Observed Survival Times Research Articles

Cox models with time-varying covariates and partly-interval censoring-A maximum penalised likelihood approach.

Time-varying covariates can be important predictors when model based predictions are considered. A Cox model that includes time-varying covariates is usually referred to as an extended Cox model. When only right censoring is presented in the observed survival times, the conventional partial likelihood method is still applicable to estimate the regression coefficients of an extended Cox model. However, if there are interval-censored survival times, then the partial likelihood method is not directly available unless an imputation, such as the middle point imputation, is used to replaced the left- and interval-censored data. However, such imputation methods are well known for causing biases. This paper considers fitting of the extended Cox models using the maximum penalised likelihood method allowing observed survival times to be partly interval censored, where a penalty function is used to regularise the baseline hazard estimate. We present simulation studies to demonstrate the performance of our proposed method, and illustrate our method with applications to two real datasets from medical research.

Using three scenarios to explain life expectancy in advanced cancer: attitudes of patients, family members, and other healthcare professionals

AimTo evaluate a web-based tool for estimating and explaining three scenarios for expected survival time to people with advanced cancer (patients), their family members (FMs), and other healthcare professionals (HCPs).MethodsThirty-three oncologists estimated the “median survival of a group of similar patients” for patients seeking quantitative prognostic information. The web-based tool generated worst-case, most likely, and best-case scenarios for survival based on the oncologist’s estimate. Oncologists presented the scenarios to each patient and provided a printed summary to patients, FMs, and HCPs. Attitudes to the information were assessed by questionnaires. Observed survival for each patient was compared with the oncologist’s estimated survival and the three scenarios.ResultsPrognosis was discussed with 222 patients: median age 67 years; 61% male; most common primary sites pancreas 15%, non-small-cell lung 15%, and colorectal 12%. The median (range) for observed survival times was 9 months (0.5–43) and for oncologist’s estimated survival times was 12 months (2–96). Ninety-one percent of patients, 91% of FMs, and 84% of HCPs agreed that it was helpful having life expectancy explained as three scenarios. The majority (77%) of patients judged the information presented about their life expectancy to be the same or better than they had expected before the consultation. The survival estimates met a priori criteria for calibration, precision, and accuracy.ConclusionsPatients, FMs, and HCPs found it helpful to receive personalized prognostic information formatted as three scenarios for survival. It was feasible, acceptable, and safe to use a web-based resource to do this.

PARAMETRIC AND SEMI-PARAMETRIC SURVIVAL MODELS WITH APPLICATION TO HYPERTENSION DATA

Correlated survival data with possible censoring are frequently encountered in survival analysis.When there are dependencies among observed survival times, conventional Cox proportionalhazards model (CPHM) and Accelerated Failure Time (AFT) models that assumes independentresponses may not be appropriate. In this study, we compare the performance of parametric andsemi-parametric survival models with application to clinical data. Specifically, the AFT modeland the CPHM with and without Random effect were compared. Data on hypertension wascollected from Federal Medical Centre Keffi and General Hospital Nasarawa for the period offive years (2016 – 2020). The results from the analysis revealed that the Weibull AFT modelwith Gamma Random effect distribution had the least AIC and BIC values indicating that itoutperformed the other models considered in this study. Hence, the interpretation of the resultswas based on the most efficient model. Based on our results, it was found that hypertensionpatient that were giving drugs on the visit to the hospital has longer survival time compared tothose that were not giving drugs. Also, Hypertension patient with blood group AB and Obesedhave lesser survival time as compared to those with blood group o+ and normal weightrespectively. The study recommend that health expert can use the Weibull AFT model withGamma Random effect for predicting the risk factors of Hypertension especially when the dataare correlated.Keywords: AFT, CPHM, Hazard, Hypertension, Survival,

Penalized likelihood estimation of the proportional hazards model for survival data with interval censoring.

This paper considers the problem of semi-parametric proportional hazards model fitting where observed survival times contain event times and also interval, left and right censoring times. Although this is not a new topic, many existing methods suffer from poor computational performance. In this paper, we adopt a more versatile penalized likelihood method to estimate the baseline hazard and the regression coefficients simultaneously. The baseline hazard is approximated using basis functions such as M-splines. A penalty is introduced to regularize the baseline hazard estimate and also to ease dependence of the estimates on the knots of the basis functions. We propose a Newton-MI (multiplicative iterative) algorithm to fit this model. We also present novel asymptotic properties of our estimates, allowing for the possibility that some parameters of the approximate baseline hazard may lie on the parameter space boundary. Comparisons of our method against other similar approaches are made through an intensive simulation study. Results demonstrate that our method is very stable and encounters virtually no numerical issues. A real data application involving melanoma recurrence is presented and an R package 'survivalMPL' implementing the method is available on R CRAN.

