Item response models for longitudinal quality of life data in clinical trials

Semiparametric multivariate joint model for skewed-longitudinal and survival data: A Bayesian approach

Joint models and statistical inference for longitudinal and survival data have been an active area of statistical research and have mostly coupled a longitudinal biomarker-based mixed-effects model with normal distribution and an event time-based survival model. In practice, however, the following issues may standout: (i) Normality of model error in longitudinal models is a routine assumption, but it may be unrealistically violating data features of subject variations. (ii) Data collected are often featured by the mixed types of multiple longitudinal outcomes which are significantly correlated, ignoring their correlation may lead to biased estimation. Additionally, a parametric model specification may be inflexible to capture the complicated patterns of longitudinal data. (iii) Missing observations in the longitudinal data are often encountered; the missing measures are likely to be informative (nonignorable) and ignoring this phenomenon may result in inaccurate inference. Multilevel item response theory (MLIRT) models have been increasingly used to analyze the multiple longitudinal data of mixed types (ie, continuous and categorical) in clinical studies. In this article, we develop an MLIRT-based semiparametric joint model with skew-t distribution that consists of an extended MLIRT model for the mixed types of multiple longitudinal data and a Cox proportional hazards model, linked through random-effects. A Bayesian approach is employed for joint modeling. Simulation studies are conducted to assess performance of the proposed models and method. A real example from primary biliary cirrhosis clinical study is analyzed to estimate parameters in the joint model and also evaluate sensitivity of parameter estimates for various plausible nonignorable missing data mechanisms.

EM algorithm estimation of a structural equation model for the longitudinal study of the quality of life

Health-related quality of life (HRQoL) data are measured via patient questionnaires, completed by the patients themselves at different time points. We focused on oncology data gathered through the use of European Organization for Research and Treatment of Cancer questionnaires, which decompose HRQoL into several functional dimensions, several symptomatic dimensions, and the global health status (GHS). We aimed to perform a global analysis of HRQoL and reduce the number of analyses required by using a two-step approach. First, a structural equation model (SEM) was used for each time point; in these models, the GHS is explained by two latent variables. Each latent variable is a factor that summarizes, respectively, the functional dimensions and the symptomatic dimensions to the global measurement. This is achieved through the maximization of the likelihood of each SEM using the EM algorithm, which has the advantage of giving an estimation of the subject-specific factors and the influence of additional explanatory variables. Then, to consider the longitudinal aspect, the GHS variable and the two factors were concatenated for each patient visit at which the questionnaire was completed. The GHS and the two factors estimated in the first step can then be explained by additional explanatory variables using a linear mixed model.

Scale development with small samples: a new application of longitudinal item response theory

PURPOSE

Measurement development in hard-to-reach populations can pose methodological challenges. Item response theory (IRT) is a useful statistical tool, but often requires large samples. We describe the use of longitudinal IRT models as a pragmatic approach to instrument development when large samples are not feasible.

METHODS

The statistical foundations and practical benefits of longitudinal IRT models are briefly described. Results from a simulation study are reported to demonstrate the model's ability to recover the generating measurement structure and parameters using a range of sample sizes, number of items, and number of time points. An example using early-phase clinical trial data in a rare condition demonstrates these methods in practice.

RESULTS

Simulation study results demonstrate that the longitudinal IRT model's ability to recover the generating parameters rests largely on the interaction between sample size and the number of time points. Overall, the model performs well even in small samples provided a sufficient number of time points are available. The clinical trial data example demonstrates that by using conditional, longitudinal IRT models researchers can obtain stable estimates of psychometric characteristics from samples typically considered too small for rigorous psychometric modeling.

CONCLUSION

Capitalizing on repeated measurements, it is possible to estimate psychometric characteristics for an assessment even when sample size is small. This allows researchers to optimize study designs and have increased confidence in subsequent comparisons using scores obtained from such models. While there are limitations and caveats to consider when using these models, longitudinal IRT modeling may be especially beneficial when developing measures for rare conditions and diseases in difficult-to-reach populations.

