The use of bootstrap methods for estimating sample size and analysing health-related quality of life outcomes

Health-related quality of life (HRQoL) measures are increasingly used in trials as primary outcome measures. Investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes. HRQoL outcomes, like the SF-36, are usual measured on an ordinal scale, although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes (the ordered categories) reflect contiguous intervals along this continuum. The ordinal scaling of HRQoL measures means they tend to generate data that have discrete, bounded and skewed distributions. Thus, standard methods of analysis that assume Normality and constant variance may not be appropriate. For this reason, conventional statistical advice would suggest non-parametric methods be used to analyse HRQoL data. The bootstrap is one such computer intensive non-parametric method for estimating sample sizes and analysing data.We describe three methods of estimating sample sizes for two-group cross-sectional comparisons of HRQoL outcomes. We then compared the power of the three methods for a two-group cross-sectional study design using bootstrap simulation. The results showed that under the location shift alternative hypothesis, conventional methods of sample size estimation performed well, particularly Whitehead's method. Whitehead's method is recommended if the HRQoL outcome has a limited number of discrete values (<7) and/or the expected proportion of cases at either of the bounds is high. If a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate, than conventional methods.Finally, we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters, in an example data set. We then compared and contrasted the bootstrap with standard methods of analysing HRQoL outcomes. In the data set studied, with the SF-36 outcome, the use of the bootstrap for estimating sample sizes and analysing HRQoL data produces results similar to conventional statistical methods. These results suggest that bootstrap methods are not more appropriate for analysing HRQoL outcome data than standard methods.     

Population norms for the AQoL derived from the 2007 Australian National Survey of Mental Health and Wellbeing

Objective : To provide Australian health‐related quality of life (HRQoL) population norms, based on utility scores from the Assessment of Quality of Life (AQoL) measure, a participant‐reported outcomes (PRO) instrument. Methods: The data were from the 2007 National Survey of Mental Health and Wellbeing. AQoL scores were analysed by age cohorts, gender, other demographic characteristics, and mental and physical health variables. Results: The AQoL utility score mean was 0.81 (95%CI 0.81–0.82), and 47% obtained scores indicating a very high HRQoL (>0.90). HRQoL gently declined by age group, with older adults’ scores indicating lower HRQoL. Based on effect sizes (ESs), there were small losses in HRQoL associated with other demographic variables (e.g. by lack of labour force participation, ES_median: 0.27). Those with current mental health syndromes reported moderate losses in HRQoL (ES_median: 0.64), while those with physical health conditions generally also reported moderate losses in HRQoL (ES_median: 0.41). Conclusions: This study has provided contemporary Australian population norms for HRQoL that may be used by researchers as indicators allowing interpretation and estimation of population health (e.g. estimation of the burden of disease), cross comparison between studies, the identification of health inequalities, and to provide benchmarks for health care interventions.     

Estimation of age‐specific incidence rates from cross‐sectional survey data

Age‐specific disease incidence rates are typically estimated from longitudinal data, where disease‐free subjects are followed over time and incident cases are observed. However, longitudinal studies have substantial cost and time requirements, not to mention other challenges such as loss to follow up. Alternatively, cross‐sectional data can be used to estimate age‐specific incidence rates in a more timely and cost‐effective manner. Such studies rely on self‐report of onset age. Self‐reported onset age is subject to measurement error and bias. In this paper, we use a Bayesian bivariate smoothing approach to estimate age‐specific incidence rates from cross‐sectional survey data. Rates are modeled as a smooth function of age and lag (difference between age and onset age), with larger values of lag effectively down weighted, as they are assumed to be less reliable. We conduct an extensive simulation study to investigate the extent to which measurement error and bias in the reported onset age affects inference using the proposed methods. We use data from a national headache survey to estimate age‐ and gender‐specific migraine incidence rates. Copyright © 2010 John Wiley & Sons, Ltd.     

Long‐Term Effects of Child Death on Parents' Health‐Related Quality of Life: A Dyadic Analysis

This study examines the long‐term effects of child death on bereaved parents' health‐related quality of life (HRQoL). Using data from the Wisconsin Longitudinal Study, we compared 233 bereaved couples and 229 comparison couples (mean age = 65.11 years) and examined the life course effects of child death on parents' HRQoL. Variations in bereavement effects were examined by gender and for different causes of death. Bereaved parents had significantly worse HRQoL than comparison group parents, and there was no evidence of gender differences for this effect. With respect to the cause of a child's death, bereaved parents whose child died in violent circumstances had particularly low levels of HRQoL. Multilevel models indicated that marital closeness mitigated the negative effects of bereavement.     

Semiparametric regression models for repeated measures of mortal cohorts with non‐monotone missing outcomes and time‐dependent covariates

We propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non‐response to estimate regression parameters interpreted as conditioned on being alive. Our proposed method accommodates outcomes and time‐dependent covariates that are missing not at random with non‐monotone missingness patterns via inverse‐probability weighting. Missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse‐probability‐weighted estimating equation. Thus, we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates. The approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition, inflammation, and age. Copyright © 2010 John Wiley & Sons, Ltd.     

