Comparison of a traditional and a multilevel Cox Proportional Hazards model

Hierarchically clustered populations are often encountered in public health research, but the traditional methods used in analyzing this type of data are not always adequate. In the case of survival time data, more appropriate methods have only begun to surface in the last couple of decades. Such methods include multilevel statistical techniques which, although more complicated to implement than traditional methods, are more appropriate. ^ One population that is known to exhibit a hierarchical structure is that of patients who utilize the health care system of the Department of Veterans Affairs where patients are grouped not only by hospital, but also by geographic network (VISN). This project analyzes survival time data sets housed at the Houston Veterans Affairs Medical Center Research Department using two different Cox Proportional Hazards regression models, a traditional model and a multilevel model. VISNs that exhibit significantly higher or lower survival rates than the rest are identified separately for each model. ^ In this particular case, although there are differences in the results of the two models, it is not enough to warrant using the more complex multilevel technique. This is shown by the small estimates of variance associated with levels two and three in the multilevel Cox analysis. Much of the differences that are exhibited in identification of VISNs with high or low survival rates is attributable to computer hardware difficulties rather than to any significant improvements in the model. ^

Choosing between Cox proportional hazards and logistic models for interval-censored data via bootstrap

This work develops a new methodology in order to discriminate models for interval-censored data based on bootstrap residual simulation by observing the deviance difference from one model in relation to another, according to Hinde (1992). Generally, this sort of data can generate a large number of tied observations and, in this case, survival time can be regarded as discrete. Therefore, the Cox proportional hazards model for grouped data (Prentice & Gloeckler, 1978) and the logistic model (Lawless, 1982) can befitted by means of generalized linear models. Whitehead (1989) considered censoring to be an indicative variable with a binomial distribution and fitted the Cox proportional hazards model using complementary log-log as a link function. In addition, a logistic model can be fitted using logit as a link function. The proposed methodology arises as an alternative to the score tests developed by Colosimo et al. (2000), where such models can be obtained for discrete binary data as particular cases from the Aranda-Ordaz distribution asymmetric family. These tests are thus developed with a basis on link functions to generate such a fit. The example that motivates this study was the dataset from an experiment carried out on a flax cultivar planted on four substrata susceptible to the pathogen Fusarium oxysoprum. The response variable, which is the time until blighting, was observed in intervals during 52 days. The results were compared with the model fit and the AIC values.

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. ^

Concordance Probability and Discriminatory Power in Proportional Hazards Regression

The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytic expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on informative pairs. The asymptotic distribution of the concordance probability estimate is derived using U-statistic theory and the methodology is applied to a predictive model in lung cancer.

Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.

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.

Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity

We develop tests of the proportional hazards assumption, with respect to a continuous covariate, in the presence of unobserved heterogeneity with unknown distribution at the individual observation level. The proposed tests are specially powerful against ordered alternatives useful for modeling non-proportional hazards situations. By contrast to the case when the heterogeneity distribution is known up to …nite dimensional parameters, the null hypothesis for the current problem is similar to a test for absence of covariate dependence. However, the two testing problems di¤er in the nature of relevant alternative hypotheses. We develop tests for both the problems against ordered alternatives. Small sample performance and an application to real data highlight the usefulness of the framework and methodology.

The Value Of The 2005 International Society Of Urological Pathology (isup) Modified Gleason Grading System As A Predictor Of Biochemical Recurrence After Radical Prostatectomy.

To compare time and risk to biochemical recurrence (BR) after radical prostatectomy of two chronologically different groups of patients using the standard and the modified Gleason system (MGS). Cohort 1 comprised biopsies of 197 patients graded according to the standard Gleason system (SGS) in the period 1997/2004, and cohort 2, 176 biopsies graded according to the modified system in the period 2005/2011. Time to BR was analyzed with the Kaplan-Meier product-limit analysis and prediction of shorter time to recurrence using univariate and multivariate Cox proportional hazards model. Patients in cohort 2 reflected time-related changes: striking increase in clinical stage T1c, systematic use of extended biopsies, and lower percentage of total length of cancer in millimeter in all cores. The MGS used in cohort 2 showed fewer biopsies with Gleason score ≤ 6 and more biopsies of the intermediate Gleason score 7. Time to BR using the Kaplan-Meier curves showed statistical significance using the MGS in cohort 2, but not the SGS in cohort 1. Only the MGS predicted shorter time to BR on univariate analysis and on multivariate analysis was an independent predictor. The results favor that the 2005 International Society of Urological Pathology modified system is a refinement of the Gleason grading and valuable for contemporary clinical practice.

Analysis Of The Contribution Of Immunologically-detectable Her2, Steroid Receptors And Of The Triple-negative" Tumor Status To Disease-free And Overall Survival Of Women With Epithelial Ovarian Cancer."

