A variance shift model for outlier detection and estimation in linear and linear mixed models

Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, !i, for the ith observation, where !i is unknown and estimated from the data. Estimated values of !i indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate Ë!i. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of !i a variance shift outlier model is approximately equivalent to the case deletion approach. We commence with a detailed review of parameter estimation and inferential procedures for the linear mixed model. The review is necessary for the development of the variance shift outlier model as a method for detecting outliers in linear fixed and linear mixed models. This review is followed by a discussion of the status of current research into linear mixed model diagnostics. Different types of residuals in the linear mixed model are defined. A decomposition of the leverage matrix for the linear mixed model leads to interpretable leverage measures. ii A detailed review of a variance shift outlier model in linear fixed effects analysis is given. The purpose of this review is firstly, to gain insight into the general case (the linear mixed model) and secondly, to develop the model further in linear fixed effects analysis. A variance shift outlier model can be formulated as a linear mixed model so that the calculations required to estimate the parameters of the model are those associated with fitting a linear mixed model, and hence the model can be fitted using standard software packages. Likelihood ratio and score test statistics are developed as objective measures for the variance shift estimates. The proposed test statistics initially assume balanced longitudinal data with a Gaussian distributed response variable. The dependence of the proposed test statistics on the second derivatives of the log-likelihood function is also examined. For the single-case outlier in linear fixed effects analysis, analytical expressions for the proposed test statistics are obtained. A resampling algorithm is proposed for assessing the significance of the proposed test statistics and for handling the problem of multiple testing. A variance shift outlier model is then adapted to detect a group of outliers in a fixed effects model. Properties and performance of the likelihood ratio and score test statistics are also investigated. A variance shift outlier model for detecting single-case outliers is also extended to linear mixed effects analysis under Gaussian assumptions for the random effects and the random errors. The variance parameters are estimated using the residual maximum likelihood method. Likelihood ratio and score tests are also constructed for this extended model. Two distinct computing algorithms which constrain the variance parameter estimates to be positive, are given. Properties of the resulting variance parameter estimates from each computing algorithm are also investigated. A variance shift outlier model for detecting single-case outliers in linear mixed effects analysis is extended to detect groups of outliers or subjects having outlying profiles with random intercepts and random slopes that are inconsistent with the corresponding model elements for the remaining subjects in the data set. The issue of influence on the fixed effects under a variance shift outlier model is also discussed

A variance shilf model for outlier detection and estimation in linear and linear mixed models

Includes abstract.Includes bibliographical references.Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, wi, for the ith observation, where wi is unknown and estimated from the data. Estimated values of wi indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate wi. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of wi a variance shift outlier model is approximately equivalent to the case deletion approach

A random effects variance shift model for detecting and accommodating outliers in meta-analysis.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Meta-analysis typically involves combining the estimates from independent studies in order to estimate a parameter of interest across a population of studies. However, outliers often occur even under the random effects model. The presence of such outliers could substantially alter the conclusions in a meta-analysis. This paper proposes a methodology for identifying and, if desired, downweighting studies that do not appear representative of the population they are thought to represent under the random effects model. METHODS: An outlier is taken as an observation (study result) with an inflated random effect variance. We used the likelihood ratio test statistic as an objective measure for determining whether observations have inflated variance and are therefore considered outliers. A parametric bootstrap procedure was used to obtain the sampling distribution of the likelihood ratio test statistics and to account for multiple testing. Our methods were applied to three illustrative and contrasting meta-analytic data sets. RESULTS: For the three meta-analytic data sets our methods gave robust inferences when the identified outliers were downweighted. CONCLUSIONS: The proposed methodology provides a means to identify and, if desired, downweight outliers in meta-analysis. It does not eliminate them from the analysis however and we consider the proposed approach preferable to simply removing any or all apparently outlying results. We do not however propose that our methods in any way replace or diminish the standard random effects methodology that has proved so useful, rather they are helpful when used in conjunction with the random effects model