Incorporating survival data into case-control studies with incident and prevalent cases.

Typically, case-control studies to estimate odds-ratios associating risk factors with disease incidence only include newly diagnosed cases. Recently proposed methods allow incorporating information on prevalent cases, individuals who survived from disease diagnosis to sampling, into cross-sectionally sampled case-control studies under parametric assumptions for the survival time after diagnosis. Here we propose and study methods to additionally use prospectively observed survival times from prevalent and incident cases to adjust logistic models for the time between diagnosis and sampling, the backward time, for prevalent cases. This adjustment yields unbiased odds-ratio estimates from case-control studies that include prevalent cases. We propose a computationally simple two-step generalized method-of-moments estimation procedure. First, we estimate the survival distribution assuming a semiparametric Cox model using an expectation-maximization algorithm that yields fully efficient estimates and accommodates left truncation for prevalent cases and right censoring. Then, we use the estimated survival distribution in an extension of the logistic model to three groups (controls, incident, and prevalent cases), to adjust for the survival bias in prevalent cases. In simulations, under modest amounts of censoring, odds-ratios from the two-step procedure were equally efficient as those estimated from a joint logistic and survival data likelihood under parametric assumptions. This indicates that utilizing the cases' prospective survival data lessens model dependencies and improves precision of association estimates for case-control studies with prevalent cases. We illustrate the methods by estimating associations between single nucleotide polymorphisms and breast cancer risk using controls, and incident and prevalent cases sampled from the US Radiologic Technologists Study cohort.

Survival analysis using a 5-step stratified testing and amalgamation routine (5-STAR) in randomized clinical trials.

Randomized clinical trials are often designed to assess whether a test treatment prolongs survival relative to a control treatment. Increased patient heterogeneity, while desirable for generalizability of results, can weaken the ability of common statistical approaches to detect treatment differences, potentially hampering the regulatory approval of safe and efficacious therapies. A novel solution to this problem is proposed. A list of baseline covariates that have the potential to be prognostic for survival under either treatment is pre-specified in the analysis plan. At the analysis stage, using all observed survival times but blinded to patient-level treatment assignment, "noise" covariates are removed with elastic net Cox regression. The shortened covariate list is used by a conditional inference tree algorithm to segment the heterogeneous trial population into subpopulations of prognostically homogeneous patients (risk strata). After patient-level treatment unblinding, a treatment comparison is done within each formed risk stratum and stratum-level results are combined for overall statistical inference. The impressive power-boosting performance of our proposed 5-step stratified testing and amalgamation routine (5-STAR), relative to that of the logrank test and other common approaches that do not leverage inherently structured patient heterogeneity, is illustrated using a hypothetical and two real datasets along with simulation results. Furthermore, the importance of reporting stratum-level comparative treatment effects (time ratios from accelerated failure time model fits in conjunction with model averaging and, as needed, hazard ratios from Cox proportional hazard model fits) is highlighted as a potential enabler of personalized medicine. An R package is available at https://github.com/rmarceauwest/fiveSTAR.

Comparison of disease progression subgroups in idiopathic pulmonary fibrosis

BackgroundIdiopathic pulmonary fibrosis (IPF) is a progressive interstitial pneumonia with an unpredictable course. The aims of this study were to retrospectively re-evaluate a cohort of patients with IPF according to the 2011 international IPF guidelines and 1) to characterize the subgroups of patients when classified according to their observed survival times and 2) to evaluate whether Composite Physiologic Index (CPI), Gender-Age-Physiology (GAP) Index or clinical variables could predict mortality.MethodsRetrospective data was collected and patients were classified into subgroups according to their observed lifespans. Differences in clinical variables, CPI and GAP stages as well as in comorbidities were investigated between the subgroups. Predictors of mortality were identified by COX proportional hazard analyses.ResultsA total of 132 patients were included in this study. The disease course was rapid (≤ 2 years) in 30.0%, moderate (2–5 years) in 28.0% and slow (≥ 5 years) in 29.0% of the patients. Pulmonary function tests (PFT) and CPI at baseline differentiated significantly between the rapid disease course group and those patients with longer survival times. However, the predictive accuracy of the investigated clinical variables was mainly less than 0.80. The proportions of patients with comorbidities did not differ between the subgroups, but more patients with a rapid disease course were diagnosed with heart failure after the diagnosis of IPF. Most patients with a rapid disease course were categorized in GAP stages I and II, but all patients in GAP stage III had a rapid disease course. The best predictive multivariable model included age, gender and CPI. GAP staging had slightly better accuracy (0.67) than CPI (0.64) in predicting 2-year mortality.ConclusionsAlthough the patients with a rapid disease course could be differentiated at baseline in terms of PFT and CPI, the predictive accuracy of any single clinical variable as well as CPI and GAP remained low. GAP staging was unable to identify the majority of patients with a rapid disease progression. It is challenging to predict disease progression and mortality in IPF even with risk prediction models.

