Characterization of the variable cow's age at last calving as a measurement of longevity by using the Kaplan-Meier estimator and the Cox model

In most studies on beef cattle longevity, only the cows reaching a given number of calvings by a specific age are considered in the analyses. With the aim of evaluating all cows with productive life in herds, taking into consideration the different forms of management on each farm, it was proposed to measure cow longevity from age at last calving (ALC), that is, the most recent calving registered in the files. The objective was to characterize this trait in order to study the longevity of Nellore cattle, using the Kaplan-Meier estimators and the Cox model. The covariables and class effects considered in the models were age at first calving (AFC), year and season of birth of the cow and farm. The variable studied (ALC) was classified as presenting complete information (uncensored = 1) or incomplete information (censored = 0), using the criterion of the difference between the date of each cow's last calving and the date of the latest calving at each farm. If this difference was >36 months, the cow was considered to have failed. If not, this cow was censored, thus indicating that future calving remained possible for this cow. The records of 11 791 animals from 22 farms within the Nellore Breed Genetic Improvement Program ('Nellore Brazil') were used. In the estimation process using the Kaplan-Meier model, the variable of AFC was classified into three age groups. In individual analyses, the log-rank test and the Wilcoxon test in the Kaplan-Meier model showed that all covariables and class effects had significant effects (P < 0.05) on ALC. In the analysis considering all covariables and class effects, using the Wald test in the Cox model, only the season of birth of the cow was not significant for ALC (P > 0.05). This analysis indicated that each month added to AFC diminished the risk of the cow's failure in the herd by 2%. Nonetheless, this does not imply that animals with younger AFC had less profitability. Cows with greater numbers of calvings were more precocious than those with fewer calvings. Copyright © The Animal Consortium 2012.

A Cox Model for Biostatistics of the Future

Professor Sir David R. Cox (DRC) is widely acknowledged as among the most important scientists of the second half of the twentieth century. He inherited the mantle of statistical science from Pearson and Fisher, advanced their ideas, and translated statistical theory into practice so as to forever change the application of statistics in many fields, but especially biology and medicine. The logistic and proportional hazards models he substantially developed, are arguably among the most influential biostatistical methods in current practice. This paper looks forward over the period from DRC's 80th to 90th birthdays, to speculate about the future of biostatistics, drawing lessons from DRC's contributions along the way. We consider "Cox's model" of biostatistics, an approach to statistical science that: formulates scientific questions or quantities in terms of parameters gamma in probability models f(y; gamma) that represent in a parsimonious fashion, the underlying scientific mechanisms (Cox, 1997); partition the parameters gamma = theta, eta into a subset of interest theta and other "nuisance parameters" eta necessary to complete the probability distribution (Cox and Hinkley, 1974); develops methods of inference about the scientific quantities that depend as little as possible upon the nuisance parameters (Barndorff-Nielsen and Cox, 1989); and thinks critically about the appropriate conditional distribution on which to base infrences. We briefly review exciting biomedical and public health challenges that are capable of driving statistical developments in the next decade. We discuss the statistical models and model-based inferences central to the CM approach, contrasting them with computationally-intensive strategies for prediction and inference advocated by Breiman and others (e.g. Breiman, 2001) and to more traditional design-based methods of inference (Fisher, 1935). We discuss the hierarchical (multi-level) model as an example of the future challanges and opportunities for model-based inference. We then consider the role of conditional inference, a second key element of the CM. Recent examples from genetics are used to illustrate these ideas. Finally, the paper examines causal inference and statistical computing, two other topics we believe will be central to biostatistics research and practice in the coming decade. Throughout the paper, we attempt to indicate how DRC's work and the "Cox Model" have set a standard of excellence to which all can aspire in the future.

Modeling in-Hospital Patient Survival During the First 28 Days After Intensive Care Unit Admission: a Prognostic Model for Clinical Trials in General Critically Ill Patients

