The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

Modelos de sobrevivência com fração de cura e erro de medida nas covariáveis

In this work, we study the survival cure rate model proposed by Yakovlev et al. (1993), based on a competing risks structure concurring to cause the event of interest, and the approach proposed by Chen et al. (1999), where covariates are introduced to model the risk amount. We focus the measurement error covariates topics, considering the use of corrected score method in order to obtain consistent estimators. A simulation study is done to evaluate the behavior of the estimators obtained by this method for finite samples. The simulation aims to identify not only the impact on the regression coefficients of the covariates measured with error (Mizoi et al. 2007) but also on the coefficients of covariates measured without error. We also verify the adequacy of the piecewise exponential distribution to the cure rate model with measurement error. At the end, model applications involving real data are made

Extensões da distribuição de Lindley para análise de dados de sobrevivência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Low serum potassium levels increase the infectious-caused mortality in peritoneal dialysis patients: a propensity-matched score study

Background and ObjectivesHypokalemia has been consistently associated with high mortality rate in peritoneal dialysis. However, studies investigating if hypokalemia is acting as a surrogate marker of comorbidities or has a direct effect in the risk for mortality have not been studied. Thus, the aim of this study was to analyze the effect of hypokalemia on overall and cause-specific mortality.Design, Setting, Participants and MeasurementsThis is an analysis of BRAZPD II, a nationwide prospective cohort study. All patients on PD for longer than 90 days with measured serum potassium levels were used to verify the association of hypokalemia with overall and cause-specific mortality using a propensity match score to reduce selection bias. In addition, competing risks were also taken into account for the analysis of cause-specific mortality.ResultsThere was a U-shaped relationship between time-averaged serum potassium and all-cause mortality of PD patients. Cardiovascular disease was the main cause of death in the normokalemic group with 133 events (41.8%) followed by PD-non related infections, n=105 (33.0%). Hypokalemia was associated with a 49% increased risk for CV mortality after adjustments for covariates and the presence of competing risks (SHR 1.49; CI95% 1.01-2.21). In contrast, in the group of patients with K < 3.5mEq/L, PD-non related infections were the main cause of death with 43 events (44.3%) followed by cardiovascular disease (n=36; 37.1%). For PD-non related infections the SHR was 2.19 (CI95% 1.52-3.14) while for peritonitis was SHR 1.09 (CI95% 0.47-2.49).ConclusionsHypokalemia had a significant impact on overall, cardiovascular and infectious mortality even after adjustments for competing risks. The causative nature of this association suggested by our study raises the need for intervention studies looking at the effect of potassium supplementation on clinical outcomes of PD patients.

Systemic lupus erythematous and clinical outcomes in peritoneal dialysis

Background: The prevalence of systemic lupus erythematous (SLE) patients requiring renal replacement therapy (RRT) is increasing but data on clinical outcomes are scarce. Interestingly, data on technique failure and peritoneal-dialysis (PD)-related infections are rarer, despite SLE patients being considered at high risk for infections. The aim of our study is to compare clinical outcomes of SLE patients on PD in a large PD cohort. Methods: We conducted a nationwide prospective observational study from the BRAZPD II cohort. For this study we identified all patients on PD for greater than 90 days. Within that subset, all those with SLE as primary renal disease were matched with PD patients without SLE for comparison of clinical outcomes, namely: patient mortality, technique survival and time to first peritonitis, then were analyzed taking into account the presence of competing risks. Results: Out of a total of 9907 patients, we identified 102 SLE patients incident in PD and with more than 90 days on PD. After matching the groups consisted of 92 patients with SLE and 340 matched controls. Mean age was 46.9 +/- 16.8 years, 77.3% were females and 58.1% were Caucasians. After adjustments SLE sub-hazard distribution ratio for mortality was 1.06 (CI 95% 0.55-2.05), for technique failure was 1.01 (CI 95% 0.54-1.91) and for time to first peritonitis episode was 1.40 (CI 95% 0.92-2.11). The probability for occurrence of competing risks in all three outcomes was similar between groups. Conclusion: PD therapy was shown to be a safe and equally successful therapy for SLE patients compared to matched non-SLE patients.

