Comparing alternative models: log vs Cox proportional hazard?

Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y|x) using the Cox model.     

Direct estimation of the area under the receiver operating characteristic curve with verification biased data

In medical diagnostic studies, verification of the true disease status might be partially missing based on results of diagnostic tests and other characteristics of subjects. Because estimates of area under the ROC curve (AUC) based on partially validated subjects are usually biased, it is usually necessary to estimate AUC from a bias-corrected ROC curve. In this article, various direct estimation methods of the AUC based on hybrid imputation [full imputations and mean score imputation (MSI)], inverse probability weighting, and the semiparametric efficient (SPE) approach are proposed and compared in the presence of verification bias when the test result is continuous under the assumption that the true disease status, if missing, is missing at random. Simulation results show that the proposed estimators are accurate for the biased sampling if the disease and verification models are correctly specified. The SPE and MSI based estimators perform well even under the misspecified disease/verification models. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. A real dataset of neonatal hearing screening study is analyzed.     

Analysis of Health Utility Data When Some Subjects Attain the Upper Bound of 1: Are Tobit and CLAD Models Appropriate?

BackgroundHealth utility data often show an apparent truncation effect, where a proportion of individuals achieve the upper bound of 1. The Tobit model and censored least absolute deviations (CLAD) have both been used as analytic solutions to this apparent truncation effect. These models assume that the observed utilities are censored at 1, and hence that the true utility can be greater than 1. We aimed to examine whether the Tobit and CLAD models yielded acceptable results when this censoring assumption was not appropriate.MethodsUsing health utility (captured through EQ5D) data from a diabetes study, we conducted a simulation to compare the performance of the Tobit, CLAD, ordinary least squares (OLS), two-part and latent class estimators in terms of their bias and estimated confidence intervals. We also illustrate the performance of semiparametric and nonparametric bootstrap methods.ResultsWhen the true utility was conceptually bounded above at 1, the Tobit and CLAD estimators were both biased. The OLS estimator was asymptotically unbiased and, while the model-based and semiparametric bootstrap confidence intervals were too narrow, confidence intervals based on the robust standard errors or the nonparametric bootstrap were acceptable for sample sizes of 100 and larger. Two-part and latent class models also yielded unbiased estimates.ConclusionsWhen the intention of the analysis is to inform an economic evaluation, and the utilities should be bounded above at 1, CLAD, and Tobit methods were biased. OLS coupled with robust standard errors or the nonparametric bootstrap is recommended as a simple and valid approach.     

Estimating medical care costs under conditions of censoring

A number of non-parametric estimators have been proposed to calculate average medical care costs in the presence of censoring. This paper assesses their performance both in terms of bias and efficiency under extreme conditions using a medical dataset which exhibits heavy censoring. The estimators are further investigated using artificially generated data. Their variances are derived from analytic formulae based on the estimators' asymptotic properties and these are compared to empirically derived bootstrap estimates. The analysis revealed various performance patterns ranging from generally stable estimators under all conditions considered to estimators which become increasingly unstable with increasing levels of censoring. The bootstrap estimates of variance were consistent with the analytically derived asymptotic variance estimates. Of the two estimators that performed best, one imposes restrictions on the censoring distribution while the other is not restricted by the censoring pattern and on this basis the second may be preferred.     

A copula‐based mixed Poisson model for bivariate recurrent events under event‐dependent censoring

In many chronic disease processes subjects are at risk of two or more types of events. We describe a bivariate mixed Poisson model in which a copula function is used to model the association between two gamma distributed random effects. The resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process. Methods for parameter estimation are described for parametric and semiparametric models based on an EM algorithm. We also consider the issue of event‐dependent censoring based on one type of event, which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study. The asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed, as well as associated treatment effects. Because the joint model is fit based on a likelihood, consistent estimates are obtained. Simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event‐dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust analysis in joint models: an application to a study on muscular dystrophy

Generalized partial ordinal models occur frequently in biomedical investigations where, along with ordinal longitudinal outcomes, there are time‐dependent covariates that act nonparametrically. In these studies, an association between such outcomes and time to an event is of considerable interest to medical practitioners. The primary objective in the present article is to study the robustness of estimators of the parameters of interest in a joint generalized partial ordinal models and a time‐to‐event model, because in many situations, the estimators in such joint models are sensitive to outliers. A Monte Carlo Metropolis–Hastings Newton Raphson algorithm is proposed for robust estimation. A detailed simulation study was performed to justify the behavior of the proposed estimators. By way of motivation, we consider a data set concerning longitudinal outcomes of children involved in a study on muscular dystrophy. Our analysis revealed some interesting findings that may be useful to medical practitioners. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust fit of Bayesian mixed effects regression models with application to colony forming unit count in tuberculosis research

