Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Birthweight and childhood cancer : preliminary findings from the International Childhood Cancer Cohort Consortium (I4C)

BACKGROUND: Evidence relating childhood cancer to high birthweight is derived primarily from registry and case-control studies. We aimed to investigate this association, exploring the potential modifying roles of age at diagnosis and maternal anthropometrics, using prospectively collected data from the International Childhood Cancer Cohort Consortium.

METHODS: We pooled data on infant and parental characteristics and cancer incidence from six geographically and temporally diverse member cohorts [the Avon Longitudinal Study of Parents and Children (UK), the Collaborative Perinatal Project (USA), the Danish National Birth Cohort (Denmark), the Jerusalem Perinatal Study (Israel), the Norwegian Mother and Child Cohort Study (Norway), and the Tasmanian Infant Health Survey (Australia)]. Birthweight metrics included a continuous measure, deciles, and categories (≥4.0 vs. <4.0 kilogram). Childhood cancer (377 cases diagnosed prior to age 15 years) risk was analysed by type (all sites, leukaemia, acute lymphoblastic leukaemia, and non-leukaemia) and age at diagnosis. We estimated hazard ratios (HR) and 95% confidence intervals (CI) from Cox proportional hazards models stratified by cohort.

RESULTS: A linear relationship was noted for each kilogram increment in birthweight adjusted for gender and gestational age for all cancers [HR = 1.26; 95% CI 1.02, 1.54]. Similar trends were observed for leukaemia. There were no significant interactions with maternal pre-pregnancy overweight or pregnancy weight gain. Birthweight ≥4.0 kg was associated with non-leukaemia cancer among children diagnosed at age ≥3 years [HR = 1.62; 95% CI 1.06, 2.46], but not at younger ages [HR = 0.7; 95% CI 0.45, 1.24, P for difference = 0.02].

CONCLUSION: Childhood cancer incidence rises with increasing birthweight. In older children, cancers other than leukaemia are particularly related to high birthweight. Maternal adiposity, currently widespread, was not demonstrated to substantially modify these associations. Common factors underlying foetal growth and carcinogenesis need to be further explored.

The metabolic syndrome and cancer: is the metabolic syndrome useful for predicting cancer risk above and beyond its individual components?

AIMS: The metabolic syndrome (MetS) is a risk factor for cancer. However, it is not known if the MetS confers a greater cancer risk than the sum of its individual components, which components drive the association, or if the MetS predicts future cancer risk. MATERIALS AND METHODS: We linked 20,648 participants from the Australian and New Zealand Diabetes and Cancer Collaboration with complete data on the MetS to national cancer registries and used Cox proportional hazards models to estimate associations of the MetS, the number of positive MetS components, and each of the five MetS components separately with the risk for overall, colorectal, prostate and breast cancer. Hazard ratios (HR) and 95% confidence intervals (95%CI) are reported. We assessed predictive ability of the MetS using Harrell's c-statistic. RESULTS: The MetS was inversely associated with prostate cancer (HR 0.85; 95% CI 0.72-0.99). We found no evidence of an association between the MetS overall, colorectal and breast cancers. For those with five positive MetS components the HR was 1.12 (1.02-1.48) and 2.07 (1.26-3.39) for overall, and colorectal cancer, respectively, compared with those with zero positive MetS components. Greater waist circumference (WC) (1.38; 1.13-1.70) and elevated blood pressure (1.29; 1.01-1.64) were associated with colorectal cancer. Elevated WC and triglycerides were (inversely) associated with prostate cancer. MetS models were only poor to moderate discriminators for all cancer outcomes. CONCLUSIONS: We show that the MetS is (inversely) associated with prostate cancer, but is not associated with overall, colorectal or breast cancer. Although, persons with five positive components of the MetS are at a 1.2 and 2.1 increased risk for overall and colorectal cancer, respectively, and these associations appear to be driven, largely, by elevated WC and BP. We also demonstrate that the MetS is only a moderate discriminator of cancer risk.

