Assessment of delay in age-appropriate vaccination using survival analysis

 Assessment of delay in age-appropriate vaccination provides more information about timeliness of vaccination than up-to-date vaccination coverage. The authors applied survival analysis methods to data from a vaccination coverage survey among children aged 13–59 months conducted in Argentina in 2002. By age 19 months, 43% of children (95% confidence interval (CI): 40, 46) were vaccinated with the fourth dose of diphtheria, tetanus, and pertussis (DTP4). By age 13 months, 55% of children (95% CI: 52, 57) were vaccinated with measles-containing vaccine. By age 7 months, 33% of children (95% CI: 27, 40) were vaccinated with the third dose of hepatitis B. Compared with firstborn children, third children were more likely to be delayed for DTP4 (relative risk (RR) = 1.41, 95% CI: 1.22, 1.62), measles-containing vaccine (RR = 1.54, 95% CI: 1.32, 1.78), and the third dose of hepatitis B (RR = 1.31, 95% CI: 1.03, 1.67). Children whose caregivers had completed secondary school were less likely to be delayed for DTP4 (RR = 0.68, 95% CI: 0.52, 0.90) compared with those whose caregivers had not completed primary school. Survival analysis methods were helpful in measuring vaccine uptake and should be considered in future surveys when assessing delay in age-appropriate vaccination. Copyright © 2006 by the Johns Hopkins Bloomberg School of Public Health All rights reserved.

Use of survival analysis as a tool for the genetic improvement of age at first conception in Nellore cattle

Restricted breeding seasons in beef cattle lead to censoring of reproductive data. In this paper, age at first conception (AFC) of Nellore females exposed to the sires for the first time between 11 and 16 months of age, was studied aiming to verify the possibility of genetically advance sexual precocity using a survival model. The final data set contained 6699 records of AFC in days. Records of females that did not calve in the next year following exposure to the sire were considered censored (77.5% of total). The model used was a Weibull mixed survival model including effects of contemporary groups, period (fixed) and animal (random). The effect of the contemporary groups on AFC was important (p < 0.01). Heritabilities were 0.51 and 0.76 in logarithmic and original scales respectively. Results indicate that it is possible to genetically advance sexual precocity, using the outcome of survival analysis of AFC as selection criterion. They also suggest that improvements of the environment could advance sexual precocity too, thus an adequate pregnancy rate for farmers could quickly be achieved.

On expectation of life in bivariate survival analysis

Includes bibliography

Quantitative genetic study of age at subsequent rebreeding in Nellore cattle by using survival analysis

The continuous trait age at subsequent rebreeding (ASR) was evaluated using survival analysis in Nellore breed cows that conceived for the first time at approximately 14 months of age. This methodology was chosen because the restricted breeding season produces censored data. The dataset contained 2885 records of ASR (in days). Records of females that did not produce calves in the following year after being exposed to a sire were considered censored (48.3% of the total). The statistical model used was a Weibull mixed survival model, which included fixed effects of contemporary groups (CG) and period and a random effect of individual animal. The effect of contemporary groups on ASR was significant (P < 0.01). Heritabilities obtained for ASR were 0.03 and 0.04 in logarithmic and original scales, respectively. These results indicate that the genetic selection response for subsequent reproduction of 2-year-old Nellore breed females is not expected to be effective based on survival analysis. Furthermore, these results suggest that environmental improvement is fundamental to this important trait. It should be highlighted that an increase in the average date of birth can produce an adverse effect in the future, since this cannot be compensated by genetic improvement.

