tobit model assumes that the error terms are normally distributed with uniform variance (Greene 2003). Unfortunately, evidence suggests that the distribution of utility scores does not follow those assumptions (Austin 2002a). The CLAD approach is based on an assumption that the median will be more robust to ceiling effects than the mean. The coefficients are estimated so as to minimize the sum of the absolute deviations from the regression line (Arabmazar and Schmidt 1981; Johnston 1997). A TPM approach is a more flexible way to address the fact that the HRQoL scores usually have mixed distributions that contain a disproportionate mass of observation at the ceiling and a left-skewed distribution of observations not at the ceiling. The “two parts” model (1) the probability that the dependent variable (e.g., EQ-5D index) can attain the full score and (2) the distribution if the full score is not attained. Both parts are combined in a joint model to predict the dependent variable using the subject's predictors. The LCM is another approach to address data with ceiling effects. This approach is considered by some to be more flexible than the TPM because LCM can handle situations where there are two (or more) classes, with one class being very healthy (i.e., higher utility index) and another group being less healthy (i.e., lower index), as opposed to a TPM which models perfectly healthy (index=1) versus other than perfectly healthy (index <1) (Deb and Trivedi 1997, 2002). Although several studies analyzing HRQoL have used the Tobit model to address ceiling effects (Austin, Escobar, and Kopec 2000; Austin 2002b; Clarke, Gray, and Holman 2002; Sullivan, Lawrence, and Ghushchyan 2005), only three have applied the CLAD (Austin 2002b; Clarke, Gray, and Holman 2002; Sullivan, Lawrence, and Ghushchyan 2005) and none have used a TPM or LCM. The purpose of this study was to compare these statistical methods to predict preference-based HRQoL scores from health profiles for persons with HIV, taking into account ceiling effects. We compared performance (predictive accuracy and error) of these methods to a standard regression model. As an example, we estimated the EQ-5D index from the MOS-HIV. We used a cross-validation method to evaluate the performance of each statistic method.