Analyzing Incomplete Data Subject to a Threshold using Empirical Likelihood Methods: An Application to a Pneumonia Risk Study in an ICU Setting

Summary .  The initial detection of ventilator-associated pneumonia (VAP) for inpatients at an intensive care unit needs composite symptom evaluation using clinical criteria such as the clinical pulmonary infection score (CPIS). When CPIS is above a threshold value, bronchoalveolar lavage (BAL) is performed to confirm the diagnosis by counting actual bacterial pathogens. Thus, CPIS and BAL results are closely related and both are important indicators of pneumonia whereas BAL data are incomplete. To compare the pneumonia risks among treatment groups for such incomplete data, we derive a method that combines nonparametric empirical likelihood ratio techniques with classical testing for parametric models. This technique augments the study power by enabling us to use any observed data. The asymptotic property of the proposed method is investigated theoretically. Monte Carlo simulations confirm both the asymptotic results and good power properties of the proposed method. The method is applied to the actual data obtained in clinical practice settings and compares VAP risks among treatment groups.     

Two-sample density-based empirical likelihood tests for incomplete data in application to a pneumonia study

In clinical trials examining the incidence of pneumonia it is a common practice to measure infection via both invasive and non-invasive procedures. In the context of a recently completed randomized trial comparing two treatments the invasive procedure was only utilized in certain scenarios due to the added risk involved, and given that the level of the non-invasive procedure surpassed a given threshold. Hence, what was observed was bivariate data with a pattern of missingness in the invasive variable dependent upon the value of the observed non-invasive observation within a given pair. In order to compare two treatments with bivariate observed data exhibiting this pattern of missingness we developed a semi-parametric methodology utilizing the density-based empirical likelihood approach in order to provide a non-parametric approximation to Neyman-Pearson-type test statistics. This novel empirical likelihood approach has both a parametric and non-parametric components. The non-parametric component utilizes the observations for the non-missing cases, while the parametric component is utilized to tackle the case where observations are missing with respect to the invasive variable. The method is illustrated through its application to the actual data obtained in the pneumonia study and is shown to be an efficient and practical method.     

Bronchoalveolar lavage in liver transplant patients

Because immunosuppression is required to control rejection, liver allograft recipients are susceptible to a variety of opportunistic pathogens. A total of 191 bronchoalveolar lavage (BAL) specimens from 89 patients (53 adults and 36 children) who underwent orthotopic liver transplantation was reviewed. One case each of cytomegalovirus (CMV), staphylococcal and Enterobacter pneumonia was diagnosed with the aid of pretransplant BAL. The pretransplant BAL in 62 patients showed rare yeasts in 24.2%; these probably represent oropharyngeal contaminants since the patients involved had no symptoms of Candida pneumonia. Among 54 patients who developed respiratory symptoms and underwent posttransplant BAL, 23 (42.6%) were infected with opportunistic pathogens, including Pneumocystis carinii (22.2%), CMV (22.2%) and herpes simplex virus (HSV) (7.4%). Frequently, infection with multiple organisms was present. Adults constituted 100% of the HSV-infected group, 69.2% of the CMV-infected group and 16.6% of the group infected with P carinii. The diagnosis of these infections was aided by a combination of cytology, microbial culture and in situ hybridization techniques. Although BAL permitted the diagnosis and treatment of opportunistic infections, high mortality (62.5%) occurred with CMV and HSV pneumonia. Further studies into methods that permit earlier diagnoses of these infections are necessary.     

Usefulness of Cellular Analysis of Bronchoalveolar Lavage Fluid for Predicting the Etiology of Pneumonia in Critically Ill Patients

Background

The usefulness of bronchoalveolar lavage (BAL) fluid cellular analysis in pneumonia has not been adequately evaluated. This study investigated the ability of cellular analysis of BAL fluid to differentially diagnose bacterial pneumonia from viral pneumonia in adult patients who are admitted to intensive care unit.

Methods

BAL fluid cellular analysis was evaluated in 47 adult patients who underwent bronchoscopic BAL following less than 24 hours of antimicrobial agent exposure. The abilities of BAL fluid total white blood cell (WBC) counts and differential cell counts to differentiate between bacterial and viral pneumonia were evaluated using receiver operating characteristic (ROC) curve analysis.