Health risks of the clean-shave chiskop haircut

The clean-shave haircut known locally as the chiskop is rare among females but popular with black South African men, who are also predisposed to folliculitis keloidalis nuchae (FKN) (keloids on the back of the head). During a previous study, participants described an unexpected symptom of haircut-associated bleeding. As this is not a widely recognised entity, we conducted the present study at an HIV clinic servicing the same population, with the objective of comparing the prevalences of haircut-associated bleeding and FKN in 390 HIV-positive subjects with published data for Langa (Western Cape, South Africa). The results for HIV-positive participants were similar to the population data, but in both groups the prevalence of haircut-associated bleeding (24.5% v. 32%; p =0.17) was much higher than that of FKN (10.2% v. 10.5%), suggesting that the hairstyle increases the risk of bleeding even in people with healthy scalps without folliculitis. This study does not (and was not intended to) prove a higher HIV prevalence in chiskop wearers or in FKN sufferers, but it confirms a history of haircut-associated bleeding in at least a quarter of our male study participants. The risk of transmission of blood-borne infection via haircuts is likely to be low, but requires formal quantification. Public education on adequate sterilisation of barber equipment between haircuts and promotion of individual hair-clipper ownership for chiskop clients should not be delayed. Depilatory creams formulated for African hair offer a non-mechanical means of achieving clean-shave hairstyles

Health risks of the clean-shave chiskop haircut

The clean-shave haircut known locally as the chiskop is rare among females but popular with black South African men, who are also predisposed to folliculitis keloidalis nuchae (FKN) (keloids on the back of the head). During a previous study, participants described an unexpected symptom of haircut-associated bleeding. As this is not a widely recognised entity, we conducted the present study at an HIV clinic servicing the same population, with the objective of comparing the prevalences of haircut-associated bleeding and FKN in 390 HIV-positive subjects with published data for Langa (Western Cape, South Africa). The results for HIV-positive participants were similar to the population data, but in both groups the prevalence of haircut-associated bleeding (24.5% v. 32%; p=0.17) was much higher than that of FKN (10.2% v. 10.5%), suggesting that the hairstyle increases the risk of bleeding even in people with healthy scalps without folliculitis. This study does not (and was not intended to) prove a higher HIV prevalence in chiskop wearers or in FKN sufferers, but it confirms a history of haircut-associated bleeding in at least a quarter of our male study participants. The risk of transmission of blood-borne infection via haircuts is likely to be low, but requires formal quantification. Public education on adequate sterilisation of barber equipment between haircuts and promotion of individual hair-clipper ownership for chiskop clients should not be delayed. Depilatory creams formulated for African hair offer a non-mechanical means of achieving clean-shave hairstyles

Pregnancy-associated heart failure: a comparison of clinical presentation and outcome between hypertensive heart failure of pregnancy and idiopathic peripartum cardiomyopathy

AIMS: There is controversy regarding the inclusion of patients with hypertension among cases of peripartum cardiomyopathy (PPCM), as the practice has contributed significantly to the discrepancy in reported characteristics of PPCM. We sought to determine whether hypertensive heart failure of pregnancy (HHFP) (i.e., peripartum cardiac failure associated with any form of hypertension) and PPCM have similar or different clinical features and outcome. Methods and RESULTS: We compared the time of onset of symptoms, clinical profile (including electrocardiographic [ECG] and echocardiographic features) and outcome of patients with HHFP (n = 53; age 29.6 ± 6.6 years) and PPCM (n = 30; age 31.5 ± 7.5 years). The onset of symptoms was postpartum in all PPCM patients, whereas it was antepartum in 85% of HHFP cases (p<0.001). PPCM was more significantly associated with the following features than HHFP (p<0.05): twin pregnancy, smoking, cardiomegaly with lower left ventricular ejection fraction on echocardiography, and longer QRS duration, QRS abnormalities, left atrial hypertrophy, left bundle branch block, T wave inversion and atrial fibrillation on ECG. By contrast, HHFP patients were significantly more likely (p<0.05) to have a family history of hypertension, hypertension and pre-eclampsia in a previous pregnancy, tachycardia at presentation on ECG, and left ventricular hypertrophy on echocardiography. Chronic heart failure, intra-cardiac thrombus and pulmonary hypertension were found significantly more commonly in PPCM than in HHFP (p<0.05). There were 5 deaths in the PPCM group compared to none among HHFP cases (p = 0.005) during follow-up. CONCLUSION: There are significant differences in the time of onset of heart failure, clinical, ECG and echocardiographic features, and outcome of HHFP compared to PPCM, indicating that the presence of hypertension in pregnancy-associated heart failure may not fit the case definition of idiopathic PPCM

Tuberculous Pericarditis is Multibacillary and Bacterial Burden Drives High Mortality

