The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

A diszkrét kiválasztási modell becslése Cox-regresszióval (Parameter estimation for multinomial discrete choice model using Cox-regression)

Considering the so-called "multinomial discrete choice" model the focus of this paper is on the estimation problem of the parameters. Especially, the basic question arises how to carry out the point and interval estimation of the parameters when the model is mixed i.e. includes both individual and choice-specific explanatory variables while a standard MDC computer program is not available for use. The basic idea behind the solution is the use of the Cox-proportional hazards method of survival analysis which is available in any standard statistical package and provided a data structure satisfying certain special requirements it yields the MDC solutions desired. The paper describes the features of the data set to be analysed.

Independent predictors and a prognostic model for surgical outcome in refractory frontal lobe epilepsy

Purpose: Refractory frontal lobe epilepsy (FLE) remains one of the most challenging surgically remediable epilepsy syndromes. Nevertheless, definition of independent predictors and predictive models of postsurgical seizure outcome remains poorly explored in FLE. Methods: We retrospectively analyzed data from 70 consecutive patients with refractory FLE submitted to surgical treatment at our center from July 1994 to December 2006. Univariate results were submitted to logistic regression models and Cox proportional hazards regression to identify isolated risk factors for poor surgical results and to construct predictive models for surgical outcome in FLE. Results: From 70 patients submitted to surgery, 45 patients (64%) had favorable outcome and 37 (47%) became seizure free. Isolated risk factors for poor surgical outcome are expressed in hazard ratio (H.R.) and were time of epilepsy (H.R.=4.2; 95% C.I.=.1.5-11.7; p=0.006), ictal EEG recruiting rhythm (H.R. = 2.9; 95% C.I. = 1.1-7.7; p=0.033); normal MRI (H.R. = 4.8; 95% C.I. = 1.4-16.6; p = 0.012), and MRI with lesion involving eloquent cortex (H.R. = 3.8; 95% C.I. = 1.2-12.0; p = 0.021). Based on these variables and using a logistic regression model we constructed a model that correctly predicted long-term surgical outcome in up to 80% of patients. Conclusion: Among independent risk factors for postsurgical seizure outcome, epilepsy duration is a potentially modifiable factor that could impact surgical outcome in FLE. Early diagnosis, presence of an MRI lesion not involving eloquent cortex, and ictal EEG without recruited rhythm independently predicted favorable outcome in this series. (C) 2011 Elsevier B.V. All rights reserved.

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

Cd8+ Tumour-infiltrating Lymphocytes And Cox2 Expression May Predict Relapse In Differentiated Thyroid Cancer.

There is an increasing rate of papillary thyroid carcinomas that may never progress to cause symptoms or death. Predicting outcome and determining tumour aggressiveness could help diminish the number of patients submitted to aggressive treatments. We aimed to evaluate whether markers of the immune system response and of tumour-associated inflammation could predict outcome of differentiated thyroid cancer (DTC) patients. Retrospective cohort study. We studied 399 consecutive patients, including 325 papillary and 74 follicular thyroid carcinomas. Immune cell markers were evaluated using immunohistochemistry, including tumour-associated macrophages (CD68) and subsets of tumour-infiltrating lymphocytes (TIL), such as CD3, CD4, CD8, CD16, CD20, CD45RO, GRANZYME B, CD69 and CD25. We also investigated the expression of cyclooxygenase 2 (COX2) in tumour cells and the presence of concurrent lymphocytic infiltration characterizing chronic thyroiditis. Concurrent lymphocytic infiltration characterizing chronic thyroiditis was observed in 29% of the cases. Among all the immunological parameters evaluated, only the enrichment of CD8+ lymphocytes (P = 0·001) and expression of COX2 (P =0·01) were associated with recurrence. A multivariate model analysis identified CD8+ TIL/COX2 as independent risk factor for recurrence. A multivariate analysis using Cox's proportional-hazards model adjusted for the presence of concurrent chronic thyroiditis demonstrated that the presence of concurrent chronic thyroiditis had no effect on prognostic prediction mediated by CD8+ TIL and COX2. In conclusion, we suggest the use of a relatively simple pathology tool to help select cases that may benefit of a more aggressive approach sparing the majority of patients from unnecessary procedures.