Early bactericidal activity of tuberculosis drugs is conventionally assessed using statistical regression modeling of colony forming unit (CFU) counts over time. Typically, most CFU counts deviate little from the regression curve, but gross outliers due to erroneous sputum sampling are occasionally present and can markedly influence estimates of the rate of change in CFU count, which is the parameter of interest. A recently introduced Bayesian nonlinear mixed effects regression model was adapted to offer a robust approach that accommodates both outliers and potential skewness in the data. At its most general, the proposed regression model fits the skew Student t distribution to residuals and random coefficients. Deviance information criterion statistics and compound Laplace‐Metropolis marginal likelihoods were used to discriminate between alternative Bayesian nonlinear mixed effects regression models. We present a relatively easy method to calculate the marginal likelihoods required to determine compound Laplace‐Metropolis marginal likelihoods, by adapting methods available in currently available statistical software. The robust methodology proposed in this paper was applied to data from 6 clinical trials. The results provide strong evidence that the distribution of CFU count is often heavy tailed and negatively skewed (suggesting the presence of outliers). Therefore, we recommend that robust regression models, such as those proposed here, should be fitted to CFU count.     

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose–response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program. Copyright © 2014 John Wiley & Sons, Ltd.     

Rank‐preserving regression: a more robust rank regression model against outliers

Mean‐based semi‐parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon‐score‐based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional‐response‐model‐based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank‐preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd.     

Too much ado about two-part models and transformation? Comparing methods of modeling Medicare expenditures

Many methods for modeling skewed health care cost and use data have been suggested in the literature. This paper compares the performance of eight alternative estimators, including OLS and GLM estimators and one- and two-part models, in predicting Medicare costs. It finds that four of the alternatives produce very similar results in practice. It then suggests an efficient method for researchers to use when selecting estimators of health care costs.     

NON-ITERATIVE ROBUST ESTIMATORS OF VARIANCE COMPONENTS IN WITHIN-SUBJECT DESIGNS

Classic estimators of variance components break down in the presence of outliers and perform less efficiently under non-normality. In this article I present simple non-iterative estimators of variance components that are resistant to outliers and robust to systematic departures from normality, such as heavy tailedness of the distribution of responses. The proposed estimators are based on a robust extension of Hocking's AVE approach and are thus called RAVE estimators. I present results from a Monte Carlo comparison of RAVE versus classic estimation methods including maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE). Under simulated deviations from normality, RAVE estimators are associated with smaller mean squared errors than all the comparators, and in the normal case they exhibit a minimal loss in relative efficiency. A numerical example illustrates the proposed methodology. © 1997 John Wiley & Sons, Ltd.     

Estimating causal effects for multivalued treatments: a comparison of approaches

Interventions with multivalued treatments are common in medical and health research, such as when comparing the efficacy of competing drugs or interventions, or comparing between various doses of a particular drug. In recent years, there has been a growing interest in the development of multivalued treatment effect estimators using observational data. In this paper, we compare the performance of commonly used regression‐based methods that estimate multivalued treatment effects based on the unconfoundedness assumption. These estimation methods fall into three general categories: (i) estimators based on a model for the outcome variable using conventional regression adjustment; (ii) weighted estimators based on a model for the treatment assignment; and (iii) ‘doubly‐robust’ estimators that model both the treatment assignment and outcome variable within the same framework. We assess the performance of these models using Monte Carlo simulation and demonstrate their application with empirical data. Our results show that (i) when models estimating both the treatment and outcome are correctly specified, all adjustment methods provide similar unbiased estimates; (ii) when the outcome model is misspecified, regression adjustment performs poorly, while all the weighting methods provide unbiased estimates; (iii) when the treatment model is misspecified, methods based solely on modeling the treatment perform poorly, while regression adjustment and the doubly robust models provide unbiased estimates; and (iv) when both the treatment and outcome models are misspecified, all methods perform poorly. Given that researchers will rarely know which of the two models is misspecified, our results support the use of doubly robust estimation. Copyright © 2015 John Wiley & Sons, Ltd.     

Covariate adjustment in clinical trials with non-ignorable missing data and non-compliance

Estimating causal effects in psychiatric clinical trials is often complicated by treatment non-compliance and missing outcomes. While new estimators have recently been proposed to address these problems, they do not allow for inclusion of continuous covariates. We propose estimators that adjust for continuous covariates in addition to non-compliance and missing data. Using simulations, we compare mean squared errors for the new estimators with those of previously established estimators. We then illustrate our findings in a study examining the efficacy of clozapine versus haloperidol in the treatment of refractory schizophrenia. For data with continuous or binary outcomes in the presence of non-compliance, non-ignorable missing data, and a covariate effect, the new estimators generally performed better than the previously established estimators. In the clozapine trial, the new estimators gave point and interval estimates similar to established estimators. We recommend the new estimators as they are unbiased even when outcomes are not missing at random and they are more efficient than established estimators in the presence of covariate effects under the widest variety of circumstances.     