Bayesian Hierarchical Joint Modeling Using Skew-Normal/Independent Distributions

The multiple longitudinal outcomes collected in many clinical trials are often analyzed by multilevel item response theory (MLIRT) models. The normality assumption for the continuous outcomes in the MLIRT models can be violated due to skewness and/or outliers. Moreover, patients' follow-up may be stopped by some terminal events (e.g., death or dropout) which are dependent on the multiple longitudinal outcomes. We proposed a joint modeling framework based on the MLIRT model to account for three data features: skewness, outliers, and dependent censoring. Our method development was motivated by a clinical study for Parkinson's disease.

Joint modeling of multivariate longitudinal measurements and survival data with applications to Parkinson's disease

In many clinical trials, studying neurodegenerative diseases including Parkinson's disease (PD), multiple longitudinal outcomes are collected in order to fully explore the multidimensional impairment caused by these diseases. The follow-up of some patients can be stopped by some outcome-dependent terminal event, e.g. death and dropout. In this article, we develop a joint model that consists of a multilevel item response theory (MLIRT) model for the multiple longitudinal outcomes, and a Cox's proportional hazard model with piecewise constant baseline hazards for the event time data. Shared random effects are used to link together two models. The model inference is conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in BUGS language. Our proposed model is evaluated by simulation studies and is applied to the DATATOP study, a motivating clinical trial assessing the effect of tocopherol on PD among patients with early PD.

Power and Sample Size Calculations in Clinical Trials with Patient-Reported Outcomes under Equal and Unequal Group Sizes Based on Graded Response Model: A Simulation Study

OBJECTIVES

To provide a valid sample size strategy based on simulation and to evaluate the statistical power in clinical trials with patient-reported outcomes (PROs) based on a polytomous item response theory model-the graded response model (GRM)-and to compare this framework with the classical test theory (CTT) approach.

METHODS

One thousand randomized clinical trials were simulated using PRO based on the GRM and under various combinations of the number of patients in each arm, the group allocation ratio, the number of items and categories, and group effects. The power and sample size estimated in the simulations were then compared with those computed using the CTT framework.

RESULTS

The results indicated that the impact of the most influential factors, including the number of patients, group allocation ratio, group effects, and the number of categories, on the power and sample size of the GRM-based and CTT-based approaches was similar. Nevertheless, the strong impact of the number of items on these issues distinguished the two approaches.

CONCLUSIONS

It is crucial to use an adapted sample size formula in a GRM-based analysis because the classical formula designed for the CTT-based approach does not consider the impact of the number of items, which could result in an inadequately sized study and a decrease in power. Thus, when clinicians design a randomized clinical trial with polytomous PRO endpoints using classical sample size formula as the base, they should be aware of the possibility of making an incorrect clinical decision.

Bayesian multiple imputation for missing multivariate longitudinal data from a Parkinson's disease clinical trial

In Parkinson's disease (PD) clinical trials, Parkinson's disease is studied using multiple outcomes of various types (e.g. binary, ordinal, continuous) collected repeatedly over time. The overall treatment effects across all outcomes can be evaluated based on a global test statistic. However, missing data occur in outcomes for many reasons, e.g. dropout, death, etc., and need to be imputed in order to conduct an intent-to-treat analysis. We propose a Bayesian method based on item response theory to perform multiple imputation while accounting for multiple sources of correlation. Sensitivity analysis is performed under various scenarios. Our simulation results indicate that the proposed method outperforms standard methods such as last observation carried forward and separate random effects model for each outcome. Our method is motivated by and applied to a Parkinson's disease clinical trial. The proposed method can be broadly applied to longitudinal studies with multiple outcomes subject to missingness.

