Stabilizing sparse cox model using statistic and semantic structures in electronic medical records

Stability in clinical prediction models is crucial for transferability between studies, yet has received little attention. The problem is paramount in high dimensional data, which invites sparse models with feature selection capability. We introduce an effective method to stabilize sparse Cox model of time-to-events using statistical and semantic structures inherent in Electronic Medical Records (EMR). Model estimation is stabilized using three feature graphs built from (i) Jaccard similarity among features (ii) aggregation of Jaccard similarity graph and a recently introduced semantic EMR graph (iii) Jaccard similarity among features transferred from a related cohort. Our experiments are conducted on two real world hospital datasets: a heart failure cohort and a diabetes cohort. On two stability measures – the Consistency index and signal-to-noise ratio (SNR) – the use of our proposed methods significantly increased feature stability when compared with the baselines.

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.

Model selection for prognostic time-to-event gene signature discovery with applications in early breast cancer data

Model selection between competing models is a key consideration in the discovery of prognostic multigene signatures. The use of appropriate statistical performance measures as well as verification of biological significance of the signatures is imperative to maximise the chance of external validation of the generated signatures. Current approaches in time-to-event studies often use only a single measure of performance in model selection, such as logrank test p-values, or dichotomise the follow-up times at some phase of the study to facilitate signature discovery. In this study we improve the prognostic signature discovery process through the application of the multivariate partial Cox model combined with the concordance index, hazard ratio of predictions, independence from available clinical covariates and biological enrichment as measures of signature performance. The proposed framework was applied to discover prognostic multigene signatures from early breast cancer data. The partial Cox model combined with the multiple performance measures were used in both guiding the selection of the optimal panel of prognostic genes and prediction of risk within cross validation without dichotomising the follow-up times at any stage. The signatures were successfully externally cross validated in independent breast cancer datasets, yielding a hazard ratio of 2.55 [1.44, 4.51] for the top ranking signature.

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. ^

Angiogenesis is an independent prognostic factor in malignant mesothelioma

Angiogenesis is essential for tumour growth beyond 1 to 2 mm in diameter. The clinical relevance of angiogenesis, as assessed by microvessel density (MVD), is unclear in malignant mesothelioma (MM). Immunohistochemistry was performed on 104 archival, paraffin-embedded, surgically resected MM samples with an anti-CD34 monoclonal antibody, using the Streptavidin-biotin complex immunoperoxidase technique. 93 cases were suitable for microvessel quantification. MVD was obtained from 3 intratumoural hotspots, using a Chalkley eyepiece graticule at × 250 power. MVD was correlated with survival by Kaplan-Meier and log-rank analysis. A stepwise, multivariate Cox model was used to compare MVD with known prognostic factors and the EORTC and CALGB prognostic scoring systems. Overall median survival from the date of diagnosis was 5.0 months. Increasing MVD was a poor prognostic factor in univariate analysis (P = 0.02). Independent indicators of poor prognosis in multivariate analysis were non-epithelial cell type (P = 0.002), performance status > 0 (P = 0.003) and increasing MVD (P = 0.01). In multivariate Cox analysis, MVD contributed independently to the EORTC (P = 0.006), but not to the CALGB (P = 0.1), prognostic groups. Angiogenesis, as assessed by MVD, is a poor prognostic factor in MM, independent of other clinicopathological variables and the EORTC prognostic scoring system. Further work is required to assess the prognostic importance of angiogenic regulatory factors in this disease. © 2001 Cancer Research Campaign.

Mortality following hip arthroplasty—inappropriate use of National Joint Registry (NJR) data

Mortality following hip arthroplasty is affected by a large number of confounding variables each of which must be considered to enable valid interpretation. Relevant variables available from the 2011 NJR data set were included in the Cox model. Mortality rates in hip arthroplasty patients were lower than in the age-matched population across all hip types. Age at surgery, ASA grade, diagnosis, gender, provider type, hip type and lead surgeon grade all had a significant effect on mortality. Schemper's statistic showed that only 18.98% of the variation in mortality was explained by the variables available in the NJR data set. It is inappropriate to use NJR data to study an outcome affected by a multitude of confounding variables when these cannot be adequately accounted for in the available data set.