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.

A Randomized Trial of Sodium Fluoride (60 mg) ± Estrogen in Postmenopausal Osteoporotic Vertebral Fractures

Postmenopausal Caucasian women aged less than 80 years (n = 99) with one or more atraumatic vertebral fracture and no hip fractures, were treated by cyclical administration of enteric coated sodium fluoride (NaF) or no NaF for 27 months, with precautions to prevent excessive stimulation of bone turnover. In the first study 65 women, unexposed to estrogen (-E study), age 70.8 +/- 0.8 years (mean SEM) were all treated with calcium (Ca) 1.0-1.2 g daily and ergocalciferol (D) 0.25 mg per 25 kg once weekly and were randomly assigned to cyclical NaF (6 months on. 3 months off, initial dose 60 mg/day; group F CaD, n = 34) or no NaF (group CaD, n = 3 1). In the second study 34 patients. age 65.5 +/- 1.2 years, on hormone replacement therapy (E) at baseline, had this standardized, and were all treated with Ca and D and similarly randomized (FE CaD, n = 17, E CaD, n = 17) (+E study). The patients were stratified according to E status and subsequently assigned randomly to NaF. Seventy-five patients completed the trial. Both groups treated with NaF showed an increase in lumbar spinal density (by DXA) above baseline by 27 months: FE CaD + 16.2% and F CaD +9.3% (both p = 0.0001). In neither group CaD nor E CaD did lumbar spinal density increase. Peripheral bone loss occurred at most sites in the F CaD group at 27 months: tibia/fibula shaft -7.3% (p = 0.005); femoral shaft -7.1% (p = 0.004); distal forearm -4.0% (p = 0.004); total hip -4.1% (p = 0. 003); and femoral neck -3.5% (p = 0.006). No significant loss occurred in group FE CaD. Differences between the two NaF groups were greatest at the total hip at 27 months but were not significant [p < 0.05; in view of the multiple bone mineral density (BMD) sites, an alpha of 0.01 was employed to denote significance in BMD changes throughout this paper]. Using Cox's proportional hazards model, in the -E study there were significantly more patients with first fresh vertebral fractures in those treated with NaF than in those not so treated (RR = 24.2, p = 0.008, 95% CI 2.3-255). Patients developing first fresh fractures in the first 9 months were markedly different between groups: -23% of F CaD, 0 of CaD, 29% of FE CaD and 0 of E CaD. The incidence of incomplete (stress) fractures was similar in the two NaF-treated groups. Complete nonvertebral fractures did not occur in the two +E groups, there were no differences between groups F CaD and CaD. Baseline BMD (spine and femoral neck) was related to incident vertebral fractures in the control groups (no NaF), but not in the two NaF groups. Our results and a literature review indicate that fluoride salts. if used, should be at low dosage, with pretreatment and co-treatment with a bone resorption inhibitor.

Impact of number of vessels disease on outcome of patients with stable coronary artery disease: 5-year follow-up of the medical, angioplasty, and bypass surgery study (MASS)