Estimators of quantile difference between two samples with length-biased and right-censored data

In this paper, the difference between the quantiles of two samples is investigated. One sample comes from a prevalent cohort with a stable incidence rate. Then, the observed survival times are length-biased and right-censored data. Another sample is drawn from an incident cohort study with right-censored data. We estimate the quantile difference based on different estimating equations. That is because the estimating equation estimators have higher efficiency than the difference of two one-sample quantile estimators in the sense of minimizing the mean squared error. Moreover, the consistency and asymptotic normality of these estimators are established. Then, the confidence intervals of quantile difference can be constructed by using the normal approximations. Finally, the performance of the proposed methods is presented in the numerical studies, especially with small sample sizes.

A Bayesian CUSUM plot: Diagnosing quality of treatment.

To present a CUSUM plot based on Bayesian diagnostic reasoning displaying evidence in favour of "healthy" rather than "sick" quality of treatment (QOT), and to demonstrate a technique using Kaplan-Meier survival curves permitting application to case series with ongoing follow-up. For a case series with known final outcomes: Consider each case a diagnostic test of good versus poor QOT (expected vs. increased failure rates), determine the likelihood ratio (LR) of the observed outcome, convert LR to weight taking log to base 2, and add up weights sequentially in a plot showing how many times odds in favour of good QOT have been doubled. For a series with observed survival times and an expected survival curve: Divide the curve into time intervals, determine "healthy" and specify "sick" risks of failure in each interval, construct a "sick" survival curve, determine the LR of survival or failure at the given observation times, convert to weights, and add up. The Bayesian plot was applied retrospectively to 39 children with acute lymphoblastic leukaemia with completed follow-up, using Nordic collaborative results as reference, showing equal odds between good and poor QOT. In the ongoing treatment trial, with 22 of 37 children still at risk for event, QOT has been monitored with average survival curves as reference, odds so far favoring good QOT 2:1. QOT in small patient series can be assessed with a Bayesian CUSUM plot, retrospectively when all treatment outcomes are known, but also in ongoing series with unfinished follow-up.

A change-point model for detecting heterogeneity in ordered survival responses.

In this article, we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time-to-event variables. The survival responses need to be ordered according to a numerical covariate. Our estimation method will aim at detecting heterogeneity that could arise through the ordering covariate. We formally introduce our model as a constrained Hidden Markov Model, where the hidden states are the unknown segmentation (breakpoint locations) and the observed states are the survival responses. We derive an efficient Expectation-Maximization framework for maximizing the likelihood of this model for a wide range of baseline hazard forms (parametrics or nonparametric). The posterior distribution of the breakpoints is also derived, and the selection of the number of segments using penalized likelihood criterion is discussed. The performance of our survival breakpoint model is finally illustrated on a diabetes dataset where the observed survival times are ordered according to the calendar time of disease onset.

Validation of a Prognostic Staging for Metastatic Uveal Melanoma: A Collaborative Study of the European Ophthalmic Oncology Group