An exploratory instrumental variable analysis of the outcomes of localized breast cancer treatments in a medicare population

This study is motivated by the potential problem of using observational data to draw inferences about treatment outcomes when experimental data are not available. We compare two statistical approaches, ordinary least-squares (OLS) and instrumental variables (IV) regression analysis, to estimate the outcomes (three-year post-treatment survival) of three treatments for early stage breast cancer in elderly women: mastectomy (MST), breast conserving surgery with radiation therapy (BCSRT), and breast conserving surgery only (BCSO). The primary data source was Medicare claims for a national random sample of 2907 women (age 67 or older) with localized breast cancer who were treated between 1992 and 1994.Contrary to randomized clinical trial (RCT) results, analysis with the observational data found highly significant differences in survival among the three treatment alternatives: 79.2% survival for BCSO, 85.3% for MST, and 93.0% for BCSRT. Using OLS to control for the effects of observable characteristics narrowed the estimated survival rate differences, which remained statistically significant. In contrast, the IV analysis estimated survival rate differences that were not significantly different from 0. However, the IV-point estimates of the treatment effects were quantitatively larger than the OLS estimates, unstable, and not significantly different from the OLS results. In addition, both sets of estimates were in the same quantitative range as the RCT results.We conclude that unadjusted observational data on health outcomes of alternative treatments for localized breast cancer should not be used for cost-effectiveness studies. Our comparisons suggest that whether one places greater confidence in the OLS or the IV results depends on at least three factors: (1) the extent of observable health information that can be used as controls in OLS estimation, (2) the outcomes of statistical tests of the validity of the instrumental variable method, and (3) the similarity of the OLS and IV estimates. In this particular analysis, the OLS estimates appear to be preferable because of the instability of the IV estimates.     

Bayesian pharmacovigilance signal detection methods revisited in a multiple comparison setting

Pharmacovigilance spontaneous reporting systems are primarily devoted to early detection of the adverse reactions of marketed drugs. They maintain large spontaneous reporting databases (SRD) for which several automatic signalling methods have been developed. A common limitation of these methods lies in the fact that they do not provide an auto‐evaluation of the generated signals so that thresholds of alerts are arbitrarily chosen. In this paper, we propose to revisit the Gamma Poisson Shrinkage (GPS) model and the Bayesian Confidence Propagation Neural Network (BCPNN) model in the Bayesian general decision framework. This results in a new signal ranking procedure based on the posterior probability of null hypothesis of interest and makes it possible to derive with a non‐mixture modelling approach Bayesian estimators of the false discovery rate (FDR), false negative rate, sensitivity and specificity. An original data generation process that can be suited to the features of the SRD under scrutiny is proposed and applied to the French SRD to perform a large simulation study. Results indicate better performances according to the FDR for the proposed ranking procedure in comparison with the current ones for the GPS model. They also reveal identical performances according to the four operating characteristics for the proposed ranking procedure with the BCPNN and GPS models but better estimates when using the GPS model. Finally, the proposed procedure is applied to the French data. Copyright © 2009 John Wiley & Sons, Ltd.     

Are generalized additive models for location, scale, and shape an improvement on existing models for estimating skewed and heteroskedastic cost data?

Generalized additive models for location, scale, and shape (GAMLSS) are a class of semi-parametric models with potential applicability to health care cost data. We compared the bias, accuracy, and coverage of GAMLSS estimators with two distributions [gamma and generalized inverse gaussian (GIG)] using a log link to the generalized linear model (GLM) with log link and gamma family and the log-transformed OLS. The evaluation using simulated gamma data showed that the GAMLSS and GLM gamma model had similar bias, accuracy, and coverage and outperformed the GAMLSS GIG. When applied to simulated GIG data, the GLM gamma was similar or improved in bias, accuracy, and coverage compared to the GAMLSS GIG and gamma; furthermore, the GAMLSS estimators produced wildly inaccurate or overly-precise results in certain circumstances. Applying all models to empirical data on health care costs after a fall-related injury, all estimators produced similar coefficient estimates, but GAMLSS estimators produced spuriously smaller standard errors. Although no single alternative was best for all simulations, the GLM gamma was the most consistent, so we recommend against using GAMLSS estimators using GIG or gamma to test for differences in mean health care costs. Since GAMLSS offers many other flexible distributions, future work should evaluate whether GAMLSS is useful when predicting health care costs.     