We assessed associations between steroid receptors including: estrogen-alpha, estrogen-beta, androgen receptor, progesterone receptor, the HER2 status and triple-negative epithelial ovarian cancer (ERα-/PR-/HER2-; TNEOC) status and survival in women with epithelial ovarian cancer. The study included 152 women with primary epithelial ovarian cancer. The status of steroid receptor and HER2 was determined by immunohistochemistry. Disease-free and overall survival were calculated and compared with steroid receptor and HER2 status as well as clinicopathological features using the Cox Proportional Hazards model. A mean follow-up period of 43.6 months (interquartile range=41.4 months) was achieved where 44% of patients had serous tumor, followed by mucinous (23%), endometrioid (9%), mixed (9%), undifferentiated (8.5%) and clear cell tumors (5.3%). ER-alpha staining was associated with grade II-III tumors. Progesterone receptor staining was positively associated with a Body Mass Index≥25. Androgen receptor positivity was higher in serous tumors. In stand-alone analysis of receptor contribution to survival, estrogen-alpha positivity was associated with greater disease-free survival. However, there was no significant association between steroid receptor expression, HER2 status, or TNEOC status, and overall survival. Although estrogen-alpha, androgen receptor, progesterone receptor and the HER2 status were associated with key clinical features of the women and pathological characteristics of the tumors, these associations were not implicated in survival. Interestingly, women with TNEOC seem to fare the same way as their counterparts with non-TNEOC.

Menopausal status: a possible predictive factor for recurrence in women with cancer of the uterine cervix without pelvic lymph node metastasis

Abstract Objectives to evaluate risk factors for recurrence of carcinoma of the uterine cervix among women who had undergone radical hysterectomy without pelvic lymph node metastasis, while taking into consideration not only the classical histopathological factors but also sociodemographic, clinical and treatment-related factors. Study desin This was an exploratory analysis on 233 women with carcinoma of the uterine cervix (stages IB and IIA) who were treated by means of radical hysterectomy and pelvic lymphadenectomy, with free surgical margins and without lymph node metastases on conventional histopathological examination. Women with histologically normal lymph nodes but with micrometastases in the immunohistochemical analysis (AE1/AE3) were excluded. Disease-free survival for sociodemographic, clinical and histopathological variables was calculated using the Kaplan-Meier method. The Cox proportional hazards model was used to identify the independent risk factors for recurrence. Twenty-seven recurrences were recorded (11.6%), of which 18 were pelvic, four were distant, four were pelvic + distant and one was of unknown location. The five-year disease-free survival rate among the study population was 88.4%. The independent risk factors for recurrence in the multivariate analysis were: postmenopausal status (HR 14.1; 95% CI: 3.7-53.6; P < 0.001), absence of or slight inflammatory reaction (HR 7.9; 95% CI: 1.7-36.5; P = 0.008) and invasion of the deepest third of the cervix (HR 6.1; 95% CI: 1.3-29.1; P = 0.021). Postoperative radiotherapy was identified as a protective factor against recurrence (HR 0.02; 95% CI: 0.001-0.25; P = 0.003). (To continue) Postmenopausal status is a possible independent risk factor for recurrence even when adjusted for classical prognostic factors (such as tumour size, depth of tumour invasion, capillary embolisation) and treatment-related factors (period of treatment and postoperative radiotherapy status)

Arrhythmias and mortality after myocardial infarction in diabetic patients - Relationship to diabetes treatment

OBJECTIVE- To assess the relationship between clinical course after acute myocardial infarction (AMI) and diabetes treatment. RESEARCH DESIGN AND METHODS- Retrospective analysis of data from all patients aged 25-64 years admitted to hospitals in Perth, Australia, between 1985 and 1993 with AMI diagnosed according to the International Classification of Diseases (9th revision) criteria was conducted. Short- (28-day) and long-term survival and complications in diabetic and nondiabetic patients were compared. For diabetic patients, 28-day survival, dysrhythmias, heart block, and pulmonary edema were treated as outcomes, and factors related to each were assessed using multiple logistic regression. Diabetes treatment was added to the model to assess its significance. Long-term survival was compared by means of a Cox proportional hazards model. RESULTS- Of 5,715 patients, 745 (12.9%) were diabetic. Mortality at 28 days was 12.0 and 28.1% for nondiabetic and diabetic patients, respectively (P < 0.001); there were no significant drug effects in the diabetic group. Ventricular fibrillation in diabetic patients taking glibenclamide (11.8%) was similar to that of nondiabetic patients (11.0%) but was lower than that for those patients taking either gliclazide (18.0%; 0.1 > P > 0.05) or insulin (22.8%; P < 0.05). There were no other treatment-related differences in acute complications. Long-term survival in diabetic patients was reduced in those taking digitalis and/or diuretics but type of diabetes treatment at discharge had no significant association with outcome. CONCLUSlONS- These results do not suggest that ischemic heart disease should influence the choice of diabetes treatment regimen in general or of sulfonylurea drug in particular.