Results

Bacterial pneumonia (n = 24) and viral pneumonia (n = 23) were frequently associated with neutrophilic pleocytosis in BAL fluid. BAL fluid median total WBC count (2,815/µL vs. 300/µL, P<0.001) and percentage of neutrophils (80.5% vs. 54.0%, P = 0.02) were significantly higher in the bacterial pneumonia group than in the viral pneumonia group. In ROC curve analysis, BAL fluid total WBC count showed the best discrimination, with an area under the curve of 0.855 (95% CI, 0.750–0.960). BAL fluid total WBC count ≥510/µL had a sensitivity of 83.3%, specificity of 78.3%, positive likelihood ratio (PLR) of 3.83, and negative likelihood ratio (NLR) of 0.21. When analyzed in combination with serum procalcitonin or C-reactive protein, sensitivity was 95.8%, specificity was 95.7%, PLR was 8.63, and NLR was 0.07. BAL fluid total WBC count ≥510/µL was an independent predictor of bacterial pneumonia with an adjusted odds ratio of 13.5 in multiple logistic regression analysis.

Conclusions

Cellular analysis of BAL fluid can aid early differential diagnosis of bacterial pneumonia from viral pneumonia in critically ill patients.     

Flexible maximum likelihood methods for bivariate proportional hazards models

This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika 65, 141-151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable.     

Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data

Summary .   In clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients.     

A Model for Adjusting for Nonignorable Verification Bias in Estimation of the ROC Curve and Its Area with Likelihood‐Based Approach

Summary In estimation of the ROC curve, when the true disease status is subject to nonignorable missingness, the observed likelihood involves the missing mechanism given by a selection model. In this article, we proposed a likelihood‐based approach to estimate the ROC curve and the area under the ROC curve when the verification bias is nonignorable. We specified a parametric disease model in order to make the nonignorable selection model identifiable. With the estimated verification and disease probabilities, we constructed four types of empirical estimates of the ROC curve and its area based on imputation and reweighting methods. In practice, a reasonably large sample size is required to estimate the nonignorable selection model in our settings. Simulation studies showed that all four estimators of ROC area performed well, and imputation estimators were generally more efficient than the other estimators proposed. We applied the proposed method to a data set from research in Alzheimer's disease.     

A unified procedure for meta-analytic evaluation of surrogate end points in randomized clinical trials

The meta-analytic approach to evaluating surrogate end points assesses the predictiveness of treatment effect on the surrogate toward treatment effect on the clinical end point based on multiple clinical trials. Definition and estimation of the correlation of treatment effects were developed in linear mixed models and later extended to binary or failure time outcomes on a case-by-case basis. In a general regression setting that covers nonnormal outcomes, we discuss in this paper several metrics that are useful in the meta-analytic evaluation of surrogacy. We propose a unified 3-step procedure to assess these metrics in settings with binary end points, time-to-event outcomes, or repeated measures. First, the joint distribution of estimated treatment effects is ascertained by an estimating equation approach; second, the restricted maximum likelihood method is used to estimate the means and the variance components of the random treatment effects; finally, confidence intervals are constructed by a parametric bootstrap procedure. The proposed method is evaluated by simulations and applications to 2 clinical trials.     

Linear parameter haplotype models with stratification

OBJECTIVES: The question of interest is estimating the relationship between haplotypes and an outcome measure, based upon unphased genotypes. The outcome of interest might be predicting the presence of disease in a logistic model, predicting a numeric drug response in a linear model, or predicting survival time in a parametric survival model with censoring. Explanatory variables may include phased haplotype design variables, environmental variables, or interactions between them. METHODS: We extend existing generalized linear haplotype models to parametric survival outcomes. To improve the stability of model variance estimates, a profile likelihood solution is proposed. An adjustment for population stratification is also considered. Here we investigate data sampled from known 'strata' (e.g., gender or ethnicity) that influence haplotype prior probabilities and thus the regression model weights. Differing linear model variance estimates, and the effect of stratification and departures from Hardy-Weinberg Equilibrium (HWE) on parameter estimates, are compared and contrasted via simulation. RESULTS: From simulations, we observed an improvement in statistical power when using a solution to profile likelihood equations. We also saw that stratification had little impact on estimates. Haplotypes that are not in HWE had a negative impact on power to test hypotheses. Finally, profile likelihood solutions for haplotypes deviating from HWE had improved power and confidence interval coverage of regression model coefficients.     

Diagnosis of ventilator-associated pneumonia

The diagnosis of ventilator pneumonia remains a controversial area. Use of standard clinical criteria has been found to be inadequate. Use of a clinical pulmonary infection score (CPIS) has improved the diagnostic utility of clinical criteria. For the intubated patient, there is ready access to the lower respiratory tract. Samples include endotracheal aspirates, bronchoalveolar lavage and protected brush specimen. The latter two can be obtained blindly or via a bronchoscope. The culture results are more meaningful if reported in a semi-quantitative model. There is increasing evidence that culture results predict mortality and can be used to direct duration and type of therapy.     

Dose–response relationship from longitudinal data with response‐dependent dose modification using likelihood methods

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose–response relationship. In this study, we consider the dose–response relationship under these situations. We show that maximum‐likelihood estimates are consistent without modeling the dose‐modification mechanisms when the selection of the dose as a time‐dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose‐modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose–response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum‐likelihood estimates of the dose–response relationship are consistent under the dose modification based only on observed responses.     