AbstractBackgroundTuberculous pericarditis is considered to be a paucibacillary process; the large pericardial fluid accumulation is attributed to an inflammatory response to tuberculoproteins. Mortality rates are high. We investigated the role of clinical and microbial factors predictive of tuberculous pericarditis mortality using the artificial intelligence algorithm termed classification and regression tree (CART) analysis.MethodsPatients were prospectively enrolled and followed in the Investigation of the Management of Pericarditis (IMPI) registry. Clinical and laboratory data of 70 patients with confirmed tuberculous pericarditis, including time-to-positive (TTP) cultures from pericardial fluid, were extracted and analyzed for mortality outcomes using CART. TTP was translated to log10 colony forming units (CFUs) per mL, and compared to that obtained from sputum in some of our patients.FindingsSeventy patients with proven tuberculous pericarditis were enrolled. The median patient age was 35 (range: 20–71) years. The median, follow up was for 11.97 (range: 0·03–74.73) months. The median TTP for pericardial fluid cultures was 22 (range: 4–58) days or 3.91(range: 0·5–8·96) log10CFU/mL, which overlapped with the range of 3.24–7.42 log10CFU/mL encountered in sputum, a multi-bacillary disease. The overall mortality rate was 1.43 per 100 person-months. CART identified follow-up duration of 5·23months on directly observed therapy, a CD4+ count of ≤199.5/mL, and TTP≤14days (bacillary load≥5.53 log10 CFU/mL) as predictive of mortality. TTP interacted with follow-up duration in a non-linear fashion.InterpretationPatients with culture confirmed tuberculous pericarditis have a high bacillary burden, and this bacterial burden drives mortality. Thus proven tuberculosis pericarditis is not a paucibacillary disease. Moreover, the severe immunosuppression suggests limited inflammation. There is a need for the design of a highly bactericidal regimen for this condition

HIV Infection Is Associated with a Lower Incidence of Constriction in Presumed Tuberculous Pericarditis: A Prospective Observational Study

The original publication is available at http:/www.plosone.orgBackground: Pericardial constriction is a serious complication of tuberculous pericardial effusion that occurs in up to a quarter of patients despite anti-tuberculosis chemotheraphy. The impact of human immunodeficiency virus (HIV) infection on the incidence of constrictive pericarditis following tuberculous pericardial effusion is unknown. Methods and Results: We conducted a prospective observational study to determine the association between HIV infection and the incidence of constrictive pericarditis among 185 patients (median age 33 years) with suspected tuberculous pericardial effusion. These patients were recruited consecutively between March and October 2004 on commencement of anti-tuberculosis treatment, from 15 hospitals in Cameroon, Nigeria and South Africa. Surviving patients (N = 119) were assessed for clinical evidence of constrictive pericarditis at 3 and 6 months of follow-up. Clinical features of HIV infection were present in 42 (35.2%) of the 119 patients at enrolment into the study.66 of the 119 (56.9%) patients consented to HIV testing at enrolment. During the 6 months of follow-up, a clinical diagnosis of constrictive pericarditis was made in 13 of the 119 patients (10.9%, 95% confidence interval [CI] 5.9-18%). Patients with clinical features of HIV infection appear less likely to develop constriction than those without (4.8% versus 14.3%; P = 0.08). None of the 33 HIV seropositive patients developed constriction, but 8 (24.2%, 95%CI 11.1-42.3%)of the 33 HIV seronegative patients did (P = 0.005). In a multivariate logistic regression model adjusting simultaneously for several baseline characteristics, only clinical signs of HIV infection were significantly associated with a lower risk of constriction (odd ratio 0.14, 95% CI 0.02-0.87, P = 0.035). Conclusions: These data suggest that HIV infection is associated with a lower incidence of pericardial constriction in patients with presumed tuberculous pericarditis. © 2008 Ntsekhe et al.This study was funded, in part, through research grants from the University of Cape Town, the Medical Scholarships for South African Blacks (MESAB), the Medical Research Council of South Africa, the National Research Foundation of South Africa.Publishers' versio

Mortality in patients treated for tuberculous pericarditis in sub-Saharan Africa.

Tuberculous pericarditis is one of the most severe forms of extrapulmonary tuberculosis, causing death or disability in a substantial proportion of affected people.1,2 In Africa, the incidence of tuberculous pericarditis is rising as a result of the HIV epidemic.3 The effect of HIV infection on survival in patients with tuberculous pericarditis is unknown.2,4 Whereas some investigators have suggested that HIV-infected patients with tuberculous pericarditis have a similar outcome to non-infected cases,5 others have shown that there may be an increase in mortality in HIV associated with tuberculous pericarditis.2,6,7 We established a prospective observational study, the Investigation of the Management of Pericarditis in Africa (IMPI Africa) registry, to obtain current information on the diagnosis, management and outcome of patients with presumed tuberculous pericarditis living in sub-Saharan Africa, where the burden of HIV infection is the greatest in the world.4,8-10 In this paper, we report the mortality rate and its predictors during the 6 months of antituberculosis treatment among patients enrolled in the regis