OBJECTIVE: The objective of the study was to develop a model for estimating patient 28-day in-hospital mortality using 2 different statistical approaches. DESIGN: The study was designed to develop an outcome prediction model for 28-day in-hospital mortality using (a) logistic regression with random effects and (b) a multilevel Cox proportional hazards model. SETTING: The study involved 305 intensive care units (ICUs) from the basic Simplified Acute Physiology Score (SAPS) 3 cohort. PATIENTS AND PARTICIPANTS: Patients (n = 17138) were from the SAPS 3 database with follow-up data pertaining to the first 28 days in hospital after ICU admission. INTERVENTIONS: None. MEASUREMENTS AND RESULTS: The database was divided randomly into 5 roughly equal-sized parts (at the ICU level). It was thus possible to run the model-building procedure 5 times, each time taking four fifths of the sample as a development set and the remaining fifth as the validation set. At 28 days after ICU admission, 19.98% of the patients were still in the hospital. Because of the different sampling space and outcome variables, both models presented a better fit in this sample than did the SAPS 3 admission score calibrated to vital status at hospital discharge, both on the general population and in major subgroups. CONCLUSIONS: Both statistical methods can be used to model the 28-day in-hospital mortality better than the SAPS 3 admission model. However, because the logistic regression approach is specifically designed to forecast 28-day mortality, and given the high uncertainty associated with the assumption of the proportionality of risks in the Cox model, the logistic regression approach proved to be superior.

Japanese-US common-arm analysis of paclitaxel plus carboplatin in advanced non-small-cell lung cancer: a model for assessing population-related pharmacogenomics

PURPOSE To explore whether population-related pharmacogenomics contribute to differences in patient outcomes between clinical trials performed in Japan and the United States, given similar study designs, eligibility criteria, staging, and treatment regimens. METHODS We prospectively designed and conducted three phase III trials (Four-Arm Cooperative Study, LC00-03, and S0003) in advanced-stage, non-small-cell lung cancer, each with a common arm of paclitaxel plus carboplatin. Genomic DNA was collected from patients in LC00-03 and S0003 who received paclitaxel (225 mg/m(2)) and carboplatin (area under the concentration-time curve, 6). Genotypic variants of CYP3A4, CYP3A5, CYP2C8, NR1I2-206, ABCB1, ERCC1, and ERCC2 were analyzed by pyrosequencing or by PCR restriction fragment length polymorphism. Results were assessed by Cox model for survival and by logistic regression for response and toxicity. Results Clinical results were similar in the two Japanese trials, and were significantly different from the US trial, for survival, neutropenia, febrile neutropenia, and anemia. There was a significant difference between Japanese and US patients in genotypic distribution for CYP3A4*1B (P = .01), CYP3A5*3C (P = .03), ERCC1 118 (P < .0001), ERCC2 K751Q (P < .001), and CYP2C8 R139K (P = .01). Genotypic associations were observed between CYP3A4*1B for progression-free survival (hazard ratio [HR], 0.36; 95% CI, 0.14 to 0.94; P = .04) and ERCC2 K751Q for response (HR, 0.33; 95% CI, 0.13 to 0.83; P = .02). For grade 4 neutropenia, the HR for ABCB1 3425C-->T was 1.84 (95% CI, 0.77 to 4.48; P = .19). CONCLUSION Differences in allelic distribution for genes involved in paclitaxel disposition or DNA repair were observed between Japanese and US patients. In an exploratory analysis, genotype-related associations with patient outcomes were observed for CYP3A4*1B and ERCC2 K751Q. This common-arm approach facilitates the prospective study of population-related pharmacogenomics in which ethnic differences in antineoplastic drug disposition are anticipated.

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. ^

Assessing time-by-covariate interactions in Cox proportional hazards regression models using cubic spline functions

This dissertation develops and explores the methodology for the use of cubic spline functions in assessing time-by-covariate interactions in Cox proportional hazards regression models. These interactions indicate violations of the proportional hazards assumption of the Cox model. Use of cubic spline functions allows for the investigation of the shape of a possible covariate time-dependence without having to specify a particular functional form. Cubic spline functions yield both a graphical method and a formal test for the proportional hazards assumption as well as a test of the nonlinearity of the time-by-covariate interaction. Five existing methods for assessing violations of the proportional hazards assumption are reviewed and applied along with cubic splines to three well known two-sample datasets. An additional dataset with three covariates is used to explore the use of cubic spline functions in a more general setting. ^

Troponina cardíaca T para estratificação de risco na insuficiência cardíaca crônica descompensada

