Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Detection of Progressive Deterioration in Early Onset Schizophrenia with a New Statistical Method

Much controversy exists over whether the course of schizophrenia, as defined by the lengths of repeated community tenures, is progressively ameliorating or deteriorating. This article employs a new statistical method proposed by Wang and Chen (2000) to analyze the Denmark registry data in Eaton, et al (1992). The new statistical method correctly handles the bias caused by induced informative censoring, which is an interaction of the heterogeneity of schizophrenia patients and long-term follow-up. The analysis shows a progressive deterioration pattern in terms of community tenures for the full registry cohort, rather than a progressive amelioration pattern as reported for a selected sub-cohort in Eaton, et al (1992). When adjusted for the long-term chronicity of calendar time, no significant progressive pattern was found for the full cohort.

Marginal Structural Models for Partial Exposure Regimes

Intensive care unit (ICU) patients are ell known to be highly susceptible for nosocomial (i.e. hospital-acquired) infections due to their poor health and many invasive therapeutic treatments. The effects of acquiring such infections in ICU on mortality are however ill understood. Our goal is to quantify these effects using data from the National Surveillance Study of Nosocomial Infections in Intensive Care Units (Belgium). This is a challenging problem because of the presence of time-dependent confounders (such as exposure to mechanical ventilation)which lie on the causal path from infection to mortality. Standard statistical analyses may be severely misleading in such settings and have shown contradicting results. While inverse probability weighting for marginal structural models can be used to accommodate time-dependent confounders, inference for the effect of ?ICU acquired infections on mortality under such models is further complicated (a) by the fact that marginal structural models infer the effect of acquiring infection on a given, fixed day ?in ICU?, which is not well defined when ICU discharge comes prior to that day; (b) by informative censoring of the survival time due to hospital discharge; and (c) by the instability of the inverse weighting estimation procedure. We accommodate these problems by developing inference under a new class of marginal structural models which describe the hazard of death for patients if, possibly contrary to fact, they stayed in the ICU for at least a given number of days s and acquired infection or not on that day. Using these models we estimate that, if patients stayed in the ICU for at least s days, the effect of acquiring infection on day s would be to multiply the subsequent hazard of death by 2.74 (95 per cent conservative CI 1.48; 5.09).

The influence of antibacterial susceptibility and pharmacodynamics on the therapeutic response of infection

This prospective cohort study estimated how antibacterial resistance affected the time until clinical response. Relative rates of improvement and cure were estimated by proportional-hazards regression for 391 patients with culture-confirmed bacterial keratitis who had the ciprofloxacin minimal inhibitory concentration (MIC) measured of the principal corneal isolate and who were treated with ciprofloxacin 0.3% solution or ointment. After adjusting for age and hypopyon status and stratifying by ulcer size, clinic, and ciprofloxacin formulation, the summary rate of clinical improvement with ciprofloxacin therapy was reduced by 42% (95% confidence limits [CL], 3%, 65%) among patients whose corneal isolate's ciprofloxacin MIC exceeded 1.0 μg/mL compared to those with more sensitive isolates. The summary rate of resolution to improvement and cure was reduced by 36% (95% CL, 11%, 53%) among corneal infections having a higher ciprofloxacin MIC. Rate ratios were modified by the size of the presenting corneal ulceration; for ulcer diameters of 4 mm or less and of more than 4 mm, improvement rate ratios were 0.56 (95% CL, 0.31, 1.02) and 0.65 (95% CL, 0.23, 1.80), respectively; resolution rate ratios were 0.63 (95% CL, 0.44, 0.91) and 0.67 (95% CL, 0.32, 1.39), respectively. Sensitivity analysis showed that the summary improvement rate ratio could be maximally overestimated by 24% (95% CL, −29%, 114%) because of informative censoring or by 33% (95% CL, −21%, 126%) from loss to follow up. Based on reported corneal pharmacokinetics of topical ciprofloxacin, the probability of clinical improvement was 90% or more if the ratio of the achievable corneal ciprofloxacin concentration to the corneal isolate's ciprofloxacin MIC was above 8 or the ratio of the area under the 24-hour corneal concentration curve to the ciprofloxacin MIC was greater than 151. This study suggests that corneal infections by bacteria having a higher ciprofloxacin MIC respond more slowly to ciprofloxacin treatment than those with a lower MIC. While the rate of clinical resolution is affected by patient age and clinical severity, antimicrobial susceptibility testing of corneal cultures can indicate the relative effectiveness of antibacterial therapy. A pharmacodynamic approach to treating bacterial keratitis offers the prospect of optimal antimicrobial selection and modification. ^