Association between ADAMTS13 polymorphisms and risk of cardiovascular events in chronic coronary disease

Introduction: Association between ADAMTS13 levels and cardiovascular events has been described recently. However, no genetic study of ADAMTS13 in coronary patients has been described. Materials and Methods: Based on related populations frequencies and functional studies, we tested three ADAMTS13 polymorphisms: C1342G (Q448E), C1852G (P618A) and C2699T (A900V) in a group of 560 patients enrolled in the Medical, Angioplasty, or Surgery Study II (MASS II), a randomized trial comparing treatments for patients with coronary artery disease (CAD) and preserved left ventricular function. The incidence of the 5-year end-points of death and death from cardiac causes, myocardial infarction, refractory angina requiring revascularization and cerebrovascular accident was determined for each polymorphim`s allele, genotype and haplotype. Risk was assessed with the use of logistic regression and Cox proportional-hazards model and multivariable adjustment was employed for possible confounders. Results: Clinical characteristics and received treatment of each genotype group were similar at baseline. In an adjusted model for cardiovascular risk variables, we were able to observe a significant association between ADAMTS13 900V variant and an increased risk of death (OR: 1,92 CI: 1,14-3,23, p = 0,015) or death from cardiac cause (OR: 2,67, CI: 1,59-4,49, p = 0,0009). No association between events and ADAMTS13 Q448E or P618A was observed. Conclusions: This first report studying the association between ADAMTS13 genotypes and cardiovascular events provides evidence for the association between ADAMTS13 900V variant and an increased risk of death in a population with multi-vessel CAD. (C) 2009 Elsevier Ltd. All rights reserved.

Prognostic value of NDRG1 and SPARC protein expression in breast cancer patients

An increasing number of studies have shown altered expression of secreted protein acidic and rich in cysteine (SPARC) and N-myc down-regulated gene (NDRG1) in several malignancies, including breast carcinoma; however, the role of these potential biomarkers in tumor development and progression is controversial. In this study, NDRG1 and SPARC protein expression was evaluated by immunohistochemistry on tissue microarrays containing breast tumor specimens from patients with 10 years of follow-up. NDRG1 and SPARC protein expression was determined in 596 patients along with other prognostic markers, such as ER, PR, and HER2. The status of NDRG1 and SPARC protein expression was correlated with prognostic variables and patient clinical outcome. Immunostaining revealed that 272 of the 596 cases (45.6%) were positive for NDRG1 and 431 (72.3%) were positive for SPARC. Statistically significant differences were found between the presence of SPARC and NDRG1 protein expression and standard clinicopathological variables. Kaplan-Meier analysis showed that NDRG1 positivity was directly associated with shorter disease-free survival (DFS, P < 0.001) and overall survival (OS, P < 0.001). In contrast, patients expressing low levels of SPARC protein had worse DFS (P = 0.001) and OS (P = 0.001) compared to those expressing high levels. Combined analysis of the two markers indicated that DFS (P < 0.001) and OS rates (P < 0.001) were lowest for patients with NDRG1-positive and SPARC-negative tumors. Furthermore, NDRG1 over-expression and SPARC down-regulation correlated with poor prognosis in patients with luminal A or triple-negative subtype breast cancer. On multivariate analysis using a Cox proportional hazards model, NDRG1 and SPARC protein expression were independent prognostic factors for both DFS and OS of breast cancer patients. These data indicate that NDRG1 over-expression and SPARC down-regulation could play important roles in breast cancer progression and serve as useful biomarkers to better define breast cancer prognosis.

Survival of adult AIDS patients in a reference hospital of a metropolitan area in Brazil

OBJECTIVE: To evaluate the influence of sociodemographic, clinical, and epidemiological factors in AIDS patients survival in a reference hospital. METHODS: A sample of 502 adult AIDS patients out of 1,494 AIDS cases registered in a hospital in Fortaleza, Brazil, was investigated between 1986 and 1998. Sixteen cases were excluded due to death at the moment of the AIDS diagnosis and 486 were analyzed in the study. Socioeconomic and clinical epidemiological were the variables studied. Statistical analysis was conducted using the Kaplan-Meier survival analysis and the Cox proportional hazards model. RESULTS: Three hundred and sixty two out of the 486 patients studied took at least one antiretroviral drug and their survival was ten times longer than those who did not take any drug (746 and 79 days, respectively, p <0.001). Patients who took two nucleoside reverse transcriptase inhibitors (NRTI) plus protease inhibitor were found to have higher survival rates (p <0.001). The risk of dying in the first year was significantly lower for patients who took NRTI and a protease inhibitor compared to those who took only NRTI. In addition, this risk was much lower from the second year on (0.10; 95%CI: 0.42-0.23). The risk of dying in the first year was significantly higher for less educated patients (15.58; 95%CI: 6.64-36.58) and those who had two or more systemic diseases (3.03; 95%CI: 1.74-5.25). After the first year post-diagnosis, there was no risk difference for these factors. CONCLUSIONS: Higher education revealed to exert a significant influence in the first-year survival. Antiretroviral drugs had a greater impact in the survival from the second year on. A more aggressive antiretroviral therapy started earlier could benefit those patients.