Anthropometric measures of obesity-their association with type 2 diabetes and hypertension across ethnic groups

Clinical trials have shown that weight reduction with lifestyles can delay or prevent diabetes and reduce blood pressure. An appropriate definition of obesity using anthropometric measures is useful in predicting diabetes and hypertension at the population level. However, there is debate on which of the measures of obesity is best or most strongly associated with diabetes and hypertension and on what are the optimal cut-off values for body mass index (BMI) and waist circumference (WC) in this regard. The aims of the study were 1) to compare the strength of the association for undiagnosed or newly diagnosed diabetes (or hypertension) with anthropometric measures of obesity in people of Asian origin, 2) to detect ethnic differences in the association of undiagnosed diabetes with obesity, 3) to identify ethnic- and sex-specific change point values of BMI and WC for changes in the prevalence of diabetes and 4) to evaluate the ethnic-specific WC cutoff values proposed by the International Diabetes Federation (IDF) in 2005 for central obesity. The study population comprised 28 435 men and 35 198 women, ≥ 25 years of age, from 39 cohorts participating in the DECODA and DECODE studies, including 5 Asian Indian (n = 13 537), 3 Mauritian Indian (n = 4505) and Mauritian Creole (n = 1075), 8 Chinese (n =10 801), 1 Filipino (n = 3841), 7 Japanese (n = 7934), 1 Mongolian (n = 1991), and 14 European (n = 20 979) studies. The prevalence of diabetes, hypertension and central obesity was estimated, using descriptive statistics, and the differences were determined with the χ2 test. The odds ratios (ORs) or  coefficients (from the logistic model) and hazard ratios (HRs, from the Cox model to interval censored data) for BMI, WC, waist-to-hip ratio (WHR), and waist-to-stature ratio (WSR) were estimated for diabetes and hypertension. The differences between BMI and WC, WHR or WSR were compared, applying paired homogeneity tests (Wald statistics with 1 df). Hierarchical three-level Bayesian change point analysis, adjusting for age, was applied to identify the most likely cut-off/change point values for BMI and WC in association with previously undiagnosed diabetes. The ORs for diabetes in men (women) with BMI, WC, WHR and WSR were 1.52 (1.59), 1.54 (1.70), 1.53 (1.50) and 1.62 (1.70), respectively and the corresponding ORs for hypertension were 1.68 (1.55), 1.66 (1.51), 1.45 (1.28) and 1.63 (1.50). For diabetes the OR for BMI did not differ from that for WC or WHR, but was lower than that for WSR (p = 0.001) in men while in women the ORs were higher for WC and WSR than for BMI (both p < 0.05). Hypertension was more strongly associated with BMI than with WHR in men (p < 0.001) and most strongly with BMI than with WHR (p < 0.001), WSR (p < 0.01) and WC (p < 0.05) in women. The HRs for incidence of diabetes and hypertension did not differ between BMI and the other three central obesity measures in Mauritian Indians and Mauritian Creoles during follow-ups of 5, 6 and 11 years. The prevalence of diabetes was highest in Asian Indians, lowest in Europeans and intermediate in others, given the same BMI or WC category. The  coefficients for diabetes in BMI (kg/m2) were (men/women): 0.34/0.28, 0.41/0.43, 0.42/0.61, 0.36/0.59 and 0.33/0.49 for Asian Indian, Chinese, Japanese, Mauritian Indian and European (overall homogeneity test: p > 0.05 in men and p < 0.001 in women). Similar results were obtained in WC (cm). Asian Indian women had lower  coefficients than women of other ethnicities. The change points for BMI were 29.5, 25.6, 24.0, 24.0 and 21.5 in men and 29.4, 25.2, 24.9, 25.3 and 22.5 (kg/m2) in women of European, Chinese, Mauritian Indian, Japanese, and Asian Indian descent. The change points for WC were 100, 85, 79 and 82 cm in men and 91, 82, 82 and 76 cm in women of European, Chinese, Mauritian Indian, and Asian Indian. The prevalence of central obesity using the 2005 IDF definition was higher in Japanese men but lower in Japanese women than in their Asian counterparts. The prevalence of central obesity was 52 times higher in Japanese men but 0.8 times lower in Japanese women compared to the National Cholesterol Education Programme definition. The findings suggest that both BMI and WC predicted diabetes and hypertension equally well in all ethnic groups. At the same BMI or WC level, the prevalence of diabetes was highest in Asian Indians, lowest in Europeans and intermediate in others. Ethnic- and sex-specific change points of BMI and WC should be considered in setting diagnostic criteria for obesity to detect undiagnosed or newly diagnosed diabetes.