A nova família de distribuições odd log-logística: teoria e aplicações

Neste trabalho, foi proposta uma nova família de distribuições, a qual permite modelar dados de sobrevivência quando a função de risco tem formas unimodal e U (banheira). Ainda, foram consideradas as modificações das distribuições Weibull, Fréchet, half-normal generalizada, log-logística e lognormal. Tomando dados não-censurados e censurados, considerou-se os estimadores de máxima verossimilhança para o modelo proposto, a fim de verificar a flexibilidade da nova família. Além disso, um modelo de regressão locação-escala foi utilizado para verificar a influência de covariáveis nos tempos de sobrevida. Adicionalmente, conduziu-se uma análise de resíduos baseada nos resíduos deviance modificada. Estudos de simulação, utilizando-se de diferentes atribuições dos parâmetros, porcentagens de censura e tamanhos amostrais, foram conduzidos com o objetivo de verificar a distribuição empírica dos resíduos tipo martingale e deviance modificada. Para detectar observações influentes, foram utilizadas medidas de influência local, que são medidas de diagnóstico baseadas em pequenas perturbações nos dados ou no modelo proposto. Podem ocorrer situações em que a suposição de independência entre os tempos de falha e censura não seja válida. Assim, outro objetivo desse trabalho é considerar o mecanismo de censura informativa, baseado na verossimilhança marginal, considerando a distribuição log-odd log-logística Weibull na modelagem. Por fim, as metodologias descritas são aplicadas a conjuntos de dados reais.

Analyzing Panel Count Data with Informative Observation Times

In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying recurrent event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the recurrent event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximizing a conditional likelihood function of observed event counts and solving estimation equations. Large sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumor study is presented to illustrate the use of the proposed methods.

Celebrating difference/censoring difference? : Marie Chouinard’s bODY rEMIX

This paper examines performances that defy established representations of disease, deformity and bodily difference. Historically, the ‘deformed’ body has been cast – onstage and in sideshows – as flawed, an object of pity, or an example of the human capacity to overcome. Such representations define the boundaries of the ‘normal’ body by displaying its Other. They bracket the ‘abnormal’ body off as an example of deviance from the ‘norm’, thus, paradoxically, decreasing the social and symbolic visibility (and agency) of disabled people. Yet, in contemporary theory and culture, these representations are reappropriated – by disabled artists, certainly, but also as what Carrie Sandahl has called a ‘master trope’ for representing a range of bodily differences. In this paper, I investigate this phenomenon. I analyse French Canadian choreographer Marie Chouinard’s bODY rEMIX/gOLDBERG vARIATIONS, in which 10 able-bodied dancers are reborn as bizarre biotechnical mutants via the use of crutches, walkers, ballet shoes and barres as prosthetic pseudo-organs. These bodies defy boundaries, defy expectations, develop new modes of expression, and celebrate bodily difference. The self-inflicted pain dancers experience during training is cast as a ‘disablement’ that is ultimately ‘enabling’. I ask what effect encountering able bodies celebrating ‘dis’ or ‘diff’ ability has on audiences. Do we see the emergence of a once-repressed Other, no longer silenced, censored or negated? Or does using ‘disability’ to express the dancers’ difference and self-determination usurp a ‘trope’ by which disabled people themselves might speak back to the dominant culture, creating further censorship?

