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.

Ancestry informative markers in Amerindians from Brazilian Amazon

Ancestry informative markers (AIMs) are genetic loci with large frequency differences between the major ethnic groups and are very useful in admixture estimation. However, their frequencies are poorly known within South American indigenous populations, making it difficult to use them in admixture studies with Latin American populations, such as the trihybrid Brazilian population. To minimize this problem, the frequencies of the AIMs FY-null RB2300, LPL, AT3-1/1), Sb19.3, APO, and PV92 were determined via PCR and PCR-RFLP in four tribes from Brazilian Amazon (Tikuna, Kashinawa, Baniwa, and Kanamari), to evaluate their potential for discriminating indigenous populations from Europeans and Africans, as well as discriminating each tribe from the others. Although capable of differentiating tribes, as evidenced by the exact test of population differentiation, a neighbor-joining tree suggests that the AIMs are useless in obtaining reliable reconstructions of the biological relationships and evolutionary history that characterize the villages and tribes studied. The mean allele frequencies from these AIMs were very similar to those observed for North American natives. They discriminated Amerindians from Africans, but not from Europeans. On the other hand, the neighbor-joining dendrogram separated Africans and Europeans from Amerindians with a high statistical support (bootstrap = 0.989). The relatively low diversity (GST = 0.042) among North American natives and Amerindians from Brazilian Amazon agrees with the lack of intra-ethnic variation previously reported for these markers. Despite genetic drift effects, the mean allelic frequencies herein presented could be used as Amerindian parental frequencies in admixture estimates in urban Brazilian populations.

Developmental vitamin D deficiency alters adult behaviour: An informative animal model of schizophrenia

Background: There is growing evidence that vitamin D is active in the brain but until recently there was a lack of evidence about its role during brain development. Guided by certain features of the epidemiology of schizophrenia, we have explored the role of vitamin D in the developing brain and behaviour using whole animal models. Methods: Sprague-Dawley rats were fed a vitamin D deficient diet (DVD) or control diet 6 weeks prior to mating and housed under UVB-free lighting conditions. On the day of birth all rats were fed a control diet for the remainder of the study. We observed behaviour at two timepoints; on the day of birth to study maternal behaviour, and at 10 weeks of age to study offspring behaviour in adulthood, under baseline and drug induced conditions (MK-801, haloperidol, amphetamine). Results: Prenatal vitamin D deficiency results in subtle alterations in maternal behaviour as well as long lasting effects on the adult offspring, despite a return to normal vitamin D levels during postnatal life. These affects were specific to transient prenatal vitamin D depletion as adult vitamin D depletion, combined prenatal and chronic postnatal vitamin D depletion, or ablation of the vitamin D receptor in mice led to markedly different outcomes. Conclusions: The developmental vitamin D (DVD) model now draws strength from epidemiological evidence of schizophrenia and animal experiments. Although the DVD model does not replicate every aspect of schizophrenia, it has several attractive features: (1) the exposure is based on clues from epidemiology; (2) it reproduces the increase in lateral ventricles; (3) it reproduces well-regarded behavioural phenotypes associated with schizophrenia (e.g. MK- 801 induced hyperlocomotion); and (4) it implicates a disturbance in dopamine signaling. In summary, low prenatal levels of vitamin D can influence critical components of orderly brain development and that this has a long lasting effect on behaviour.

Assessing Individual Interethnic Admixture and Population Substructure Using a 48-Insertion-Deletion (INSEL) Ancestry-Informative Marker (AIM) Panel

Estimating the proportions of different ancestries in admixed populations is very important in population genetics studies, and it is particularly important for detecting population substructure effects in case-control association studies. In this work, a set of 48 ancestry, informative insertion, deletion polymorphisms (INDELs) were selected with the goal of efficiently measuring the proportions of three different ancestries (sub-Saharan African, European, and Native American) in mixed populations. All selected markers can be easily analyzed via multiplex PCR and detected with standard capillary electrophoresis. A total of 593 unrelated individuals representative of European, African, and Native American parental populations were typed, as were 380 individuals from three Brazilian populations with known admixture patterns. As expected, the interethnic admixture estimates show that individuals from southern Brazil present an almost exclusively European ancestry; Afro-descendant communities in the Amazon region, apart from the major African contribution, present some degree of admixture with Europeans and Native Americans; and a sample from Belem, in the northeastern Amazon, shows a significant contribution of the three ethnic groups, although with a greater European proportion. In summary, a panel of ancestry-informative INDELs was optimized and proven to be a variable tool for estimating individual and global ancestry proportions in admixed populations. The ability to accurately infer interethnic admixtures highlights the usefulness of this marker set for assessing population substructure in association studies, particularly those conducted in Brazilian and other Latin American populations sharing trihybrid ancestry patterns. Hum Mutat 31:184-190, 2010. (C) 2009 Wiley-Liss, Inc.

The Analysis of interval censoring and double censoring via Markov chain Monte Carlo methods

L'Anàlisi de la supervivència s'utilitza en diferents camps per analitzar el temps transcorregut entre dos esdeveniments. El que distingeix l'anàlisi de la supervivència d'altres àrees de l'estadística és que les dades normalment estan censurades. La censura en un interval apareix quan l'esdeveniment final d'interès no és directament observable i només se sap que el temps de fallada està en un interval concret. Un esquema de censura més complex encara apareix quan tant el temps inicial com el temps final estan censurats en un interval. Aquesta situació s'anomena doble censura. En aquest article donem una descripció formal d'un mètode bayesà paramètric per a l'anàlisi de dades censurades en un interval i dades doblement censurades així com unes indicacions clares de la seva utilització o pràctica. La metodologia proposada s'ilustra amb dades d'una cohort de pacients hemofílics que es varen infectar amb el virus VIH a principis dels anys 1980's.

Intergenerational Mobility and the Informative Content of Surnames

We propose a new methodology for measuring intergenerational mobility in economic wellbeing. Our method is based on the joint distribution of surnames and economic outcomes. It circumvents the need for intergenerational panel data, a long-standing stumbling block for understanding mobility. A single cross-sectional dataset is su cient. Our main idea is simple. If `inheritance' is important for economic outcomes, then rare surnames should predict economic outcomes in the cross-section. This is because rare surnames are indicative of familial linkages. Of course, if the number of rare surnames is small, this won't work. But rare surnames are abundant in the highly-skewed nature of surname distributions from most Western societies. We develop a model that articulates this idea and shows that the more important is inheritance, the more informative will be surnames. This result is robust to a variety of di erent assumptions about fertility and mating. We apply our method using the 2001 census from Catalonia, a large region of Spain. We use educational attainment as a proxy for overall economic well-being. Our main nding is that mobility has decreased among the di erent generations of the 20th century. A complementary analysis based on sibling correlations con rms our results and provides a robustness check on our method. Our model and our data allow us to examine one possible explanation for the observed decrease in mobility. We nd that the degree of assortative mating has increased over time. Overall, we argue that our method has promise because it can tap the vast mines of census data that are available in a heretofore unexploited manner.

Unobserved heterogeneity and censoring in the demand for health care

This paper analyses the demand for private health care by Spanishhouseholds using a micro budget survey. The methodology used takescare of the three part decision process involved in this type ofbehaviour, namely the decision to use private health care, howoften to do so and how much to spend each time and also the effectsof unobserved heterogeneity. Since the theoretical frameworkcorresponds to the Grossman model of health investment, the resultsalso provide a test of the theory when these issues are considered.Finally, the obtained evidence also suggest that the current systemof tax deductions for private health care expenditures is regressive.