FUNDAMENTO: As troponinas cardíacas são marcadores altamente sensíveis e específicos de lesão miocárdica. Esses marcadores foram detectados na insuficiência cardíaca (IC) e estão associadas com mau prognóstico. OBJETIVO: Avaliar a relação da troponina T (cTnT) e suas faixas de valores com o prognóstico na IC descompensada. MÉTODOS: Estudaram-se 70 pacientes com piora da IC crônica que necessitaram de hospitalização. Na admissão, o modelo de Cox foi utilizado para avaliar as variáveis capazes de predizer o desfecho composto por morte ou re-hospitalização em razão de piora da IC durante um ano. RESULTADOS: Durante o seguimento, ocorreram 44 mortes, 36 re-hospitalizações por IC e 56 desfechos compostos. Na análise multivariada, os preditores de eventos clínicos foram: cTnT (cTnT > 0,100 ng/ml; hazard ratio (HR) 3,95 intervalo de confiança (IC) 95%: 1,64-9,49, p = 0,002), diâmetro diastólico final do ventrículo esquerdo (DDVE >70 mm; HR 1,92, IC95%: 1,06-3,47, p = 0,031) e sódio sérico (Na <135 mEq/l; HR 1,79, IC95%: 1,02-3,15, p = 0,044). Para avaliar a relação entre a elevação da cTnT e o prognóstico na IC descompensada, os pacientes foram estratificados em três grupos: cTnT-baixo (cTnT < 0,020 ng/ml, n = 22), cTnT-intermediário (cTnT > 0,020 e < 0,100 ng/ml, n = 36) e cTnT-alto (cTnT > 0,100 ng/ml, n = 12). As probabilidades de sobrevida e sobrevida livre de eventos foram: 54,2%, 31,5%, 16,7% (p = 0,020), e 36,4%, 11,5%, 8,3% (p = 0,005), respectivamente. CONCLUSÃO: A elevação da cTnT está associada com mau prognóstico na IC descompensada, e o grau dessa elevação pode facilitar a estratificação de risco

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

Nodules Less Than 20 mm and Vascular Invasion are Predictors of Survival in Small Hepatocellular Carcinoma

Background: The aims of this study were to analyze the overall survival of patients with cirrhosis and small hepatocellular carcinoma (HCC) and identify independent pretreatment predictors of survival in Brazil. Methods: Between 1998 and 2003, 74 patients with cirrhosis and small HCC were evaluated. Predictors of survival were identified using the Kaplan-Meier survival curves and the Cox model. Results: The overall survival rates were 80%, 41%, and 17% at 12, 36, and 60 months, respectively. The mean length of follow-up after HCC diagnosis was 23 months (median 22 mo, range: I to 86 mo) for the entire group. Univariate analysis showed that model for endstage liver disease (MELD) score (P = 0.016), Child-Pugh classification (P = 0.007), alpha-fetoprotein level (P = 0.006), number of nodules (P = 0.041), tumor diameter (P = 0.009), and vascular invasion (P < 0.0001) were significant predictors Of Survival. Cox regression analysis identified vascular invasion (relative risk = 14.60, confidence interval 95% = 3.3-64.56, P < 0.001) and tumor size > 20 mm (relative risk = 2.14, confidence interval 95% = 1.07-4.2, P = 0.030) as independent predictors of decreased survival. Treatment of HCC was related to increased overall survival. Conclusions: Identification of HCC smaller than 20 mm is associated with longer survival. Presence of vascular invasion, even in small tumors, maybe associated with poor prognosis. Treatment of small tumors Of LIP to 20 mm diameter is related to increased survival.

Extent of Pelvic Lymphadenectomy in Women With Squamous Cell Carcinoma of the Uterine Cervix: Is There Any Prognostic Value?

Background and Objectives: Some authors states that the removal of lymph node would only contribute towards assessing the lymph node status and regional disease control, without any benefit for the patients` survival. The aim of this paper was to assess the influence of the number of surgically dissected pelvic lymph nodes (PLN) on disease-free Survival. Methods: Retrospective cohort study on 42 women presenting squamous cell carcinoma (SCC) of the uterine cervix, with metastases in PLN treated by radical surgery. The Cox model was used to identify risk factors for recurrence. The model variables were adjusted for treatment-related factors (year of treatment, surgical margins and postoperative radiotherapy). The cutoff value for classifying the lymphadenectomy as comprehensive (15 PLN or more) or non-comprehensive (<15 PLN) was determined from analysis of the ROC curve. Results: Fourteen recurrences (32.6%) were recorded: three pelvic, eight distant, two both pelvic and distant, and one at an unknown location. The following risk factors for recurrence were identified: invasion of the deep third of the cervix and number of dissected lymph nodes <15. Conclusions: Deep invasion and non-comprehensive pelvic lymphadenectomy are possible risk factors for recurrence of SCC of the uterine cervix with metastases in PLN. J. Surg. Oncol. 2009;100:252-257. (C) 2009 Wiley-Liss, Inc.

