Impact of the model-building strategy on inference about nonlinear and time-dependent covariate effects in survival analysis

Temporal effect of imatinib adherence on time to remission in chronic myeloid leukemia patients

INTRODUCTION

Adherence to imatinib in chronic myeloid leukemia (CML) patients is estimated to be as low as 70% despite its clinical benefit, and our understanding of the impact of nonadherence in this population is limited. This study presents a novel application of the Alternating Conditional Estimation (ACE) algorithm in newly diagnosed CML patients to map the full dose-response curve (DRC) and determine how the strength of this curve varies over time.

METHODS

We applied the ACE algorithm alongside a backward elimination procedure to detect the presence of time dependence and nonlinearity in the relationship between imatinib adherence and time-to-remission. An extended Cox model allowing for the flexible modeling of identified effects via unpenalized B-splines was subsequently fit and assessed.

RESULTS

The substantial improvement in model fit associated with the extended Cox approach suggests that traditional Cox proportional hazards model assumptions do not hold in this setting. Results indicate that the DRC for imatinib is non-linearly increasing, with an attenuated effect above a 74% adherence rate. The strength of this effect on remission varied over time and was strongest in the initial months of treatment, reaching a peak around 90 days post-initiation (log hazard ratio: 2.12, 95% confidence interval: 1.47 to 2.66).

CONCLUSION

Most patients that achieved remission did so by 4 months (120 days) with consistently high adherence, suggesting that this could be a critical time and duration for realizing treatment benefit and patient monitoring. Findings regarding the relationship between adherence and remission can additionally help guide the design of future studies.

Comparison of Different Modeling Approaches for Prescription Opioid Use and Its Association With Adverse Events

Previous research linking opioid prescribing to adverse drug events has failed to properly account for the time-varying nature of opioid exposure. This study aimed to explore how the risk of opioid-related emergency department visits, readmissions, or deaths (composite outcome) varies with opioid dose and duration, comparing different novel modeling techniques. A prospective cohort of 1,511 hospitalized patients discharged from 2 McGill-affiliated hospitals in Montreal, 2014-2016, was followed from the first postdischarge opioid dispensation until 1 year after discharge. Marginal structural Cox proportional hazards models and their flexible extensions were used to explore the association between time-varying opioid use and the composite outcome. Weighted cumulative exposure models assessed cumulative effects of past use and explored how its impact depends on the recency of exposure. The patient mean age was 69.6 (standard deviation = 14.9) years; 57.7% were male. In marginal structural model analyses, current opioid use was associated with a 71% increase in the hazard of opioid-related adverse events (adjusted hazard ratio = 1.71, 95% confidence interval: 1.21, 2.43). The weighted cumulative exposure results suggested that the risk cumulates over the previous 50 days of opioid consumption. Flexible modeling techniques helped assess how the risk of opioid-related adverse events may be associated with time-varying opioid exposures while accounting for nonlinear relationships and the recency of past use.

Partially linear Bayesian modeling of longitudinal rank and time-to-event data using accelerated failure time model with application to brain tumor data

Joint modeling of longitudinal rank and time-to-event data with random effects model using a Bayesian approach is presented. Accelerated failure time (AFT) models can be used for the analysis of time-to-event data to estimate the effects of covariates on acceleration/deceleration of the survival time. The parametric AFT models require determining the event time distribution. So, we suppose that the time variable is modeled with Weibull AFT distribution. In many real-life applications, it is difficult to determine the appropriate distribution. To avoid this restriction, several semiparametric AFT models were proposed, containing spline-based model. So, we propose a flexible extension of the accelerated failure time model. Furthermore, the usual joint linear model, a joint partially linear model, is also considered containing the nonlinear effect of time on the longitudinal rank responses and nonlinear and time-dependent effects of covariates on the hazard. Also, a Bayesian approach that yields Bayesian estimates of the model's parameters is used. Some simulation studies are conducted to estimate parameters of the considered models. The model is applied to a real brain tumor patient's data set that underwent surgery. The results of analyzing data are presented to represent the method.