Comparison of anthropometric measures as predictors of cancer incidence: a pooled collaborative analysis of 11 Australian cohorts

Obesity is a risk factor for cancer. However, it is not known if general adiposity, as measured by body mass index (BMI) or central adiposity [e.g., waist circumference (WC)] have stronger associations with cancer, or which anthropometric measure best predicts cancer risk. We included 79,458 men and women from the Australian and New Zealand Diabetes and Cancer Collaboration with complete data on anthropometry [BMI, WC, Hip Circumference (HC), WHR, waist to height ratio (WtHR), A Body Shape Index (ABSI)], linked to the Australian Cancer Database. Cox proportional hazards models assessed the association between each anthropometric marker, per standard deviation and the risk of overall, colorectal, post-menopausal (PM) breast, prostate and obesity-related cancers. We assessed the discriminative ability of models using Harrell's c-statistic. All anthropometric markers were associated with overall, colorectal and obesity-related cancers. BMI, WC and HC were associated with PM breast cancer and no significant associations were seen for prostate cancer. Strongest associations were observed for WC across all outcomes, excluding PM breast cancer for which HC was strongest. WC had greater discrimination compared to BMI for overall and colorectal cancer in men and women with c-statistics ranging from 0.70 to 0.71. We show all anthropometric measures are associated with the overall, colorectal, PM breast and obesity-related cancer in men and women, but not prostate cancer. WC discriminated marginally better than BMI. However, all anthropometric measures were similarly moderately predictive of cancer risk. We do not recommend one anthropometric marker over another for assessing an individuals' risk of cancer.

Fracture prediction from repeat BMD measurements in clinical practice

Summary: We investigated whether repeat BMD measurements in clinical populations are useful for fracture risk assessment. We report that repeat BMD measurements are a robust predictor of fracture in clinical populations; this is not affected by preceding BMD change or recent osteoporosis therapy. Introduction: In clinical practice, many patients selectively undergo repeat bone mineral density (BMD) measurements. We investigated whether repeat BMD measurements in clinical populations are useful for fracture risk assessment and whether this is affected by preceding change in BMD or recent osteoporosis therapy. Methods: We identified women and men aged ≥50 years who had a BMD measurement during 1990–2009 from a large clinical BMD database for Manitoba, Canada (n = 50,215). Patient subgroups aged ≥50 years at baseline with repeat BMD measures were identified. Data were linked to an administrative data repository, from which osteoporosis therapy, fracture outcomes, and covariates were extracted. Using Cox proportional hazards models, we assessed covariate-adjusted risk for major osteoporotic fracture (MOF) and hip fracture according to BMD (total hip, lumbar spine, femoral neck) at different time points. Results: Prevalence of osteoporosis therapy increased from 18 % at baseline to 55 % by the fourth measurement. Total hip BMD was predictive of MOF at each time point. In the patient subgroup with two repeat BMD measurements (n = 13,481), MOF prediction with the first and second measurements was similar: adjusted-hazard ratio (HR) per SD 1.45 (95 % CI 1.34–1.56) vs. 1.64 (95 % CI 1.48–1.81), respectively. No differences were seen when the second measurement results were stratified by preceding change in BMD or osteoporosis therapy (both p-interactions >0.2). Similar results were seen for hip fracture prediction and when spine and femoral neck BMD were analyzed. Conclusion: Repeat BMD measurements are a robust predictor of fracture in clinical populations; this is not affected by preceding BMD change or recent osteoporosis therapy.

Avaliação genética da eficiência reprodutiva em vacas pardo-suíças por meio da análise de sobrevivência

Among the traits of economic importance to dairy cattle livestock those related to sexual precocity and longevity of the herd are essential to the success of the activity, because the stayability time of a cow in a herd is determined by their productive and reproductive lives. In Brazil, there are few studies about the reproductive efficiency of Swiss-Brown cows and no study was found using the methodology of survival analysis applied to this breed. Thus, in the first chapter of this study, the age at first calving from Swiss-Brown heifers was analyzed as the time until the event by the nonparametric method of Kaplan-Meier and the gamma shared frailty model, under the survival analysis methodology. Survival and hazard rate curves associated with this event were estimated and identified the influence of covariates on such time. The mean and median times at the first calving were 987.77 and 1,003 days, respectively, and significant covariates by the Log-Rank test, through Kaplan-Meier analysis, were birth season, calving year, sire (cow s father) and calving season. In the analysis by frailty model, the breeding values and the frailties of the sires (fathers) for the calving were predicted modeling the risk function of each cow as a function of the birth season as fixed covariate and sire as random covariate. The frailty followed the gamma distribution. Sires with high and positive breeding values possess high frailties, what means shorter survival time of their daughters to the event, i.e., reduction in the age at first calving of them. The second chapter aimed to evaluate the longevity of dairy cows using the nonparametric Kaplan-Meier and the Cox and Weibull proportional hazards models. It were simulated 10,000 records of the longevity trait from Brown-Swiss cows involving their respective times until the occurrence of five consecutive calvings (event), considered here as typical of a long-lived cow. The covariates considered in the database were age at first calving, herd and sire (cow s father). All covariates had influence on the longevity of cows by Log-Rank and Wilcoxon tests. The mean and median times to the occurrence of the event were 2,436.285 and 2,437 days, respectively. Sires that have higher breeding values also have a greater risk of that their daughters reach the five consecutive calvings until 84 months