To validate a staging system for metastatic uveal melanoma that will facilitate planning, reporting, and interpreting the results of clinical trials. Reliability and validity study. The performance index, the largest diameter of the largest metastasis and alkaline phosphatase level at the time of diagnosis of metastases, and overall survival of 249 patients from 7 ocular oncology centers who died of dissemination were analyzed. Predicted median survival time calculated according to the Helsinki University Hospital Working Formulation was used to assign patients to stages IVa, IVb, and IVc, which correspond to predicted survival times of ≥12, <12-6, and <6months, respectively. The predictions were compared against observed survival. The 3 variables used to assign stage were independent predictors of survival in the validation dataset. Of the 249 patients, 110 (44%), 109 (44%), and 30 (12%) were classified to Working Formulation stages IVa, IVb, and IVc, respectively. Corresponding median observed survival times were 18.6, 10.7, and 4.6months and worsened by increasing stage (P < .001). Of 201 patients managed without surgical resection of metastases, 83 (41%), 89 (44%), and 29 (15%) were classified to stages IVa, IVb, and IVc, respectively, and their median observed survival times were 17.2, 10.0, and 4.6months (P < .001). Survival of 47 patients who underwent resection did not differ by working formulation stage (P= .69). This multicenter study confirms that the Working Formulation is a reliable and valid,repeatable system for dividing metastatic uveal melanoma into distinct prognostic subgroups, especially for stage-specific reporting of survival in prospective clinical trials.

Bayesian variable selection and modelling for metastatic breast cancer data

A Bayesian model selection procedure is applied to data on 90 women with metastatic breast cancer. Protein covariates are measured on nucleus, cytoplasm, membrane, and stroma of primary breast carcinoma and lymph node metastasis tissue. Multiple imputation is performed to deal with missing data. Zellner's g-prior is used in the Bayesian variable selection procedure. The model space is reduced using posterior variable inclusion probabilities, and then posterior model probabilities are used to derive a candidate set of models. Bayesian model averaging is employed to robustly estimate survival time, and the goodness of fit of the derived model assessed by the correlation between estimated and observed survival times. The results show evidence of proteins having different rules in different parts of the tissue cell with respect to patient survival. Therefore, a recommendation is given on which part of the cell to observe certain proteins for prognosis. The models obtained are robust toward censoring and showed correlations between the observed and the predicted data between 0.7 and 0.84. References J. Adams, P. J. Carder, S. Downey, M. A. Forbes, K. MacLennan, V. Allgar, S. Kaufman, S. Hallam, R. Bicknell, J. J. Walker, F. Cairnduff, P. J. Selby, T. J. Perren, M. Lansdown, and R. E. Banks. Vascular endothelial growth factor (VEGF) in breast cancer: comparison of plasma, serum, and tissue VEGF and microvessel density and effects of tamoxifen. Cancer Res., 60(11):2898–2905, 2000. http://cancerres.aacrjournals.org/content/60/11/2898 . F. Bray, J.-S. Ren, E. Masuyer, and J. Ferlay. Global estimates of cancer prevalence for 27 sites in the adult population in 2008. Int. J. Cancer, 132(5):1133–1145, 2013. doi:10.1002/ijc.27711 . M. Clyde and E. I. George. Model uncertainty. Stat. Sci., 19(1):81–94, 2004. http://projecteuclid.org/download/pdfview_1/euclid.ss/1089808274 . A. R. T. Donders, G. J. M. G. van der Heijden, T. Stijnen, and K. G. M. Moons. Review: a gentle introduction to imputation of missing values. J. Clin. Epidemiol., 59(10):1087–1091, 2006. doi:10.1016/j.jclinepi.2006.01.014 . J. Ferlay, I. Soerjomataram, D. F. M. Ervik, F. Bray, R. Dikshit, S. Elser, C. Mathers, M. Rebelo, and D. M. Parkin. GLOBOCAN 2012: Estimated cancer incidence, mortality and prevalence worldwide in 2012. International Agency for Research on Cancer, World Health Organization, 2014. http://globocan.iarc.fr . E. I. George and R. E. McCulloch. Variable selection via Gibbs sampling. J. Am. Stat. Assoc., 88(423):881–889, 1993. doi:10.1080/01621459.1993.10476353 . E. I. George and R. E. McCulloch. Approaches for Bayesian variable selection. Stat. Sinica, 7(2):339–373, 1997. http://www3.stat.sinica.edu.tw/statistica/j7n2/j7n26/j7n26.htm . J. Geweke. Variable selection and model comparison in regression, volume 5 of Bayesian statistics, pages 609–620. Oxford University Press, 1996. J. A. Hoeting, D. Madigan, A. E. Raftery, and C. T. Volinsky. Bayesian model averaging: a tutorial. Stat. Sci., 14(4):382–401, 1999. http://www.jstor.org/stable/2676803 . D. G. Kleinbaum and M. Klein. Survival Analysis: A self-learning text. Statistics for Biology and Health. New York, Springer-Verlag, 2011. doi:10.1007/0-387-29150-4 . E. E. Leamer. Regression selection strategies and revealed priors. J. Am. Stat. Assoc., 73(363):580–587, 1978. doi:10.1080/01621459.1978.10480058 . E. E. Leamer. Specification searches: Ad hoc inference with nonexperimental data. Wiley New York, 1978. S. Mallett, P. Royston, R. Waters, S. Dutton, and D. G. Altman. Reporting performance of prognostic models in cancer: a review. BMC Med., 8(1):21, 2010. doi:10.1186/1741-7015-8-21 . H. C. McCosker. Prognostic significance of IGF and ECM induced signalling proteins in breast cancer patients. PhD thesis, School of Biomedical Sciences, QUT, 2012. http://eprints.qut.edu.au/53580/ . T. J. Mitchell and J. J. Beauchamp. Bayesian variable selection in linear regression. J. Am. Stat. Assoc., 83(404):1023–1032, 1988. doi:10.1080/01621459.1988.10478694 . K. Pantel and R. H. Brakenhoff. Dissecting the metastatic cascade. Nat. Rev. Cancer, 4(6):448–456, 2004. doi:10.1038/nrc1370 . R. Radpour, Z. Barekati, C. Kohler, W. Holzgreve, and X. Y. Zhong. New trends in molecular biomarker discovery for breast cancer. Genet. Test. Mol. Bioma., 13(5):565–571, 2009. doi:10.1089/gtmb.2009.0060 . A. E. Raftery, D. Madigan, and J. A. Hoeting. Bayesian model averaging for linear regression models. J. Am. Stat. Assoc., 92(437):179–191, 1997. doi:10.1080/01621459.1997.10473615 . A. Zellner. On assessing prior distributions and Bayesian regression analysis with g-prior distributions, volume 6 of Bayesian inference and decision techniques: Essays in Honor of Bruno De Finetti, pages 233–243. North-Holland, Amsterdam, The Netherlands, 1986. A. Zellner. An introduction to Bayesian inference in econometrics. New York: John Wiley and Sons, 1996.