Estimating hazard ratios in cohort data with missing disease information due to death

In clinical and epidemiological studies information on the primary outcome of interest, that is, the disease status, is usually collected at a limited number of follow‐up visits. The disease status can often only be retrieved retrospectively in individuals who are alive at follow‐up, but will be missing for those who died before. Right‐censoring the death cases at the last visit (ad‐hoc analysis) yields biased hazard ratio estimates of a potential risk factor, and the bias can be substantial and occur in either direction. In this work, we investigate three different approaches that use the same likelihood contributions derived from an illness‐death multistate model in order to more adequately estimate the hazard ratio by including the death cases into the analysis: a parametric approach, a penalized likelihood approach, and an imputation‐based approach. We investigate to which extent these approaches allow for an unbiased regression analysis by evaluating their performance in simulation studies and on a real data example. In doing so, we use the full cohort with complete illness‐death data as reference and artificially induce missing information due to death by setting discrete follow‐up visits. Compared to an ad‐hoc analysis, all considered approaches provide less biased or even unbiased results, depending on the situation studied. In the real data example, the parametric approach is seen to be too restrictive, whereas the imputation‐based approach could almost reconstruct the original event history information.     

Reactive type II pneumocytes in bronchoalveolar lavage fluid

OBJECTIVE: To evaluate the prevalence of reactive type II pneumocytes (RPII) in bronchoalveolar lavage (BAL) fluid samples obtained from patients with various pulmonary disorders. STUDY DESIGN: Consecutive BAL fluid samples were screened for the presence of RPII on May-Grünwald-Giemsa-stained cytocentrifuge preparations. BAL fluid samples with and without RPII were compared with regard to prevalence, associated clinical diagnoses and cytologic findings. RESULTS: RPII were generally large cells with a high nuclear:cytoplasmic ratio and deeply blue-stained, vacuolated cytoplasm. Most RPII occurred in cohesive cell groups, and the vacuoles tended to be confluent. Cytologic findings associated with RPII were foamy alveolar macrophages, activated lymphocytes and plasma cells. RPII were present in 94 (21.7%) of 433 included BAL fluid samples. The highest prevalences were noted in patients with systemic inflammatory response syndrome and alveolar hemorrhage. In addition, RPII tended to occur more frequently in ventilator-associated pneumonia, Pneumocystis carinii pneumonia, extrinsic allergic alveolitis and drug-induced pulmonary disorders. In contrast, RPII were not observed in BAL fluid samples obtained from patients with sarcoidosis. CONCLUSION: RPII were prevalent in about 20% of BAL fluid specimens. They were associated mainly with conditions of acute lung injury and not observed in sarcoidosis.     

Semi‐parametric analysis of overdispersed count and metric data with varying follow‐up times: Asymptotic theory and small sample approximations

Count data are common endpoints in clinical trials, for example magnetic resonance imaging lesion counts in multiple sclerosis. They often exhibit high levels of overdispersion, that is variances are larger than the means. Inference is regularly based on negative binomial regression along with maximum‐likelihood estimators. Although this approach can account for heterogeneity it postulates a common overdispersion parameter across groups. Such parametric assumptions are usually difficult to verify, especially in small trials. Therefore, novel procedures that are based on asymptotic results for newly developed rate and variance estimators are proposed in a general framework. Moreover, in case of small samples the procedures are carried out using permutation techniques. Here, the usual assumption of exchangeability under the null hypothesis is not met due to varying follow‐up times and unequal overdispersion parameters. This problem is solved by the use of studentized permutations leading to valid inference methods for situations with (i) varying follow‐up times, (ii) different overdispersion parameters, and (iii) small sample sizes.     

Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics

Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well‐being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate‐adjusted response‐adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well‐being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response‐adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well‐being of patients under a logit model with categorical covariates. Results from our simulation studies and application to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF) show that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction.     

Protein expression profiles distinguish between experimental invasive pulmonary aspergillosis and Pseudomonas pneumonia