Using fractional polynomials and restricted cubic splines to model non-proportional hazards or time-varying covariate effects in the Cox regression model

The Cox proportional hazards model is used extensively in clinical and epidemiological research. A key assumption of this model is that of proportional hazards. A variable satisfies the proportional hazards assumption if the effect of that variable on the hazard function is constant over time. When the proportional hazards assumption is violated for a given variable, a common approach is to modify the model so that the regression coefficient associated with the given variable is assumed to be a linear function of time (or of log‐time), rather than being constant or fixed. However, this is an unnecessarily restrictive assumption. We describe two different methods to allow a regression coefficient, and thus the hazard ratio, in a Cox model to vary as a flexible function of time. These methods use either fractional polynomials or restricted cubic splines to model the log‐hazard ratio as a function of time. We illustrate the utility of these methods using data on 12 705 patients who presented to a hospital emergency department with a primary diagnosis of heart failure. We used a Cox model to assess the association between elevated cardiac troponin at presentation and the hazard of death after adjustment for an extensive set of covariates. SAS code for implementing the restricted cubic spline approach is provided, while an existing Stata function allows for the use of fractional polynomials.

Flexible extension of the accelerated failure time model to account for nonlinear and time-dependent effects of covariates on the hazard

The accelerated failure time model is an alternative to the Cox proportional hazards model in survival analysis. However, conclusions regarding the associations of prognostic factors with event times are valid only if the underlying modeling assumptions are met. In contrast to several flexible methods for relaxing the proportional hazards and linearity assumptions in the Cox model, formal investigation of the constant-over-time time ratio and linearity assumptions in the accelerated failure time model has been limited. Yet, in practice, prognostic factors may have time-dependent and/or nonlinear effects. Furthermore, parametric accelerated failure time models require correct specification of the baseline hazard function, which is treated as a nuisance parameter in the Cox proportional hazards model, and is rarely known in practice. To address these challenges, we propose a flexible extension of the accelerated failure time model where unpenalized regression B-splines are used to model (i) the baseline hazard function of arbitrary shape, (ii) the time-dependent covariate effects on the hazard, and (iii) nonlinear effects for continuous covariates. Simulations evaluate the accuracy of the time-dependent and/or nonlinear estimates, and of the resulting survival functions, in multivariable settings. The proposed flexible extension of the accelerated failure time model is applied to re-assess the effects of prognostic factors on mortality after septic shock.

Analysis of time-to-event for observational studies: Guidance to the use of intensity models

This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time-dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.

Nurse staffing practices and adverse events in acute care hospitals: The research protocol of a multisite patient-level longitudinal study

Aims

We describe an innovative research protocol to: (a) examine patient‐level longitudinal associations between nurse staffing practices and the risk of adverse events in acute care hospitals and; (b) determine possible thresholds for safe nurse staffing.

Design

A dynamic cohort of adult medical, surgical and intensive care unit patients admitted to 16 hospitals in Quebec (Canada) between January 2015–December 2019.

Methods

Patients in the cohort will be followed from admission until 30‐day postdischarge to assess exposure to selected nurse staffing practices in relation to the subsequent occurrence of adverse events. Five staffing practices will be measured for each shift of an hospitalization episode, using electronic payroll data, with the following time‐varying indicators: (a) nursing worked hours per patient; (b) skill mix; (c) overtime use; (d) education mix and; and (e) experience. Four high‐impact adverse events, presumably associated with nurse staffing practices, will be measured from electronic health record data retrieved at the participating sites: (a) failure‐to‐rescue; (b) in‐hospital falls; (c) hospital‐acquired pneumonia and; and (d) venous thromboembolism. To examine the associations between the selected nurse staffing exposures and the risk of each adverse event, separate multivariable Cox proportional hazards frailty regression models will be fitted, while adjusting for patient, nursing unit and hospital characteristics, and for clustering. To assess for possible staffing thresholds, flexible non‐linear spline functions will be fitted. Funding for the study began in October 2019 and research ethics/institutional approval was granted in February 2020.

Discussion

To our knowledge, this study is the first multisite patient‐level longitudinal investigation of the associations between common nurse staffing practices and the risk of adverse events. It is hoped that our results will assist hospital managers in making the most effective use of the scarce nursing resources and in identifying staffing practices that minimize the occurrence of adverse events.