Objective: To evaluate whether the number of vessels disease has an impact on clinical outcomes as well as on therapeutic results accordingly to medical, percutaneous, or surgery treatment in chronic coronary artery disease. Methods: We evaluated 825 individuals enrolled in MASS study, a randomized study to compare treatment options for single or multivessel coronary artery disease with preserved left ventricular function, prospectively followed during 5 years. The incidence of overall mortality and the composite end-point of death, myocardial infarction, and refractory angina were compared in three groups: single vessel disease (SVD n = 214), two-vessel disease (2VD n = 253) and three-vessel disease (3VD n = 358). The relationship between baseline variables and the composite end-point was assessed using a Cox proportional hazards survival model. Results: Most baseline characteristics were similar among groups, except age (younger in SVD and older in 3VD, p < 0.001), lower incidence of hypertension in SVD (p < 0.0001), and lower levels of total and LDL-cholesterol in 3VD (p = 0.004 and p = 0.005, respectively). There were no statistical differences in composite end-point in 5 years among groups independent of the kind of treatment; however, there was a higher mortality rate in 3VD (p < 0.001). When we stratified our analysis for each treatment option, bypass surgery was associated with a tower number of composite end-point in all groups (SVD p < 0.001, 2VD p = 0.002, 3VD p < 0.001). In multivariate analysis, we found higher mortality risk in 3VD comparing to SVD (p = 0.005, HR 3.14, 95%Cl 1.4-7.0). Conclusion: Three-vessel disease was associated with worse prognosis compared to single-or two-vessel disease in patients with stable coronary disease and preserved ventricular function at 5-year follow-up. In addition, event-free survival rates were higher after bypass surgery, independent of the number of vessels diseased in these subsets of patients. (c) 2008 European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved.

Glycemia and prognosis of patients with chronic heart failure-Subanalysis of the Long-term Prospective Randomized Controlled Study Using Repetitive Education at Six-Month Intervals and Monitoring for Adherence in Heart Failure Outpatients (REMADHE) trial

Background Heart failure and diabetes often occur simultaneously in patients, but the prognostic value of glycemia in chronic heart failure is debatable. We evaluated the role of glycemia on prognosis of heart failure. Methods Outpatients with chronic heart failure from the Long-term Prospective Randomized Controlled Study Using Repetitive Education at Six-Month Intervals and Monitoring for Adherence in Heart Failure Outpatients (REMADHE) trial were grouped according to the presence of diabetes and level of glycemia. All-cause mortality/heart transplantation and unplanned hospital admission were evaluated. Results Four hundred fifty-six patients were included (135 [29.5%] female, 124 [27.2%] with diabetes mellitus, age of w50.2 +/- 11.4 years, and left-ventricle ejection fraction of 34.7% +/- 10.5%). During follow-up (3.6 +/- 2.2 years), 27 (5.9%) patients were submitted to heart transplantation and 202 (44.2%) died; survival was similar in patients with and without diabetes mellitus. When patients with and without diabetes were categorized according to glucose range (glycemia <= 100 mg/dL [5.5 mmol/L]), as well as when distributed in quintiles of glucose, the survival was significantly worse among patients with lower levels of glycemia. This finding persisted in Cox proportional hazards regression model that included gender, etiology, left ventricle ejection fraction, left ventricle diastolic diameter, creatinine level and beta-blocker therapy, and functional status (hazard ratio 1.45, 95% CI 1.09-1.69, P = .039). No difference regarding unplanned hospital admission was found. Conclusion We report on an inverse association between glycemia and mortality in outpatients with chronic heart failure. These results point to a new pathophysiologic understanding of the interactions between diabetes mellitus, hyperglycemia, and heart disease. (Am Heart J 2010; 159: 90-7.)

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)

Risk Score to Predict the Outcome of Patients with Cerebral Vein and Dural Sinus Thrombosis