A stochastic frontier approach to survival analysis

In spite of the best set of covariates and statistical tools for the survival analysis, there are instances when experts do not rule out the existence of many non-observable factors that could influence the survival probability of an individual. The fact that every human body, sick or otherwise, strives to maximize time to death, renders the stochastic frontier analysis (vide 2) as a meaningful tool to measure the unobservable individual-specific deficiency factor that accounts for the difference between the optimal and observed survival times. In this paper, given the survival data, an attempt is made to measure the deficiency factor for each individual in the data on adopting the stochastic frontier analysis. Such an attempt to quantify the effect of these unobservable factors can provide ample scope for further research in bio-medical studies. The utility of these estimates in the survival analysis is also highlighted using a real-life data.

The importance of adjusting for treatment crossover bias in oncology clinical trials: An analysis of the EGF104900 trial in metastatic breast cancer (mBC).

636 Background: EGF104900 is a phase III trial in mBC that compared lapatinib + trastuzumab (LAPTRZ, n=146) with LAP monotherapy (LAP, n=145). The trial allowed LAP subjects to switch to LAPTRZ on documented disease progression (following ≥4 weeks of LAP). Conventional intent-to-treat (ITT) analysis does not control for potential bias due to treatment crossover. The Rank Preserving Structural Failure Time Model (RPSFTM) estimates event times had patients not switched, and performs re-censoring. The approach preserves randomization and ordering of patients’ observed survival times, assuming that patients switching benefit from the treatment effect seen in those initially randomized to the treatment arm. The method is recognized by NICE, UK, as an appropriate method for adjusting for crossover bias. Methods: 53% of LAP subjects crossed over to LAPTRZ. Analyses were stratified by hormone receptor status and visceral/non-visceral disease. RPSFTM was implemented in Stata (using White’s strbee procedure). Absolute overall survival (OS) was estimated using a parametric survival distribution fitted to the trial data with/without crossover adjustment. The unadjusted ITT Cox hazard ratio (HR) was compared with the crossover adjusted RPSFTM estimate, and the absolute gain in OS evaluated. Results: Median OS in the LAPTRZ and LAP arms was 61 and 41 weeks, respectively (ITT HR 0.74, 95% CI: 0.56, 0.96); RPSFTM crossover-adjusted median OS for LAP was 32 weeks (RPSFTM HR 0.52; 95% CI: 0.29, 0.92). Mean OS for LAPTRZ was estimated under a Weibull distribution as 74 weeks, compared with 57 (ITT) and 44 (RPSFTM) weeks for LAP. Treatment with LAPTRZ was estimated to extend mean OS by 30 weeks controlling for treatment crossover using RPSFTM compared with 17 weeks by ITT. Conclusions: Oncology trials are often subject to treatment crossover. Controlling for potential treatment crossover bias can result in greater estimates of gain in OS compared with ITT analysis. In the context of mBC such differences are of great importance to patients, clinicians, and healthcare payers. Treatment crossover-analyses are therefore also important for estimating cost-effectiveness in oncology.