Automated peritoneal dialysis is associated with better survival rates compared to continuous ambulatory peritoneal dialysis: a propensity score matching analysis

The impact of peritoneal dialysis modality on patient survival and peritonitis rates is not fully understood, and no large-scale randomized clinical trial (RCT) is available. In the absence of a RCT, the use of an advanced matching procedure to reduce selection bias in large cohort studies may be the best approach. The aim of this study is to compare automated peritoneal dialysis (APD) and continuous ambulatory peritoneal dialysis (CAPD) according to peritonitis risk, technique failure and patient survival in a large nation-wide PD cohort. This is a prospective cohort study that included all incident PD patients with at least 90 days of PD recruited in the BRAZPD study. All patients who were treated exclusively with either APD or CAPD were matched for 15 different covariates using a propensity score calculated with the nearest neighbor method. Clinical outcomes analyzed were overall mortality, technique failure and time to first peritonitis. For all analysis we also adjusted the curves for the presence of competing risks with the Fine and Gray analysis. After the matching procedure, 2,890 patients were included in the analysis (1,445 in each group). Baseline characteristics were similar for all covariates including: age, diabetes, BMI, Center-experience, coronary artery disease, cancer, literacy, hypertension, race, previous HD, gender, pre-dialysis care, family income, peripheral artery disease and year of starting PD. Mortality rate was higher in CAPD patients (SHR1.44 CI95%1.21-1.71) compared to APD, but no difference was observed for technique failure (SHR0.83 CI95%0.69-1.02) nor for time till the first peritonitis episode (SHR0.96 CI95%0.93-1.11). In the first large PD cohort study with groups balanced for several covariates using propensity score matching, PD modality was not associated with differences in neither time to first peritonitis nor in technique failure. Nevertheless, patient survival was significantly better in APD patients.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

Facets of Gender : Analyses of the Family and the Labour Market

This thesis contains four different studies on the dynamics of gender in households and workplaces. The relationship between family life and work life is in focus, particularly in the paper on labour market outcomes after divorce. In the introductory chapter, the Swedish context is briefly described. The description focuses on gender differences in the labour market and in the home. Theories concerning the division of work in the household are discussed, as are two theories on labour market discrimination, viz. taste discrimination and statistical discrimination. The theory part is concluded with a discussion of social closure processes and gendered organizational structures. The Reproduction of Gender. Housework and Attitudes Towards Gender Equality in the Home Among Swedish Boys and Girls. The housework boys and girls age 10 to 18 do, and their attitudes towards gender equality in the home are studied. One aim is to see whether the work children do is gendered and if so, whether they follow their parents’, often gendered, pattern in housework. A second aim is to see whether parents’ division of work is related to the children’s attitude towards gender equality in the home. The data used are taken from the Swedish Child Level of Living Survey (Child-LNU) 2000. Results indicate that girls and boys in two-parent families are more prone to engage in gender-atypical work the more their parent of the same sex engages in this kind of work. The fact that girls still do more housework than boys indicates that housework is gendered work also among children. No relation between parents’ division of work and the child’s attitude towards gender equality in the home was found. Dependence within Families and the Household Division of Labor – A Comparison between Sweden and the United States. This paper assesses the relative explanatory value of the resource-bargaining perspective and the doing-gender approach in analysing the division of housework in the United States and Sweden from the mid-1970s to 2000. Data from the Swedish Level of Living Survey (LNU) and the Panel Study of Income Dynamics (PSID) were used. Overall results indicate that housework is truly gendered work in both countries during the entire period. Even so, the results also indicate that gender deviance neutralization is more pronounced in the United States than in Sweden. Unlike Swedish women, American women seem to increase their time spent in housework when their husbands are to some extent economically dependent on them, as if to neutralize the presumed gender deviance. Divorce and Labour Market Outcomes. Do Women Suffer or Gain? In this paper, the interconnected nature of work and family is studied by looking at labour market outcomes after divorce. The data used are retrospective work and family histories collected in LNU 1991. A hazard regression model with competing risks reveals that women’s chances of improving their occupational prestige appear to be better after divorce compared to before. Increased working hours and perhaps also increased energy invested in the job may pay off in better occupational opportunities. Worth noting, however, is that the outcome among women with a less firm labour market attachment is more often to a job of lower prestige than one of higher prestige. Hence, the labour market outcome for women after divorce is to some extent conditioned by their labour market attachment at the time of divorce. Men, on the other hand, in most cases seem to suffer occupationally from divorce. For separated men the risk of negative changes in occupational prestige is greater than for cohabiting men. Formal On-the-job Training. A Gender-Typed Experience and Wage- Related Advantage? Formal on-the-job training (FOJT) can have a positive impact on wages and on promotion opportunities. According to theory and earlier research, a two-step model of gender inequality in FOJT is predicted: First, women are less likely than men to take part in FOJT and, second, once women do get the more remunerative training, they are not rewarded for their new skills to the same extent as men are. Pooled cross-sectional data from the Swedish Survey of Living Conditions (ULF) in the mid-nineties were used. Results show that women are significantly less likely than men to take part in FOJT. Among those who do receive training, women are more likely to take part in industry-specific training, whereas men are more likely to participate in general training and training that increases promotion opportunities. The two latter forms of training significantly raise a man’s annual earnings but not a woman’s. Hence, the theoretical model is supported and it is argued that this gender inequality is partly due to employers’ discriminatory practices.