Robust Bayesian hierarchical model using normal/independent distributions

The multilevel item response theory (MLIRT) models have been increasingly used in longitudinal clinical studies that collect multiple outcomes. The MLIRT models account for all the information from multiple longitudinal outcomes of mixed types (e.g., continuous, binary, and ordinal) and can provide valid inference for the overall treatment effects. However, the continuous outcomes and the random effects in the MLIRT models are often assumed to be normally distributed. The normality assumption can sometimes be unrealistic and thus may produce misleading results. The normal/independent (NI) distributions have been increasingly used to handle the outlier and heavy tail problems in order to produce robust inference. In this article, we developed a Bayesian approach that implemented the NI distributions on both continuous outcomes and random effects in the MLIRT models and discussed different strategies of implementing the NI distributions. Extensive simulation studies were conducted to demonstrate the advantage of our proposed models, which provided parameter estimates with smaller bias and more reasonable coverage probabilities. Our proposed models were applied to a motivating Parkinson's disease study, the DATATOP study, to investigate the effect of deprenyl in slowing down the disease progression.

Comparison of three longitudinal analysis models for the health-related quality of life in oncology: a simulation study

BACKGROUND

Health-Related Quality of Life (HRQoL) is an important endpoint in oncology clinical trials aiming to investigate the clinical benefit of new therapeutic strategies for the patient. However, the longitudinal analysis of HRQoL remains complex and unstandardized. There is clearly a need to propose accessible statistical methods and meaningful results for clinicians. The objective of this study was to compare three strategies for longitudinal analyses of HRQoL data in oncology clinical trials through a simulation study.

METHODS

The methods proposed were: the score and mixed model (SM); a survival analysis approach based on the time to HRQoL score deterioration (TTD); and the longitudinal partial credit model (LPCM). Simulations compared the methods in terms of type I error and statistical power of the test of an interaction effect between treatment arm and time. Several simulation scenarios were explored based on the EORTC HRQoL questionnaires and varying the number of patients (100, 200 or 300), items (1, 2 or 4) and response categories per item (4 or 7). Five or 10 measurement times were considered, with correlations ranging from low to high between each measure. The impact of informative missing data on these methods was also studied to reflect the reality of most clinical trials.

RESULTS

With complete data, the type I error rate was close to the expected value (5%) for all methods, while the SM method was the most powerful method, followed by LPCM. The power of TTD is low for single-item dimensions, because only four possible values exist for the score. When the number of items increases, the power of the SM approach remained stable, those of the TTD method increases while the power of LPCM remained stable. With 10 measurement times, the LPCM was less efficient. With informative missing data, the statistical power of SM and TTD tended to decrease, while that of LPCM tended to increase.

CONCLUSIONS

To conclude, the SM model was the most powerful model, irrespective of the scenario considered, and the presence or not of missing data. The TTD method should be avoided for single-item dimensions of the EORTC questionnaire. While the LPCM model was more adapted to this kind of data, it was less efficient than the SM model. These results warrant validation through comparisons on real data.

Longitudinal mixed-effects models for latent cognitive function

A mixed-effects regression model with a bent-cable change-point predictor is formulated to describe potential decline of cognitive function over time in the older population. For the individual trajectories, cognitive function is considered to be a latent variable measured through an item response theory model given longitudinal test data. Individual-specific parameters are defined for both cognitive function and the rate of change over time, using the change-point predictor for non-linear trends. Bayesian inference is used, where the Deviance Information Criterion and the L-criterion are investigated for model comparison. Special attention is given to the identifiability of the item response parameters. Item response theory makes it possible to use dichotomous and polytomous test items, and to take into account missing data and survey-design change during follow-up. This will be illustrated in an application where data stem from the Cambridge City over-75s Cohort Study.

Bayesian hierarchical model for multiple repeated measures and survival data: an application to Parkinson's disease

Multilevel item response theory models have been increasingly used to analyze the multivariate longitudinal data of mixed types (e.g., continuous and categorical) in clinical studies. To address the possible correlation between multivariate longitudinal measures and time to terminal events (e.g., death and dropout), joint models that consist of a multilevel item response theory submodel and a survival submodel have been previously developed. However, in multisite studies, multiple patients are recruited and treated by the same clinical site. There can be a significant site correlation because of common environmental and socioeconomic status, and similar quality of care within site. In this article, we develop and study several hierarchical joint models with the hazard of terminal events dependent on shared random effects from various levels. We conduct extensive simulation study to evaluate the performance of various models under different scenarios. The proposed hierarchical joint models are applied to the motivating deprenyl and tocopherol antioxidative therapy of Parkinsonism study to investigate the effect of tocopherol in slowing Parkinson's disease progression.