Anemia at one year is an independent risk factor of graft survival

Background Post-transplant anemia is multifactorial and highly prevalent. Some studies have associated anemia with mortality and graft failure. The purpose of this study was to assess whether the presence of anemia at 1 year is an independent risk factor of mortality and graft survival. Methods All patients transplanted at a single center who survived at least 1 year after transplantation and showed no graft loss (n = 214) were included. Demographic and clinical data were collected at baseline and at 1 year. Patients were divided into two groups (anemic and nonanemic) based on the presence of anemia (hemoglobin<130 g/l in men and 120 g/l in women). Results Baseline characteristics such as age, gender, type of donor, CKD etiology, rejection, andmismatches were similar in both groups. Creatinine clearance was similar in both anemic and nonanemic groups (69.32 ± 29.8 × 75.69 ± 30.5 ml/mim; P = 0.17). A Kaplan- Meier plot showed significantly poorer death-censored graft survival in the anemic group, P = 0.003. Multivariate analysis revealed that anemic patients had a hazard ratio for the graft loss of 3.85 (95% CI: 1.49-9.96; P = 0.005). Conclusions In this study, anemia at 1 year was independently associated with death-censored graft survival and anemic patients were 3.8-fold more likely to lose the graft. © 2010 Springer Science+Business Media, B.V.

Pathological and behavioral risk factors for higher serum c-reactive protein concentrations in free-living adults - A Brazilian community-based study

Low-grade chronic systemic inflammation is often associated with chronic non-communicable diseases, and its most frequently used marker, the C-reactive protein (CRP), has become an identifier of such diseases as well as an independent predictor for cardiovascular disorders and mortality. CRP is produced in response to pro-inflammatory signaling and to individual and behavioral factors, leading to pathological states. The aim of this study was to rank the predicting factors of high CRP concentrations in free-living adults from a community-based sample. We evaluated 522 adults (40-84 years old; 381 women) for anthropometric characteristics, dietary intake, clinical and physical tests, and blood analysis. Subjects were assigned to groups, according to CRP concentrations, as normal CRP (G1;<3.0 mg/L; n = 269), high CRP (G2; 3.0-6.0 mg/L; n = 139), and very high CRP (G3; >6.0 mg/dL; n = 116). Statistical comparison between groups used one-way ANOVA or Kruskal-Wallis tests, and prediction of altered values in increasing CRP was evaluated by proportional hazard models (odds ratio). CRP distribution was influenced by gender, body mass index, body and abdominal fatness, blood leukocytes, and neutrophil counts. The higher CRP group was discriminated by the above variables in addition to lower VO2max, serum metabolic syndrome components (triglycerides, glucose, and HDL cholesterol), higher insulin, homeostasis assessment of insulin resistance, uric acid, gamma-GT, and homocysteine. After adjustments, only fatness, blood leukocytes, and hyperglycemia remained as independent predictors for increased serum CRP concentrations. Intervention procedures to treat low-grade chronic inflammation in overweight women would mainly focus on restoring muscle mass and functions in addition to an antioxidant-rich diet. © 2012 Springer Science+Business Media, LLC.

Absence of RKIP expression is an independent prognostic biomarker for gastric cancer patients

Gastric cancer is a leading cause of cancer-related mortality, and the presence of lymph node metastasis an important prognostic factor. Downregulation of RKIP has been associated with tumor progression and metastasis in several types of neoplasms, being currently categorized as a metastasis suppressor gene. Our aim was to determine the expression levels of RKIP in gastric tissues and to evaluate its impact in the clinical outcome of gastric carcinoma patients. RKIP expression levels were studied by immunohistochemistry in a series of gastric tissues. Overall, we analysed 222 non-neoplastic gastric tissues, 152 primary tumors and 42 lymph node metastasis samples. We observed that RKIP was highly expressed in ∼83% of non-neoplastic tissues (including normal tissue and metaplasia), was lost in ∼56% of primary tumors and in ∼90% of lymph node metastasis samples. Loss of RKIP expression was significantly associated with several markers of poor clinical outcome, including the presence of lymph node metastasis. Furthermore, the absence of RKIP protein constitutes an independent prognostic marker for these patients. In conclusion, RKIP expression is significantly lost during gastric carcinoma progression being almost absent in lymph node metastasis samples. Of note, we showed that the absence of RKIP expression is associated with poor outcome features of gastric cancer patients, this being also an independent prognostic marker.