Outcomes in patients waiting for antiretroviral treatment in the Free State Province, South Africa: prospective linkage study

Objective: In South Africa, many HIV-infected patients experience delays in accessing antiretroviral therapy (ART). We examined pretreatment mortality and access to treatment in patients waiting for ART. Design: Cohort of HIV-infected patients assessed for ART eligibility at 36 facilities participating in the Comprehensive HIV and AIDS Management (CHAM) program in the Free State Province. Methods: Proportion of patients initiating ART, pre-ART mortality and risk factors associated with these outcomes were estimated using competing risks survival analysis. Results: Forty-four thousand, eight hundred and forty-four patients enrolled in CHAM between May 2004 and December 2007, of whom 22 083 (49.2%) were eligible for ART; pre-ART mortality was 53.2 per 100 person-years [95% confidence interval (CI) 51.8–54.7]. Median CD4 cell count at eligibility increased from 87 cells/ml in 2004 to 101 cells/ml in 2007. Two years after eligibility an estimated 67.7% (67.1–68.4%) of patients had started ART, and 26.2% (25.6–26.9%) died before starting ART. Among patients with CD4 cell counts below 25 cells/ml at eligibility, 48% died before ART and 51% initiated ART. Men were less likely to start treatment and more likely to die than women. Patients in rural clinics or clinics with low staffing levels had lower rates of starting treatment and higher mortality compared with patients in urban/peri-urban clinics, or better staffed clinics. Conclusions: Mortality is high in eligible patients waiting for ART in the Free State Province. The most immunocompromised patients had the lowest probability of starting ART and the highest risk of pre-ART death. Prioritization of these patients should reduce waiting times and pre-ART mortality.

MULTIPLE DISEASES IN CARRIER PROBABILITY ESTIMATION: ACCOUNTING FOR SURVIVING ALL CANCERS OTHER THAN BREAST AND OVARY IN BRCAPRO

Mendelian models can predict who carries an inherited deleterious mutation of known disease genes based on family history. For example, the BRCAPRO model is commonly used to identify families who carry mutations of BRCA1 and BRCA2, based on familial breast and ovarian cancers. These models incorporate the age of diagnosis of diseases in relatives and current age or age of death. We develop a rigorous foundation for handling multiple diseases with censoring. We prove that any disease unrelated to mutations can be excluded from the model, unless it is sufficiently common and dependent on a mutation-related disease time. Furthermore, if a family member has a disease with higher probability density among mutation carriers, but the model does not account for it, then the carrier probability is deflated. However, even if a family only has diseases the model accounts for, if the model excludes a mutation-related disease, then the carrier probability will be inflated. In light of these results, we extend BRCAPRO to account for surviving all non-breast/ovary cancers as a single outcome. The extension also enables BRCAPRO to extract more useful information from male relatives. Using 1500 familes from the Cancer Genetics Network, accounting for surviving other cancers improves BRCAPRO’s concordance index from 0.758 to 0.762 (p = 0.046), improves its positive predictive value from 35% to 39% (p < 10−6) without impacting its negative predictive value, and improves its overall calibration, although calibration slightly worsens for those with carrier probability < 10%. Copyright c 2000 John Wiley & Sons, Ltd.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Extracapsular tumor spread and the risk of local, axillary and supraclavicular recurrence in node-positive, premenopausal patients with breast cancer

BACKGROUND: Extracapsular tumor spread (ECS) has been identified as a possible risk factor for breast cancer recurrence, but controversy exists regarding its role in decision making for regional radiotherapy. This study evaluates ECS as a predictor of local, axillary, and supraclavicular recurrence. PATIENTS AND METHODS: International Breast Cancer Study Group Trial VI accrued 1475 eligible pre- and perimenopausal women with node-positive breast cancer who were randomly assigned to receive three to nine courses of classical combination chemotherapy with cyclophosphamide, methotrexate, and fluorouracil. ECS status was determined retrospectively in 933 patients based on review of pathology reports. Cumulative incidence and hazard ratios (HRs) were estimated using methods for competing risks analysis. Adjustment factors included treatment group and baseline patient and tumor characteristics. The median follow-up was 14 years. RESULTS: In univariable analysis, ECS was significantly associated with supraclavicular recurrence (HR = 1.96; 95% confidence interval 1.23-3.13; P = 0.005). HRs for local and axillary recurrence were 1.38 (P = 0.06) and 1.81 (P = 0.11), respectively. Following adjustment for number of lymph node metastases and other baseline prognostic factors, ECS was not significantly associated with any of the three recurrence types studied. CONCLUSIONS: Our results indicate that the decision for additional regional radiotherapy should not be based solely on the presence of ECS.