Bias correction by use of errors-in-variables regression models in studies with K-X-ray fluorescence bone lead measurements

In-vivo measurement of bone lead by means of K-X-ray fluorescence (KXRF) is the preferred biological marker of chronic exposure to lead. Unfortunately, considerable measurement error associated with KXRF estimations can introduce bias in estimates of the effect of bone lead when this variable is included as the exposure in a regression model. Estimates of uncertainty reported by the KXRF instrument reflect the variance of the measurement error and, although they can be used to correct the measurement error bias, they are seldom used in epidemiological statistical analyzes. Errors-in-variables regression (EIV) allows for correction of bias caused by measurement error in predictor variables, based on the knowledge of the reliability of such variables. The authors propose a way to obtain reliability coefficients for bone lead measurements from uncertainty data reported by the KXRF instrument and compare, by the use of Monte Carlo simulations, results obtained using EIV regression models vs. those obtained by the standard procedures. Results of the simulations show that Ordinary Least Square (OLS) regression models provide severely biased estimates of effect, and that EIV provides nearly unbiased estimates. Although EIV effect estimates are more imprecise, their mean squared error is much smaller than that of OLS estimates. In conclusion, EIV is a better alternative than OLS to estimate the effect of bone lead when measured by KXRF.     

High-dimensional single-index models with censored responses

In this article, we study the estimation of high-dimensional single index models when the response variable is censored. We hybrid the estimation methods for high-dimensional single-index models (but without censorship) and univariate nonparametric models with randomly censored responses to estimate the index parameters and the link function and apply the proposed methods to analyze a genomic dataset from a study of diffuse large B-cell lymphoma. We evaluate the finite sample performance of the proposed procedures via simulation studies and establish large sample theories for the proposed estimators of the index parameter and the nonparametric link function under certain regularity conditions.     

The implications of noncompliance for randomized trials with partial nesting due to group treatment

Analyses of trials of group administered treatments require an identifier for therapy group to account for clustering by group. All patients randomized to receive the group administered treatment could be assigned an intended group identifier following randomization. Alternatively, an actual group could be based on those patients that comply with group therapy. We investigate the implications for intention‐to‐treat (ITT) analyses of using either the intended or actual group to adjust for the clustering effect. We also consider causal models using the actual group. A simulation study showed that ITT estimates based on random effects models or GEE with an exchangeable correlation matrix performed much better when using the intended group than the actual group. OLS with robust standard errors performed well with both. Most compliance average causal effect (CACE) models performed well. While practical constraints of the clinical setting may determine the choice between an intended or actual group analyses, it is desirable to record both. An ITT analysis using mixed models can then be fitted using the intended group with data generation assumptions checked by a causal model using the actual group. Where an ITT analysis is based on the actual group, worse outcome for never‐takers than compliers may allow one to infer that some estimators are biased toward no treatment effect. The work here is motivated and illustrated by a trial of a group therapy, but also has relevance to trials with treatment related clustering due to therapist examples of which include physical and talking therapies or surgery.     

Predicting EQ-5D utility scores from the 25-item National Eye Institute Vision Function Questionnaire (NEI-VFQ 25) in patients with age-related macular degeneration

Purpose  In this study, we explored different statistical approaches to identify the best algorithm to predict EQ-5D utility scores from the NEI-VFQ 25 in patients with age-related macular degeneration (AMD). Methods  Ordinary least squares (OLS), Tobit, and censored least absolute deviation (CLAD) approaches were compared using cross-sectional data (primary dataset, n = 151) at screening from a phase I/II clinical trial in patients with AMD. Three models were specified in this study: full (includes all 12 dimensions of the NEI-VFQ 25), short (includes only the general health dimension and the composite score), and reduced model (using stepwise regression). To evaluate the predictive accuracy of the models, the mean absolute prediction error (MAPE), mean error, and root means squared error were calculated using in-sample cross-validation (within the primary dataset) and out-of-sample validation using an independent dataset (n = 393). The model that provided the lowest prediction errors was chosen as the best model. Results  In-sample cross-validation and out-of-sample validation consistently demonstrated that, compared to other approaches, heteroscedasticity-adjusted OLS produced the lowest MAPE (mean values were 0.1400, 0.1593, respectively) for the full model, while CLAD performed best for the short and reduced models (mean values were 0.1299, 0.1483, respectively). The normality and homoscedasticity assumptions of both OLS and Tobit were rejected. CLAD, however, can accommodate these particular violations. Conclusions  The CLAD-short model is recommended for producing the EQ-5D utility scores when only the NEI-VFQ 25 data are available.