A Cohort Study of Caries Incidence and Baseline Socioeconomic, Clinical and Demographic Variables: A Kaplan-Meier Survival Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Survival Analysis of Patients with Heart Failure: Implications of Time-Varying Regression Effects in Modeling Mortality

Background: Several models have been designed to predict survival of patients with heart failure. These, while available and widely used for both stratifying and deciding upon different treatment options on the individual level, have several limitations. Specifically, some clinical variables that may influence prognosis may have an influence that change over time. Statistical models that include such characteristic may help in evaluating prognosis. The aim of the present study was to analyze and quantify the impact of modeling heart failure survival allowing for covariates with time-varying effects known to be independent predictors of overall mortality in this clinical setting. Methodology: Survival data from an inception cohort of five hundred patients diagnosed with heart failure functional class III and IV between 2002 and 2004 and followed-up to 2006 were analyzed by using the proportional hazards Cox model and variations of the Cox's model and also of the Aalen's additive model. Principal Findings: One-hundred and eighty eight (188) patients died during follow-up. For patients under study, age, serum sodium, hemoglobin, serum creatinine, and left ventricular ejection fraction were significantly associated with mortality. Evidence of time-varying effect was suggested for the last three. Both high hemoglobin and high LV ejection fraction were associated with a reduced risk of dying with a stronger initial effect. High creatinine, associated with an increased risk of dying, also presented an initial stronger effect. The impact of age and sodium were constant over time. Conclusions: The current study points to the importance of evaluating covariates with time-varying effects in heart failure models. The analysis performed suggests that variations of Cox and Aalen models constitute a valuable tool for identifying these variables. The implementation of covariates with time-varying effects into heart failure prognostication models may reduce bias and increase the specificity of such models.

Survival analysis and iniquities in older Brazilians: a six year follow up survey in São Paulo, Brazil

Maria Lucia Lebrão is the Coordinator of the SABE study. Jair LF Santos and Yeda AO Duarte receive support from National Council of Research (CNPq). The SABE study is supported by The São Paulo Research Foundation (FAPESP).

Markers Models in Survival Analysis and Applications to Issues Associated with AIDS

Jewell and Kalbfleisch (1992) consider the use of marker processes for applications related to estimation of the survival distribution of time to failure. Marker processes were assumed to be stochastic processes that, at a given point in time, provide information about the current hazard and consequently on the remaining time to failure. Particular attention was paid to calculations based on a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. Specific applications to the analysis of AIDS data included the use of markers as surrogate responses for onset of AIDS with censored data and as predictors of the time elapsed since infection in prevalent individuals. Here we review recent work on the use of marker data to tackle these kinds of problems with AIDS data. The Poisson marker process with an additive model, introduced in Jewell and Kalbfleisch (1992) may be a useful "test" example for comparison of various procedures.

Survival Analysis with Large Dimensional Covariates: An Application in Microarray Studies

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT- based counterparts.

Survival analysis of longevity in siblings

Do siblings of centenarians tend to have longer life spans? To answer this question, life spans of 184 siblings for 42 centenarians have been evaluated. Two important questions have been addressed in analyzing the sibling data. First, a standard needs to be established, to which the life spans of 184 siblings are compared. In this report, an external reference population is constructed from the U.S. life tables. Its estimated mortality rates are treated as baseline hazards from which the relative mortality of the siblings are estimated. Second, the standard survival models which assume independent observations are invalid when correlation within family exists, underestimating the true variance. Methods that allow correlations are illustrated by three different methods. First, the cumulative relative excess mortality between siblings and their comparison group is calculated and used as an effective graphic tool, along with the Product Limit estimator of the survival function. The variance estimator of the cumulative relative excess mortality is adjusted for the potential within family correlation using Taylor linearization approach. Second, approaches that adjust for the inflated variance are examined. They are adjusted one-sample log-rank test using design effect originally proposed by Rao and Scott in the correlated binomial or Poisson distribution setting and the robust variance estimator derived from the log-likelihood function of a multiplicative model. Nether of these two approaches provide correlation estimate within families, but the comparison with the comparison with the standard remains valid under dependence. Last, using the frailty model concept, the multiplicative model, where the baseline hazards are known, is extended by adding a random frailty term that is based on the positive stable or the gamma distribution. Comparisons between the two frailty distributions are performed by simulation. Based on the results from various approaches, it is concluded that the siblings of centenarians had significant lower mortality rates as compared to their cohorts. The frailty models also indicate significant correlations between the life spans of the siblings. ^