Association of Caveolin-1 gene polymorphism with kidney transplant fibrosis and allograft failure

Context: Caveolin-1 (CAV1) is an inhibitor of tissue fibrosis.
Objective: To study the association of CAV1 gene variation with kidney transplant outcome, using kidney transplantation as a model of accelerated fibrosis.
Design, Setting, and Patients: Candidate gene association and validation study. Genomic DNA from 785 white kidney transplant donors and their respective recipients (transplantations in Birmingham, England, between 1996 and 2006; median followup, 81 months) were analyzed for common variation in CAV1 using a singlenucleotide polymorphism (SNP) tagging approach. Validation of positive findings was sought in an independent kidney transplant donor-recipient cohort (transplantations in Belfast, Northern Ireland, between 1986 and 2005; n=697; median follow-up, 69 months). Association between genotype and allograft failure was initially assessed by Kaplan-Meier analysis, then in an adjusted Cox model.
Main Outcome Measure: Death-censored allograft failure, defined as a return to dialysis or retransplantation.
Results: The presence of donor AA genotype for the CAV1 rs4730751 SNP was associated with increased risk of allograft failure in the Birmingham group (donor AA vs non-AA genotype in adjusted Cox model, hazard ratio [HR], 1.97; 95% confidence interval [CI], 1.29-3.16; P=.002). No other tag SNPs showed a significant association. This finding was validated in the Belfast cohort (in adjusted Cox model, HR, 1.56; 95% CI, 1.07-2.27; P=.02). Overall graft failure rates were as follows: for the Birmingham cohort, donor genotype AA, 22 of 57 (38.6%); genotype CC, 96 of 431 (22.3%); and genotype AC, 66 of 297 (22.2%); and for the Belfast cohort, donor genotype AA, 32 of 48 (67%); genotype CC, 150 of 358 (42%); and genotype AC, 119 of 273 (44%).
Conclusion: Among kidney transplant donors, the CAV1 rs4730751 SNP was significantly associated with allograft failure in 2 independent cohorts.

Métodos probabilísticos e estatísticos na gestão de fogos florestais

Tese de doutoramento, Estatística e Investigação Operacional (Probabilidades e Estatística), Universidade de Lisboa, Faculdade de Ciências, 2014

New statistical methods to assess the effect of time-dependent exposures in case-control studies

Contexte. Les études cas-témoins sont très fréquemment utilisées par les épidémiologistes pour évaluer l’impact de certaines expositions sur une maladie particulière. Ces expositions peuvent être représentées par plusieurs variables dépendant du temps, et de nouvelles méthodes sont nécessaires pour estimer de manière précise leurs effets. En effet, la régression logistique qui est la méthode conventionnelle pour analyser les données cas-témoins ne tient pas directement compte des changements de valeurs des covariables au cours du temps. Par opposition, les méthodes d’analyse des données de survie telles que le modèle de Cox à risques instantanés proportionnels peuvent directement incorporer des covariables dépendant du temps représentant les histoires individuelles d’exposition. Cependant, cela nécessite de manipuler les ensembles de sujets à risque avec précaution à cause du sur-échantillonnage des cas, en comparaison avec les témoins, dans les études cas-témoins. Comme montré dans une étude de simulation précédente, la définition optimale des ensembles de sujets à risque pour l’analyse des données cas-témoins reste encore à être élucidée, et à être étudiée dans le cas des variables dépendant du temps. Objectif: L’objectif général est de proposer et d’étudier de nouvelles versions du modèle de Cox pour estimer l’impact d’expositions variant dans le temps dans les études cas-témoins, et de les appliquer à des données réelles cas-témoins sur le cancer du poumon et le tabac. Méthodes. J’ai identifié de nouvelles définitions d’ensemble de sujets à risque, potentiellement optimales (le Weighted Cox model and le Simple weighted Cox model), dans lesquelles différentes pondérations ont été affectées aux cas et aux témoins, afin de refléter les proportions de cas et de non cas dans la population source. Les propriétés des estimateurs des effets d’exposition ont été étudiées par simulation. Différents aspects d’exposition ont été générés (intensité, durée, valeur cumulée d’exposition). Les données cas-témoins générées ont été ensuite analysées avec différentes versions du modèle de Cox, incluant les définitions anciennes et nouvelles des ensembles de sujets à risque, ainsi qu’avec la régression logistique conventionnelle, à des fins de comparaison. Les différents modèles de régression ont ensuite été appliqués sur des données réelles cas-témoins sur le cancer du poumon. Les estimations des effets de différentes variables de tabac, obtenues avec les différentes méthodes, ont été comparées entre elles, et comparées aux résultats des simulations. Résultats. Les résultats des simulations montrent que les estimations des nouveaux modèles de Cox pondérés proposés, surtout celles du Weighted Cox model, sont bien moins biaisées que les estimations des modèles de Cox existants qui incluent ou excluent simplement les futurs cas de chaque ensemble de sujets à risque. De plus, les estimations du Weighted Cox model étaient légèrement, mais systématiquement, moins biaisées que celles de la régression logistique. L’application aux données réelles montre de plus grandes différences entre les estimations de la régression logistique et des modèles de Cox pondérés, pour quelques variables de tabac dépendant du temps. Conclusions. Les résultats suggèrent que le nouveau modèle de Cox pondéré propose pourrait être une alternative intéressante au modèle de régression logistique, pour estimer les effets d’expositions dépendant du temps dans les études cas-témoins