Semiparametric regression analysis of failure time data with dependent interval censoring

Interval‐censored failure‐time data arise when subjects are examined or observed periodically such that the failure time of interest is not examined exactly but only known to be bracketed between two adjacent observation times. The commonly used approaches assume that the examination times and the failure time are independent or conditionally independent given covariates. In many practical applications, patients who are already in poor health or have a weak immune system before treatment usually tend to visit physicians more often after treatment than those with better health or immune system. In this situation, the visiting rate is positively correlated with the risk of failure due to the health status, which results in dependent interval‐censored data. While some measurable factors affecting health status such as age, gender, and physical symptom can be included in the covariates, some health‐related latent variables cannot be observed or measured. To deal with dependent interval censoring involving unobserved latent variable, we characterize the visiting/examination process as recurrent event process and propose a joint frailty model to account for the association of the failure time and visiting process. A shared gamma frailty is incorporated into the Cox model and proportional intensity model for the failure time and visiting process, respectively, in a multiplicative way. We propose a semiparametric maximum likelihood approach for estimating model parameters and show the asymptotic properties, including consistency and weak convergence. Extensive simulation studies are conducted and a data set of bladder cancer is analyzed for illustrative purposes. Copyright © 2017 John Wiley & Sons, Ltd.     

Choice of time-scale in Cox's model analysis of epidemiologic cohort data: a simulation study

Cox's regression model is widely used for assessing associations between potential risk factors and disease occurrence in epidemiologic cohort studies. Although age is often a strong determinant of disease risk, authors have frequently used time-on-study instead of age as the time-scale, as for clinical trials. Unless the baseline hazard is an exponential function of age, this approach can yield different estimates of relative hazards than using age as the time-scale, even when age is adjusted for. We performed a simulation study in order to investigate the existence and magnitude of bias for different degrees of association between age and the covariate of interest. Age to disease onset was generated from exponential, Weibull or piecewise Weibull distributions, and both fixed and time-dependent dichotomous covariates were considered. We observed no bias upon using age as the time-scale. Upon using time-on-study, we verified the absence of bias for exponentially distributed age to disease onset. For non-exponential distributions, we found that bias could occur even when the covariate of interest was independent from age. It could be severe in case of substantial association with age, especially with time-dependent covariates. These findings were illustrated on data from a cohort of 84,329 French women followed prospectively for breast cancer occurrence. In view of our results, we strongly recommend not using time-on-study as the time-scale for analysing epidemiologic cohort data.     

Incorporating prognostic factors into causal estimators: A comparison of methods for randomised controlled trials with a time‐to‐event outcome

In randomised controlled trials, the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it. We compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model and quantify the bias due to omitting baseline prognostic factors. Causal estimates are found directly by maximising a novel partial likelihood; based on a structural proportional hazards model; and based on a ‘corrected dataset’ derived after fitting a rank‐preserving structural failure time model. Where necessary, we extend these methods to incorporate baseline covariates. Comparisons use simulated data and a real data example. Analysing the simulated data, we found that all three methods are accurate when an important covariate was included in the proportional hazards model (maximum bias 5.4%). However, failure to adjust for this prognostic factor meant that causal treatment effects were underestimated (maximum bias 11.4%), because estimators were based on a misspecified marginal proportional hazards model. Analysing the real data example, we found that adjusting causal estimators is important to correct for residual imbalances in prognostic factors present between trial arms after randomisation. Our results show that methods of estimating causal treatment effects for time‐to‐event outcomes should be extended to incorporate covariates, thus providing an informative compliment to the corresponding intention‐to‐treat analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Obesity,metabolic abnormality,and health-related quality of life by gender: a cross-sectional study in Korean adults

Purpose

This study sought to compare the association between health-related quality of life (HRQoL) and four body health types by gender.

Methods

The study included 6217 men and 8243 women over 30 years of age chosen from a population-based survey. Participants were grouped by body mass index and metabolic abnormality into four types: metabolically healthy normal weight, metabolically abnormal but normal weight (MANW), metabolically healthy obesity (MHO), and metabolically abnormal obesity (MAO). HRQoL was measured using the EQ-5D health questionnaire. The outcomes encompassed five dimensions (mobility, self-care, usual activity, pain/discomfort, and anxiety/depression), and the impaired HRQoL dichotomized by the EQ-5D preference score. Complex sample multivariate binary logistic regression analyses were conducted to adjust for sociodemographic variables, lifestyle factors, and disease comorbidity.

Results

Among men, those in the MANW group presented worse conditions on all dimensions and the impaired HRQoL compared to other men. However, no significant effect remained after adjusting for relevant covariates. For women, those in the MAO group had the most adversely affected HRQoL followed by those females in the MHO group. The domain of mobility and impaired HRQoL variable of the MAO and MHO groups remained significant when controlling for all covariates in the model.

Conclusions

The MANW is the least favorable condition of HRQoL for men, suggesting that metabolic health may associate with HRQoL more than obesity for males. In women, the MAO and MHO groups had the most adversely affected HRQoL, implying that MHO is not a favorable health condition and that obesity, in general, may be strongly associated with HRQoL in women.

     

Sensitivity of regression calibration to non‐perfect validation data with application to the Norwegian Women and Cancer Study

Measurement error occurs when we observe error‐prone surrogates, rather than true values. It is common in observational studies and especially so in epidemiology, in nutritional epidemiology in particular. Correcting for measurement error has become common, and regression calibration is the most popular way to account for measurement error in continuous covariates. We consider its use in the context where there are validation data, which are used to calibrate the true values given the observed covariates. We allow for the case that the true value itself may not be observed in the validation data, but instead, a so‐called reference measure is observed. The regression calibration method relies on certain assumptions.This paper examines possible biases in regression calibration estimators when some of these assumptions are violated. More specifically, we allow for the fact that (i) the reference measure may not necessarily be an ‘alloyed gold standard’ (i.e., unbiased) for the true value; (ii) there may be correlated random subject effects contributing to the surrogate and reference measures in the validation data; and (iii) the calibration model itself may not be the same in the validation study as in the main study; that is, it is not transportable. We expand on previous work to provide a general result, which characterizes potential bias in the regression calibration estimators as a result of any combination of the violations aforementioned. We then illustrate some of the general results with data from the Norwegian Women and Cancer Study. Copyright © 2015 John Wiley & Sons, Ltd.