An indication that non-informative vision eliminates the Kinaesthetic Fusion Effect

This study investigated the Kinaesthetic Fusion Effect (KFE) first described by Craske and Kenny in 1981. The current study did not replicate these findings. Participants did not perceive any reduction in the sagittal separation of a button pressed by the index finger of one arm and a probe touching the other, following repeated exposure to the tactile stimuli present on both unseen arms. This study’s failure to replicate the widely-cited KFE as described by Craske et al. (1984) suggests that it may be contingent on several aspects of visual information, especially the availability of a specific visual reference, the role of instructions regarding gaze direction, and the potential use of a line of sight strategy when referring felt positions to an interposed surface. In addition, a foreshortening effect was found; this may result from a line-of-sight judgment and represent a feature of the reporting method used. The transformed line of sight data were regressed against the participant reported values, resulting in a slope of 1.14 (right arm) and 1.11 (left arm), and r > 0.997 for each. The study also provides additional evidence that mis-perceptions of the mediolateral position of the limbs specifically their separation and consistent with notions of Gestalt grouping, is somewhat labile and can be influenced by active motions causing touch of one limb by the other. Finally, this research will benefit future studies that require participants to report the perceived locations of the unseen limbs.

Learning informative features for indoor traversability

This paper presents a method for automatic terrain classification, using a cheap monocular camera in conjunction with a robot’s stall sensor. A first step is to have the robot generate a training set of labelled images. Several techniques are then evaluated for preprocessing the images, reducing their dimensionality, and building a classifier. Finally, the classifier is implemented and used online by an indoor robot. Results are presented, demonstrating an increased level of autonomy.

Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

International stock market linkages : are overnight returns on the U.S. Market informative?

Based on the theory of international stock market co-movements, this study shows that a profitable trading strategy can be developed. The U.S. market return is considered as overnight information by ordinary investors in the Asian and the European stock markets, and opening prices in local markets reflect the U.S. overnight return. However, smart traders would either judge the impact of overnight information more correctly, or predict unreleased information. Thus, the difference between expected opening prices based on the U.S. return and actual opening prices is counted as smart traders’ prediction power, which is either a buy or a sell signal. Using index futures price data from 12 countries from 2000 to 2011, cumulative returns on the trading strategy are calculated with taking into account transaction costs. The empirical results show that the proposed trading strategy generates higher riskadjusted returns than that of the benchmarks in 12 sample countries. The trading performances for the Asian markets surpass those for the European markets because the U.S. return is the only overnight information for the Asian markets whereas the Asian markets returns are additional information to the European investors.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Purpose: Flat-detector, cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. Methods: The rich sources of prior information in IGRT are incorporated into a hidden Markov random field (MRF) model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk (OAR). The voxel labels are estimated using the iterated conditional modes (ICM) algorithm. Results: The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom (CIRS, Inc. model 062). The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. Conclusions: By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2\%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Gas-Phase Transformation of Phosphatidylcholine Cations to Structurally Informative Anions via Ion/Ion Chemistry

Gas-phase transformation of synthetic phosphatidylcholine (PC) monocations to structurally informative anions is demonstrated via ion/ion reactions with doubly deprotonated 1,4-phenylenedipropionic acid (PDPA). Two synthetic PC isomers, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (PC16:0/18:1) and 1-oleoyl-2-palmitoyl-sn-glycero-3-phosphocholine (PC18:1/16:0), were subjected to this ion/ion chemistry. The product of the ion/ion reaction is a negatively charged complex, \[PC + PDPA - H](-). Collisional activation of the long-lived complex causes transfer of a proton and methyl cation to PDPA, generating \[PC - CH3](-). Subsequent collisional activation of the demethylated PC anions produces abundant fatty acid carboxylate anions and low-abundance acyl neutral losses as free acids and ketenes. Product ion spectra of \[PC - CH3](-) suggest favorable cleavage at the sn-2 position over the sn-1 due to distinct differences in the relative abundances. In contrast, collisional activation of PC cations is absent of abundant fatty acid chain-related product ions and typically indicates only the lipid class via formation of the phosphocholine cation. A solution phase method to produce the gas-phase adducted PC anion is also demonstrated. Product ion spectra derived from the solution phase method are similar to the results generated via ion/ion chemistry. This work demonstrates a gas-phase means to increase structural characterization of phosphatidylcholines via ion/ion chemistry. Grant Number ARC/CE0561607, ARC/DP120102922