Analysis of diabetic retinopathy data using shared inverse Gaussian frailty model

The dependence between individuals in a group is modeled by the group specific quantity, which can be interpreted as an unobserved covariates or “frailties” common to the individuals in the group and assumed to follow some distribution. We consider the shared frailty model in the frame work of parametric Cox proportional hazard model. The Cox regression model with the shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing life time data. In this paper, we consider shared inverse Gaussian frailty model with bivariate exponential of Marshall-Olkin [20] distribution as baseline hazard for bivariate survival times. We fit the model to the real life bivariate survival data set of diabetic retinopathy data. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty for diabetic retinopathy data is the interest of this paper. Also, we carried out a test for independence using information criteria.

Composite Partial Likelihood Estimation Under Length-Biased Sampling, With Application to a Prevalent Cohort Study of Dementia

The Canadian Study of Health and Aging (CSHA) employed a prevalent cohort design to study survival after onset of dementia, where patients with dementia were sampled and the onset time of dementia was determined retrospectively. The prevalent cohort sampling scheme favors individuals who survive longer. Thus, the observed survival times are subject to length bias. In recent years, there has been a rising interest in developing estimation procedures for prevalent cohort survival data that not only account for length bias but also actually exploit the incidence distribution of the disease to improve efficiency. This article considers semiparametric estimation of the Cox model for the time from dementia onset to death under a stationarity assumption with respect to the disease incidence. Under the stationarity condition, the semiparametric maximum likelihood estimation is expected to be fully efficient yet difficult to perform for statistical practitioners, as the likelihood depends on the baseline hazard function in a complicated way. Moreover, the asymptotic properties of the semiparametric maximum likelihood estimator are not well-studied. Motivated by the composite likelihood method (Besag 1974), we develop a composite partial likelihood method that retains the simplicity of the popular partial likelihood estimator and can be easily performed using standard statistical software. When applied to the CSHA data, the proposed method estimates a significant difference in survival between the vascular dementia group and the possible Alzheimer's disease group, while the partial likelihood method for left-truncated and right-censored data yields a greater standard error and a 95% confidence interval covering 0, thus highlighting the practical value of employing a more efficient methodology. To check the assumption of stable disease for the CSHA data, we also present new graphical and numerical tests in the article. The R code used to obtain the maximum composite partial likelihood estimator for the CSHA data is available in the online Supplementary Material, posted on the journal web site.

Usefulness of medical oncologists’ estimates of survival time in people with advanced cancer.

9087 Background: We sought to determine the calibration, precision, prognostic significance and suitability of estimated survival time (EST) as a basis for estimating and explaining prognosis in advanced cancer. Methods: Medical oncologists recorded their EST as the “median survival of a group of identical patients” in patients with advanced cancer and a life expectancy &gt;3 months recruited to a randomized trial of sertraline (Lancet Oncol 2007; 8: 603). Calibration, precision and suitability were defined by the proportions of patients whose observed survival times (OST) were bounded by simple multiples of their EST (based on our previous studies), i.e. 50% expected to live longer (or shorter) than their EST; 30% expected to live from 0.75 to 1.33 times their EST (arbitrary criterion for precision); 50% expected to live from half to double their EST (range for typical scenario); 10% expected to live &gt;3 times their EST (best case scenario), or &lt;¼ of their EST (worst case scenario). Results: Characteristics of the 114 patients were: median age 63 years, Karnofsky performance status (KPS) ≤70 in 25%, and a median of 8.5 months since diagnosis of advanced cancer. Primary cancer sites included breast (18%), colorectal (16%), lung (15%), prostate (12%) and ovary (10%). Median survival was 10.6 months after a median follow-up of 14 months and 68 deaths. EST were well-calibrated: 54% of patients lived longer than their EST and 46% lived shorter than their EST. EST were imprecise (21% within 0.75 to 1.33 times OST) but equally likely to be over-optimistic (34% &gt;1.33 x OST) or over-pessimistic (39% &lt;0.75 x OST). 6% of patients lived &lt;¼ of their EST; 62% lived from half to double their EST and 9% lived &gt;3 times their EST. Independently significant predictors of OST in a multivariable Cox model included EST (HR=0.92, p=0.004), dry mouth (HR=5.07, p&lt;0.0001), alkaline phosphatase &gt;101U/L (HR=2.80, p=0.0002), KPS ≤70 (HR=2.30, p=0.007), prostate primary (HR=0.23, p=0.002), and steroid use (HR=2.35, p=0.02). Conclusions: Medicaloncologists’ EST were well-calibrated, imprecise, independently associated with OST, and useful for estimating and explaining best case, worse case, and typical scenarios for survival time in patients with advanced cancer.