Item response theory and factor analysis as a mean to characterize occurrence of response shift in a longitudinal quality of life study in breast cancer patients

BACKGROUND

The occurrence of response shift (RS) in longitudinal health-related quality of life (HRQoL) studies, reflecting patient adaptation to disease, has already been demonstrated. Several methods have been developed to detect the three different types of response shift (RS), i.e. recalibration RS, 2) reprioritization RS, and 3) reconceptualization RS. We investigated two complementary methods that characterize the occurrence of RS: factor analysis, comprising Principal Component Analysis (PCA) and Multiple Correspondence Analysis (MCA), and a method of Item Response Theory (IRT).

METHODS

Breast cancer patients (n = 381) completed the EORTC QLQ-C30 and EORTC QLQ-BR23 questionnaires at baseline, immediately following surgery, and three and six months after surgery, according to the "then-test/post-test" design. Recalibration was explored using MCA and a model of IRT, called the Linear Logistic Model with Relaxed Assumptions (LLRA) using the then-test method. Principal Component Analysis (PCA) was used to explore reconceptualization and reprioritization.

RESULTS

MCA highlighted the main profiles of recalibration: patients with high HRQoL level report a slightly worse HRQoL level retrospectively and vice versa. The LLRA model indicated a downward or upward recalibration for each dimension. At six months, the recalibration effect was statistically significant for 11/22 dimensions of the QLQ-C30 and BR23 according to the LLRA model (p ≤ 0.001). Regarding the QLQ-C30, PCA indicated a reprioritization of symptom scales and reconceptualization via an increased correlation between functional scales.

CONCLUSIONS

Our findings demonstrate the usefulness of these analyses in characterizing the occurrence of RS. MCA and IRT model had convergent results with then-test method to characterize recalibration component of RS. PCA is an indirect method in investigating the reprioritization and reconceptualization components of RS.

Bayesian inference for an illness-death model for stroke with cognition as a latent time-dependent risk factor

Longitudinal data can be used to estimate the transition intensities between healthy and unhealthy states prior to death. An illness-death model for history of stroke is presented, where time-dependent transition intensities are regressed on a latent variable representing cognitive function. The change of this function over time is described by a linear growth model with random effects. Occasion-specific cognitive function is measured by an item response model for longitudinal scores on the Mini-Mental State Examination, a questionnaire used to screen for cognitive impairment. The illness-death model will be used to identify and to explore the relationship between occasion-specific cognitive function and stroke. Combining a multi-state model with the latent growth model defines a joint model which extends current statistical inference regarding disease progression and cognitive function. Markov chain Monte Carlo methods are used for Bayesian inference. Data stem from the Medical Research Council Cognitive Function and Ageing Study in the UK (1991-2005).

Item response modelling for clinical and laboratory testing

BACKGROUND

Item response models using exponential modelling are more sensitive than classical linear methods for making predictions from psychological questionnaires.

OBJECTIVE

To assess whether they can also be used for making predictions from quality of life questionnaires and clinical and laboratory diagnostic-tests.

METHODS

Of 1000 anginal patients assessed for quality of life and 1350 patients assessed for peripheral vascular disease with diagnostic laboratory tests, items response modelling was applied using the Latent Trait Analysis program -2 of Uebersax.

RESULTS

The 32 different response patterns obtained from test batteries of five items produced 32 different quality of life scores ranging from 3·4% to 74·5% and 32 different levels of peripheral vascular disease ranging from 9·9% to 83·5% with overall mean scores, by definition, of 50%, whereas the classical method of analysis produced the discrete scores of only 0-5. The item response models produced an adequate fit for the data as demonstrated by chi-square goodness of fit values/degrees of freedom of 0·86 and 0·64.