Background: Around 15% of patients die or become dependent after cerebral vein and dural sinus thrombosis (CVT). Method: We used the International Study on Cerebral Vein and Dural Sinus Thrombosis (ISCVT) sample (624 patients, with a median follow-up time of 478 days) to develop a Cox proportional hazards regression model to predict outcome, dichotomised by a modified Rankin Scale score > 2. From the model hazard ratios, a risk score was derived and a cut-off point selected. The model and the score were tested in 2 validation samples: (1) the prospective Cerebral Venous Thrombosis Portuguese Collaborative Study Group (VENO-PORT) sample with 91 patients; (2) a sample of 169 consecutive CVT patients admitted to 5 ISCVT centres after the end of the ISCVT recruitment period. Sensitivity, specificity, c statistics and overall efficiency to predict outcome at 6 months were calculated. Results: The model (hazard ratios: malignancy 4.53; coma 4.19; thrombosis of the deep venous system 3.03; mental status disturbance 2.18; male gender 1.60; intracranial haemorrhage 1.42) had overall efficiencies of 85.1, 84.4 and 90.0%, in the derivation sample and validation samples 1 and 2, respectively. Using the risk score (range from 0 to 9) with a cut-off of 6 3 points, overall efficiency was 85.4, 84.4 and 90.1% in the derivation sample and validation samples 1 and 2, respectively. Sensitivity and specificity in the combined samples were 96.1 and 13.6%, respectively. Conclusions: The CVT risk score has a good estimated overall rate of correct classifications in both validation samples, but its specificity is low. It can be used to avoid unnecessary or dangerous interventions in low-risk patients, and may help to identify high-risk CVT patients. Copyright (C) 2009 S. Karger AG, Basel

Optimal patch-leaving behaviour: a case study using the parasitoid Cotesia rubecular

1. Parasitoids are predicted to spend longer in patches with more hosts, but previous work on Cotesia rubecula (Marshall) has not upheld this prediction, Tests of theoretical predictions may be affected by the definition of patch leaving behaviour, which is often ambiguous. 2. In this study whole plants were considered as patches and assumed that wasps move within patches by means of walking or flying. Within-patch and between-patch flights were distinguished based on flight distance. The quality of this classification was tested statistically by examination of log-survivor curves of flight times. 3. Wasps remained longer in patches with higher host densities, which is consistent with predictions of the marginal value theorem (Charnov 1976). tinder the assumption that each flight indicates a patch departure, there is no relationship between host density and leaving tendency. 4. Oviposition influences the patch leaving behaviour of wasps in a count down fashion (Driessen et al. 1995), as predicted by an optimal foraging model (Tenhumberg, Keller & Possingham 2001). 5. Wasps spend significantly longer in the first patch encountered following release, resulting in an increased rate of superparasitism.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Clinical and economic impact of exercise electrocardiography and exercise echocardiography in clinical practice

Background Patients with known or suspected coronary disease are often investigated to facilitate risk assessment. We sought to examine the cost-effectiveness of strategies based on exercise echocardiography and exercise electrocardiography. Methods and results We studied 7656 patients undergoing exercise testing; of whom half underwent exercise echocardiography. Risk was defined with the Duke treadmill score for those undergoing exercise electrocardiography alone, and by the extent of ischaemia by exercise echocardiography. Cox proportional hazards models, risk adjusted for pretest likelihood of coronary artery disease, were used to estimate time to cardiac death or myocardial infarction. Costs (including diagnostic and revascularisation procedures, hospitalisations, and events) were calculated, inflation-corrected to year 2000 using Medicare trust fund rates and discounted at a rate of 5%. A decision model was employed to assess the marginal cost effectiveness (cost/life year saved) of exercise echo compared with exercise electrocardiography. Exercise echocardiography identified more patients as low-risk (51% vs 24%, p<0.001), and fewer as intermediate- (27% vs 51%, p<0.001) and high-risk (22% vs 4%); survival was greater in low- and intermediate- risk and less in high-risk patients. Although initial procedural costs and revascularisation costs (in intermediate- high risk patients) were greater, exercise echocardiography was associated with a greater incremental life expectancy (0.2 years) and a lower use of additional diagnostic procedures when compared with exercise electrocardiography (especially in lower risk patients). Using decision analysis, exercise echocardiography (Euro 2615/life year saved) was more cost effective than exercise electrocardiography. Conclusion Exercise echocardiography may enhance cost-effectiveness for the detection and management of at risk patients with known or suspected coronary disease. (C) 2003 Published by Elsevier Science Ltd on behalf of The European Society of Cardiology.