Semiparametric estimation in copula models for bivariate sequential survival times

Sequentially observed survival times are of interest in many studies but there are difficulties in analyzing such data using nonparametric or semiparametric methods. First, when the duration of followup is limited and the times for a given individual are not independent, induced dependent censoring arises for the second and subsequent survival times. Non-identifiability of the marginal survival distributions for second and later times is another issue, since they are observable only if preceding survival times for an individual are uncensored. In addition, in some studies a significant proportion of individuals may never have the first event. Fully parametric models can deal with these features, but robustness is a concern. We introduce a new approach to address these issues. We model the joint distribution of the successive survival times by using copula functions, and provide semiparametric estimation procedures in which copula parameters are estimated without parametric assumptions on the marginal distributions. This provides more robust estimates and checks on the fit of parametric models. The methodology is applied to a motivating example involving relapse and survival following colon cancer treatment.

Prolongation of Rat Intestinal Allograft Survival by Administration of Triptolide-Modified Donor Bone Marrow-Derived Dendritic Cells

Severe graft rejection remains an important obstacle in intestinal transplantation. In this study, dendritic cells (DCs) isolated from rat bone marrow were cultured for 5 days, and triptolide applied for 3 more days. The recipient rats were pretreated with donor triptolide-modified or not modified DC. Small bowel transplantation was performed to observed survival times. We demonstrated that triptolide markedly inhibited both the expression of CD80 and MHCII expression on DCs. Triptolide-modified DCs stimulated lower proliferative responses among allogeneic T cells, prolonging the survival of intestinal allografts in rats. These results suggested that pretreatment with triptolide-modified DC prolonged the survival of rat small bowel allografts after transplantation.

Validating the Helsinki University Central Hospital (HUCH) working formulation for staging metastatic uveal melanoma

Abstract Purpose: To validate the Helsinki University Central Hospital (HUCH) Working Formulation, the first substaging system designed to predict prognosis of metastatic uveal melanoma and to facilitate design, reporting and interpretation of controlled clinical trials. Methods: Data of 226 patients who died of disseminated uveal melanoma were collected from members of the European Ophthalmic Oncology Group (OOG). Karnofsky or WHO performance status, largest diameter of largest metastasis and serum alkaline phosphatase (AP) level at diagnosis of metastases, and time to death were requested. The working formulation is based on a multivariate model that identified these variables as independent predictors of survival, modeling time on chemotherapy as a confounding variable (Eskelin et al. Cancer 2003; 97: 65–75). Patients whose predicted survival was less than 6 months were assigned to stage IVc, between 6 and 12 months to stage IVb and over 12 months to stage IVa. Observed survival time was calculated for each stage. Results: The median AP level was 0.69 (range, 0.24‐11) times upper normal limit, median largest metastasis was 3.5 cm (range, 0.8‐19), and percentage of patients representing WHO performance index 0, 1‐2 and 3 was 61%, 38% and 1%, respectively. Of the 226 patients, 100 (44%) were assigned to stage IVa, 97 (43%) to IVb and 29 (13%) to IVc. The median observed survival times were 18.3, 10.0 and 4.6 months, respectively. In Kaplan‐Meier analysis, the stages reflected best to worst survival (P&lt;0.0001, log‐rank test for trend). Conclusions: The collaborative OOG study confirms the HUCH Working Formulation as a repeatable, valid system for dividing patients with metastatic uveal melanoma into groups of differing prognosis.