CONCLUSIONS

1 Quality of life assessments and diagnostic tests can be analysed through item response modelling, and provide more sensitivity than do classical linear models. 2 Item response modelling can change largely qualitative data into fairly accurate quantitative data, and can, even with limited sets of items, produce fairly accurate frequency distribution patterns of quality of life, severity of disease and other latent traits.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Longitudinal profiling of health care units based on continuous and discrete patient outcomes

Monitoring health care quality involves combining continuous and discrete outcomes measured on subjects across health care units over time. This article describes a Bayesian approach to jointly modeling multilevel multidimensional continuous and discrete outcomes with serial dependence. The overall goal is to characterize trajectories of traits of each unit. Underlying normal regression models for each outcome are used and dependence among different outcomes is induced through latent variables. Serial dependence is accommodated through modeling the pairwise correlations of the latent variables. Methods are illustrated to assess trends in quality of health care units using continuous and discrete outcomes from a sample of adult veterans discharged from 1 of 22 Veterans Integrated Service Networks with a psychiatric diagnosis between 1993 and 1998.

In a randomized controlled trial, missing data led to biased results regarding anxiety

BACKGROUND AND OBJECTIVE

Randomization does not protect against bias due to missing observations. In addition, different reasons for missing observations may lead to different invalid results. The purpose of this study was to illustrate how randomized intervention studies can be threatened by bias due to missing observations because of death or nonresponse.

METHODS

A randomized clinical trial of the effect of psychosocial intervention on well-being after an operation for colorectal cancer was conducted in Denmark. Patients were interviewed 3, 6, 12, and 24 months after discharge from hospital.

RESULTS

We found that the probability of nonresponse decreased with increasing anxiety score in the intervention group, but it increased with increasing anxiety score in the control group. This could lead to severe bias in an analysis of the effect of intervention on anxiety. Low physical functioning and low global health status and quality of life were related to an increased probability of dying before the next follow-up, and this association could explain the associations between anxiety and depression, respectively, and the probability of dying observed in crude analyses.

CONCLUSION

Our study emphasizes the importance of performing specific missing data analyses in any study of well-being variables.

Classical Test Theory versus Rasch analysis for quality of life questionnaire reduction

BACKGROUND

Although health-related quality of life (HRQOL) instruments may offer satisfactory results, their length often limits the extent to which they are actually applied in clinical practice. Efforts to develop short questionnaires have largely focused on reducing existing instruments. The approaches most frequently employed for this purpose rely on statistical procedures that are considered exponents of Classical Test Theory (CTT). Despite the popularity of CTT, two major conceptual limitations have been pointed out: the lack of an explicit ordered continuum of items that represent a unidimensional construct, and the lack of additivity of rating scale data. In contrast to the CTT approach, the Rasch model provides an alternative scaling methodology that enables the examination of the hierarchical structure, unidimensionality and additivity of HRQOL measures.

METHODS

In order to empirically compare CTT and Rasch Analysis (RA) results, this paper presents the parallel reduction of a 38-item questionnaire, the Nottingham Health Profile (NHP), through the analysis of the responses of a sample of 9,419 individuals.

RESULTS

CTT resulted in 20 items (4 dimensions) whereas RA in 22 items (2 dimensions). Both instruments showed similar characteristics under CTT requirements: item-total correlation ranged 0.45-0.75 for NHP20 and 0.46-0.68 for NHP22, while reliability ranged 0.82-0.93 and 0.87-94 respectively.

CONCLUSIONS

Despite the differences in content, NHP20 and NHP22 convergent scores also showed high degrees of association (0.78-0.95). Although the unidimensional view of health of the NHP20 and NHP22 composite scores was also confirmed by RA, NHP20 dimensions failed to meet the goodness-of fit criteria established by the Rasch model, precluding the interval-level of measurement of its scores.