Prediction of cancer survival for cohorts of patients most recently diagnosed using multi-model inference

Despite a large choice of models, functional forms and types of effects, the selection of excess hazard models for prediction of population cancer survival is not widespread in the literature. We propose multi-model inference based on excess hazard model(s) selected using Akaike information criteria or Bayesian information criteria for prediction and projection of cancer survival. We evaluate the properties of this approach using empirical data of patients diagnosed with breast, colon or lung cancer in 1990-2011. We artificially censor the data on 31 December 2010 and predict five-year survival for the 2010 and 2011 cohorts. We compare these predictions to the observed five-year cohort estimates of cancer survival and contrast them to predictions from an a priori selected simple model, and from the period approach. We illustrate the approach by replicating it for cohorts of patients for which stage at diagnosis and other important prognosis factors are available. We find that model-averaged predictions and projections of survival have close to minimal differences with the Pohar-Perme estimation of survival in many instances, particularly in subgroups of the population. Advantages of information-criterion based model selection include (i) transparent model-building strategy, (ii) accounting for model selection uncertainty, (iii) no a priori assumption for effects, and (iv) projections for patients outside of the sample.

How are missing data in covariates handled in observational time-to-event studies in oncology? A systematic review

Background

Missing data in covariates can result in biased estimates and loss of power to detect associations. It can also lead to other challenges in time-to-event analyses including the handling of time-varying effects of covariates, selection of covariates and their flexible modelling. This review aims to describe how researchers approach time-to-event analyses with missing data.

Methods

Medline and Embase were searched for observational time-to-event studies in oncology published from January 2012 to January 2018. The review focused on proportional hazards models or extended Cox models. We investigated the extent and reporting of missing data and how it was addressed in the analysis. Covariate modelling and selection, and assessment of the proportional hazards assumption were also investigated, alongside the treatment of missing data in these procedures.

Results

148 studies were included. The mean proportion of individuals with missingness in any covariate was 32%. 53% of studies used complete-case analysis, and 22% used multiple imputation. In total, 14% of studies stated an assumption concerning missing data and only 34% stated missingness as a limitation. The proportional hazards assumption was checked in 28% of studies, of which, 17% did not state the assessment method. 58% of 144 multivariable models stated their covariate selection procedure with use of a pre-selected set of covariates being the most popular followed by stepwise methods and univariable analyses. Of 69 studies that included continuous covariates, 81% did not assess the appropriateness of the functional form.

Conclusion

While guidelines for handling missing data in epidemiological studies are in place, this review indicates that few report implementing recommendations in practice. Although missing data are present in many studies, we found that few state clearly how they handled it or the assumptions they have made. Easy-to-implement but potentially biased approaches such as complete-case analysis are most commonly used despite these relying on strong assumptions and where often more appropriate methods should be employed. Authors should be encouraged to follow existing guidelines to address missing data, and increased levels of expectation from journals and editors could be used to improve practice.

Automatic variable selection for exposure-driven propensity score matching with unmeasured confounders

Multivariable model building for propensity score modeling approaches is challenging. A common propensity score approach is exposure-driven propensity score matching, where the best model selection strategy is still unclear. In particular, the situation may require variable selection, while it is still unclear if variables included in the propensity score should be associated with the exposure and the outcome, with either the exposure or the outcome, with at least the exposure or with at least the outcome. Unmeasured confounders, complex correlation structures, and non-normal covariate distributions further complicate matters. We consider the performance of different modeling strategies in a simulation design with a complex but realistic structure and effects on a binary outcome. We compare the strategies in terms of bias and variance in estimated marginal exposure effects. Considering the bias in estimated marginal exposure effects, the most reliable results for estimating the propensity score are obtained by selecting variables related to the exposure. On average this results in the least bias and does not greatly increase variances. Although our results cannot be generalized, this provides a counterexample to existing recommendations in the literature based on simple simulation settings. This highlights that recommendations obtained in simple simulation settings cannot always be generalized to more complex, but realistic settings and that more complex simulation studies are needed.