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.

Overall Survival Improvement in Patients with Lung Cancer and Bone Metastases Treated with Denosumab Versus Zoledronic Acid Subgroup Analysis from a Randomized Phase 3 Study

Introduction: Denosumab, a fully human anti-RANKL monoclonal antibody, reduces the incidence of skeletal-related events in patients with bone metastases from solid tumors. We present survival data for the subset of patients with lung cancer, participating in the phase 3 trial of denosumab versus zoledronic acid (ZA) in the treatment of bone metastases from solid tumors (except breast or prostate) or multiple myeloma. Methods: Patients were randomized 1:1 to receive monthly subcutaneous denosumab 120 mg or intravenous ZA 4 mg. An exploratory analysis, using Kaplan-Meier estimates and proportional hazards models, was performed for overall survival among patients with non-small-cell lung cancer (NSCLC) and SCLC. Results: Denosumab was associated with improved median overall survival versus ZA in 811 patients with any lung cancer (8.9 versus 7.7 months; hazard ratio [HR] 0.80) and in 702 patients with NSCLC (9.5 versus 8.0 months; HR 0.78) (p = 0.01, each comparison). Further analysis of NSCLC by histological type showed a median survival of 8.6 months for denosumab versus 6.4 months for ZA in patients with squamous cell carcinoma (HR 0.68; p = 0.035). Incidence of overall adverse events was balanced between treatment groups; serious adverse events occurred in 66.0% of denosumab-treated patients and 72.9% of ZA-treated patients. Cumulative incidence of osteonecrosis of the jaw was similar between groups (0.7% denosumab versus 0.8% ZA). Hypocalcemia rates were 8.6% with denosumab and 3.8% with ZA. Conclusion: In this exploratory analysis, denosumab was associated with improved overall survival compared with ZA, in patients with metastatic lung cancer.

Virologic failure and second-line antiretroviral therapy in children in South Africa--the IeDEA Southern Africa collaboration

Background: With expanding pediatric antiretroviral therapy (ART) access, children will begin to experience treatment failure and require second-line therapy. We evaluated the probability and determinants of virologic failure and switching in children in South Africa. Methods: Pooled analysis of routine individual data from children who initiated ART in 7 South African treatment programs with 6-monthly viral load and CD4 monitoring produced Kaplan-Meier estimates of probability of virologic failure (2 consecutive unsuppressed viral loads with the second being >1000 copies/mL, after ≥24 weeks of therapy) and switch to second-line. Cox-proportional hazards models stratified by program were used to determine predictors of these outcomes. Results: The 3-year probability of virologic failure among 5485 children was 19.3% (95% confidence interval: 17.6 to 21.1). Use of nevirapine or ritonavir alone in the initial regimen (compared with efavirenz) and exposure to prevention of mother to child transmission regimens were independently associated with failure [adjusted hazard ratios (95% confidence interval): 1.77 (1.11 to 2.83), 2.39 (1.57 to 3.64) and 1.40 (1.02 to 1.92), respectively]. Among 252 children with ≥1 year follow-up after failure, 38% were switched to second-line. Median (interquartile range) months between failure and switch was 5.7 (2.9-11.0). Conclusions: Triple ART based on nevirapine or ritonavir as a single protease inhibitor seems to be associated with a higher risk of virologic failure. A low proportion of virologically failing children were switched.

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.

Inference on Survival Data with Covariate Measurement Error - An Imputation-based Approach

We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerative distribution. Simulations indicate high efficiency and robustness. We consider the special case where error-prone replicates are available on the unobserved true covariates. As expected, increasing the number of replicate for the unobserved covariates increases efficiency and reduces bias. We illustrate the practical utility of the proposed method with an Eastern Cooperative Oncology Group clinical trial where a genetic marker, c-myc expression level, is subject to measurement error.