Outcomes research at the National Cancer Institute: measuring, understanding, and improving the outcomes of cancer care

What is the National Cancer Institute (NCI) doing to enhance the state of the science for measuring and understanding patient-centered outcomes of cancer care and to make this information useful for improved decision making? The NCI has a new focus on research that describes, interprets, and predicts the impact of various influences, especially interventions, on end points that matter to decision makers. The research includes end points such as survival, health-related quality of life, satisfaction and patient experience, and economic burden. To further this work, NCI supports and conducts research to (1) identify valid, reliable, responsive, and feasible end-point measures; (2) collect high-quality evidence about the impact of interventions on the end points of interest; (3) improve our understanding of the effects of other factors that shape this interaction; and (4) expand our capacity to translate research findings into information that is useful to patients, clinical policy makers, payers, regulators, standard setters, and providers of cancer care.

Use of item response theory to link 3 modules of functional status items from the Asset and Health Dynamics Among the Oldest Old study

OBJECTIVE

To link, by using item response theory (IRT), 3 modules of functional status items in the Asset and Health Dynamics Among the Oldest Old (AHEAD) study.

DESIGN

Secondary data analysis of the functional status items in the AHEAD study. In that study, participants completed a common set of functional status items and were randomly assigned to complete 1 of 2 modules containing different functional status items.

SETTING

A nationally representative panel study of elderly.

PARTICIPANTS

US baseline data from 4655 respondents.

INTERVENTIONS

Not applicable.

MAIN OUTCOME MEASURES

Nineteen common items and 2 sets of supplemental items that measure functional status.

RESULTS

A 2-parameter model for dichotomous items was used for linking the 3 modules of items. By using this model, both sets of supplemental items were successfully linked to the common items, allowing the placement of all items on the same underlying measure of ability. The small-muscle instrumental activities of daily living were the easiest of all the items for respondents to perform. The item on walking from the Longitudinal Study of Aging was the most difficult for respondents to perform.

CONCLUSIONS

IRT-based linking methods were a useful way to overcome test dependency and to place items on a common metric even if different respondents answer different sets of items. Numerous important design features can degrade linking results and should be attended to in future linking studies.

Item response models for joint analysis of quality of life and survival

A complication when assessing quality of life data longitudinally is that in many trials a substantial percentage of patients die before completing all of the assessments. Furthermore, a patient's risk of dying might be predicted by his current quality of life. This suggests jointly modelling quality of life and survival, and using this combined information to summarize the outcome. The aim of this paper is to address the complicated issues, such as death, present in analysing multiple-item ordinal quality of life data in clinical trials while recognizing the psychometric properties of the quality of life instrument being used. This is done by combining an item response model and Cox's proportional hazard model, where a latent variable process for quality of life determines the probability of selecting various options on quality of life items, and also serves as a time-dependent covariate in the survival model. We accomplish this by using Markov chain Monte Carlo methods to obtain parameter estimates. Then we compute a summary measure, area-under-QOL curve, to compare the efficacy of the treatments. The methods are illustrated with analysis of data from the Vesnarinone trial of patients with severe heart failure, in which quality of life was assessed with the Minnesota Living with Heart Failure Questionnaire.

Application of random effect ordinal regression model for outcome evaluation of two randomized controlled trials

Cluster randomization is often used in intervention trials, yet when individuals nested within clusters are considered as the units of analysis for outcome evaluation, it cannot be assumed that the observations are statistically independent. Observations that are not statistically independent also result when repeated measures are taken over time for the same individual. Ignoring clustered observations when performing data analysis can lead to the erroneous conclusion that the intervention under study had a statistically significant effect. Moreover, individual responses are often collected on ordinal scales; thus models for continuous or categorical data are usually not appropriate. We applied a random effect ordinal regression model to data sets from two randomized controlled intervention trials that measured graded scale non-independent responses. The first trial compared two school programmes for AIDS prevention in terms of impact (i.e., changes in the frequency of condom use). The second trial used the MOS-HIV questionnaire to measure the quality of life of new AIDS cases four times over a one-year follow-up period (only results of the role-functioning scale are reported). Regarding the first data set, the effect of the intervention was not significant, and the post-intervention frequency of condom use was mainly attributable to the pre-intervention frequency (p<0.01), with no differences among schools. Regarding the second data set, a borderline significant increase in the role-functioning scale scores was observed over the follow-up period; the results differed only slightly by intervention group; a significant (p<0.01) intra-individual correlation of 0.4 was found.