Benefit of antiretroviral therapy on survival of human immunodeficiency virus-infected patients admitted to an intensive care unit

Objective: To evaluate the impact of antiretroviral therapy (ART) and the prognostic factors for in-intensive care unit (ICU) and 6-month mortality in human immunodeficiency virus (HIV)-infected patients. Design: A retrospective cohort study was conducted in patients admitted to the ICU from 1996 through 2006. The follow-up period extended for 6 months after ICU admission. Setting: The ICU of a tertiary-care teaching hospital at the Universidade de Sao Paulo, Brazil. Participants: A total of 278 HIV-infected patients admitted to the ICU were selected. We excluded ICU readmissions (37), ICU admissions who stayed less than 24 hours (44), and patients with unavailable medical charts (36). Outcome Measure: In-ICU and 6-month mortality. Main Results: Multivariate logistic regression analysis and Cox proportional hazards models demonstrated that the variables associated with in-ICU and 6-month mortality were sepsis as the cause of admission (odds ratio [OR] = 3.16 [95% confidence interval [CI] 1.65-6.06]); hazards ratio [HR] = 1.37 [95% Cl 1.01-1.88)), an Acute Physiology and Chronic Health Evaluation 11 score >19 [OR = 2.81 (95% CI 1.57-5.04); HR = 2.18 (95% CI 1.62-2.94)], mechanical ventilation during the first 24 hours [OR = 3.92 (95% CI 2.20-6.96); HR = 2.25 (95% CI 1.65-3.07)], and year of ICU admission [OR = 0.90 (95% CI 0.81-0.99); HR = 0.92 [95% CI 0.87-0.97)]. CD4 T-cell count <50 cells/mm(3) Was only associated with ICU mortality [OR = 2.10 (95% Cl 1.17-3.76)]. The use of ART in the ICU was negatively predictive of 6-month mortality in the Cox model [HR = 0.50 (95% CI 0.35-0.71)], especially if this therapy was introduced during the first 4 days of admission to the ICU [HR = 0.58 (95% CI 0.41-0.83)]. Regarding HIV-infected patients admitted to ICU without using ART, those who have started this treatment during ICU, stay presented a better prognosis when time and potential confounding factors were adjusted for [HR 0.55 (95% CI 0.31-0.98)]. Conclusions: The ICU outcome of HIV-infected patients seems to be dependent not only on acute illness severity, but also on the administration of antiretroviral treatment. (Crit Care Med 2009; 37: 1605-1611)

Genetic Analysis of Age-at-Onset for Cardiovascular Risk Factors in a Brazilian Family Study

Background/Aims: Statistical analysis of age-at-onset involving family data is particularly complicated because there is a correlation pattern that needs to be modeled and also because there are measurements that are censored. In this paper, our main purpose was to evaluate the effect of genetic and shared family environmental factors on age-at-onset of three cardiovascular risk factors: hypertension, diabetes and high cholesterol. Methods: The mixed-effects Cox model proposed by Pankratz et al. [2005] was used to analyze the data from 81 families, involving 1,675 individuals from the village of Baependi, in the state of Minas Gerais, Brazil. Results: The analyses performed showed that the polygenic effect plays a greater role than the shared family environmental effect in explaining the variability of the age-at-onset of hypertension, diabetes and high cholesterol. The model which simultaneously evaluated both effects indicated that there are individuals which may have risk of hypertension due to polygenic effects 130% higher than the overall average risk for the entire sample. For diabetes and high cholesterol the risks of some individuals were 115 and 45%, respectively, higher than the overall average risk for the entire population. Conclusions: Results showed evidence of significant polygenic effects indicating that age-at-onset is a useful trait for gene mapping of the common complex diseases analyzed. In addition, we found that the polygenic random component might absorb the effects of some covariates usually considered in the risk evaluation, such as gender, age and BMI. Copyright (C) 2008 S. Karger AG, Basel

Survival of a cohort of women with cervical cancer diagnosed in a Brazilian cancer center

OBJECTIVE: To assess overall survival of women with cervical cancer and describe prognostic factors associated. METHODS: A total of 3,341 cases of invasive cervical cancer diagnosed at the Brazilian Cancer Institute, Rio de Janeiro, southeastern Brazil, between 1999 and 2004 were selected. Clinical and pathological characteristics and follow-up data were collected. There were performed a survival analysis using Kaplan-Meier curves and a multivariate analysis through Cox model. RESULTS: Of all cases analyzed, 68.3% had locally advanced disease at the time of diagnosis. The 5-year overall survival was 48%. After multivariate analysis, tumor staging at diagnosis was the single variable significantly associated with prognosis (p<0.001). There was seen a dose-response relationship between mortality and clinical staging, ranging from 27.8 to 749.6 per 1,000 cases-year in women stage I and IV, respectively. CONCLUSIONS: The study showed that early detection through prevention programs is crucial to increase cervical cancer survival.