We hypothesized that invasive pulmonary aspergillosis (IPA) may generate a distinctive proteomic signature in plasma and bronchoalveolar lavage (BAL). Proteins in plasma and BAL from two neutropenic rabbit models of IPA and Pseudomonas pneumonia were analyzed by SELDI-TOF MS. Hierarchical clustering analysis of plasma time course spectra demonstrated two clusters of peaks that were differentially regulated between IPA and Pseudomonas pneumonia (57 and 34 peaks, respectively, p<0.001). PCA of plasma proteins demonstrated a time-dependent separation of the two infections. A random forest analysis that ranked the top 30 spectral points distinguished between late Aspergillus and Pseudomonas pneumonias with 100% sensitivity and specificity. Based on spectral data analysis, three proteins were identified using SDS-PAGE and LC/MS and quantified using reverse phase arrays. Differences in the temporal sequence of plasma haptoglobin (p<0.001), apolipoprotein A1 (p<0.001) and transthyretin (p<0.038) were observed between IPA and Pseudomonas pneumonia, as was C-reactive protein (p<0.001). In summary, proteomic analysis of plasma and BAL proteins of experimental Aspergillus and Pseudomonas pneumonias demonstrates unique protein profiles with principal components and spectral regions that are shared in early infection and diverge at later stages of infection. Haptoglobin, apolipoprotein A1, transthyretin, and C-reactive protein are differentially expressed in these infections suggesting important contributions to host defense against IPA.     

Galactomannan-Based and PCR-Based Assays in Bronchoalveolar Lavage to Diagnose Invasive Aspergillosis: Current Status and Future Prospects

Invasive pulmonary aspergillosis (IPA) is a life-threatening complication in patients receiving chemotherapy or undergoing allogeneic haematopoietic stem cell transplantation for acute leukemia. The existing tools to diagnose IPA lack specificity or sensitivity, or both; the search for improved diagnostic tools for IPA has focused on novel serologic and molecular methods. Aspergillus Galactomannan enzyme-linked immunosorbent assay (GM) analyses showed sensitivity rates in serum samples ranging in a wide span; testing GM in bronchoalveolar lavage (BAL) originated from the primary site of the infection seems to be more sensitive in patients with IPA. Other novel diagnostic markers to detect fungal DNA directly in clinical samples, rapidly, early, sensitively and specifically, are provided by polymerase chain reaction (PCR) based assays; higher sensitivity and specificity rates have been observed for BAL samples in IPA, even under antifungal treatment. The clinical place value of a diagnostic approach combining PCR and GM in BAL is unclear.     

Estimation in Longitudinal or Panel Data Models with Random‐Effect‐Based Missing Responses

Summary In studies with longitudinal or panel data, missing responses often depend on values of responses through a subject‐level unobserved random effect. Besides the likelihood approach based on parametric models, there exists a semiparametric method, the approximate conditional model (ACM) approach, which relies on the availability of a summary statistic and a linear or polynomial approximation to some random effects. However, two important issues must be addressed in applying ACM. The first is how to find a summary statistic and the second is how to estimate the parameters in the original model using estimates of parameters in ACM. Our study is to address these two issues. For the first issue, we derive summary statistics under various situations. For the second issue, we propose to use a grouping method, instead of linear or polynomial approximation to random effects. Because the grouping method is a moment‐based approach, the conditions we assumed in deriving summary statistics are weaker than the existing ones in the literature. When the derived summary statistic is continuous, we propose to use a classification tree method to obtain an approximate summary statistic for grouping. Some simulation results are presented to study the finite sample performance of the proposed method. An application is illustrated using data from the study of Modification of Diet in Renal Disease.     

The exponential‐Poisson model for recurrent event data: An application to a set of data on malaria in Brazil

In this paper, we introduce a new model for recurrent event data characterized by a baseline rate function fully parametric, which is based on the exponential‐Poisson distribution. The model arises from a latent competing risk scenario, in the sense that there is no information about which cause was responsible for the event occurrence. Then, the time of each recurrence is given by the minimum lifetime value among all latent causes. The new model has a particular case, which is the classical homogeneous Poisson process. The properties of the proposed model are discussed, including its hazard rate function, survival function, and ordinary moments. The inferential procedure is based on the maximum likelihood approach. We consider an important issue of model selection between the proposed model and its particular case by the likelihood ratio test and score test. Goodness of fit of the recurrent event models is assessed using Cox‐Snell residuals. A simulation study evaluates the performance of the estimation procedure in the presence of a small and moderate sample sizes. Applications on two real data sets are provided to illustrate the proposed methodology. One of them, first analyzed by our team of researchers, considers the data concerning the recurrence of malaria, which is an infectious disease caused by a protozoan parasite that infects red blood cells.     

Sensitivity analysis for causal inference using inverse probability weighting

Evaluation of impact of potential uncontrolled confounding is an important component for causal inference based on observational studies. In this article, we introduce a general framework of sensitivity analysis that is based on inverse probability weighting. We propose a general methodology that allows both non‐parametric and parametric analyses, which are driven by two parameters that govern the magnitude of the variation of the multiplicative errors of the propensity score and their correlations with the potential outcomes. We also introduce a specific parametric model that offers a mechanistic view on how the uncontrolled confounding may bias the inference through these parameters. Our method can be readily applied to both binary and continuous outcomes and depends on the covariates only through the propensity score that can be estimated by any parametric or non‐parametric method. We illustrate our method with two medical data sets.