Nonlinear and time-dependent effects of sparsely measured continuous time-varying covariates in time-to-event analysis

Many flexible extensions of the Cox proportional hazards model incorporate time-dependent (TD) and/or nonlinear (NL) effects of time-invariant covariates. In contrast, little attention has been given to the assessment of such effects for continuous time-varying covariates (TVCs). We propose a flexible regression B-spline-based model for TD and NL effects of a TVC. To account for sparse TVC measurements, we added to this model the effect of time elapsed since last observation (TEL), which acts as an effect modifier. TD, NL, and TEL effects are estimated with the iterative alternative conditional estimation algorithm. Furthermore, a simulation extrapolation (SIMEX)-like procedure was adapted to correct the estimated effects for random measurement errors in the observed TVC values. In simulations, TD and NL estimates were unbiased if the TVC was measured with a high frequency. With sparse measurements, the strength of the effects was underestimated but the TEL estimate helped reduce the bias, whereas SIMEX helped further to correct for bias toward the null due to "white noise" measurement errors. We reassessed the effects of systolic blood pressure (SBP) and total cholesterol, measured at two-year intervals, on cardiovascular risks in women participating in the Framingham Heart Study. Accounting for TD effects of SBP, cholesterol and age, the NL effect of cholesterol, and the TEL effect of SBP improved substantially the model's fit to data. Flexible estimates yielded clinically important insights regarding the role of these risk factors. These results illustrate the advantages of flexible modeling of TVC effects.

Comparison of model-building strategies for excess hazard regression models in the context of cancer epidemiology

BACKGROUND

Large and complex population-based cancer data are becoming broadly available, thanks to purposeful linkage between cancer registry data and health electronic records. Aiming at understanding the explanatory power of factors on cancer survival, the modelling and selection of variables need to be understood and exploited properly for improving model-based estimates of cancer survival.

METHOD

We assess the performances of well-known model selection strategies developed by Royston and Sauerbrei and Wynant and Abrahamowicz that we adapt to the relative survival data setting and to test for interaction terms.

RESULTS

We apply these to all male patients diagnosed with lung cancer in England in 2012 (N = 15,688), and followed-up until 31/12/2015. We model the effects of age at diagnosis, tumour stage, deprivation, comorbidity and emergency presentation, as well as interactions between age and all of the above. Given the size of the dataset, all model selection strategies favoured virtually the same model, except for a non-linear effect of age at diagnosis selected by the backward-based selection strategies (versus a linear effect selected otherwise).

CONCLUSION

The results from extensive simulations evaluating varying model complexity and sample sizes provide guidelines on a model selection strategy in the context of excess hazard modelling.

Estimation of the adjusted cause-specific cumulative probability using flexible regression models for the cause-specific hazards

In competing risks setting, we account for death according to a specific cause and the quantities of interest are usually the cause-specific hazards (CSHs) and the cause-specific cumulative probabilities. A cause-specific cumulative probability can be obtained with a combination of the CSHs or via the subdistribution hazard. Here, we modeled the CSH with flexible hazard-based regression models using B-splines for the baseline hazard and time-dependent (TD) effects. We derived the variance of the cause-specific cumulative probabilities at the population level using the multivariate delta method and showed how we could easily quantify the impact of a covariate on the cumulative probability scale using covariate-adjusted cause-specific cumulative probabilities and their difference. We conducted a simulation study to evaluate the performance of this approach in its ability to estimate the cumulative probabilities using different functions for the cause-specific log baseline hazard and with or without a TD effect. In the scenario with TD effect, we tested both well-specified and misspecified models. We showed that the flexible regression models perform nearly as well as the nonparametric method, if we allow enough flexibility for the baseline hazards. Moreover, neglecting the TD effect hardly affects the cumulative probabilities estimates of the whole population but impacts them in the various subgroups. We illustrated our approach using data from people diagnosed with monoclonal gammopathy of undetermined significance and provided the R-code to derive those quantities, as an extension of the R-package mexhaz.

Penalized estimation of complex, non-linear exposure-lag-response associations

We propose a novel approach for the flexible modeling of complex exposure-lag-response associations in time-to-event data, where multiple past exposures within a defined time window are cumulatively associated with the hazard. Our method allows for the estimation of a wide variety of effects, including potentially smooth and smoothly time-varying effects as well as cumulative effects with leads and lags, taking advantage of the inference methods that have recently been developed for generalized additive mixed models. We apply our method to data from a large observational study of intensive care patients in order to analyze the association of both the timing and the amount of artificial nutrition with the short term survival of critically ill patients. We evaluate the properties of the proposed method by performing extensive simulation studies and provide a systematic comparison with related approaches.

Flexible and structured survival model for a simultaneous estimation of non-linear and non-proportional effects and complex interactions between continuous variables: Performance of this multidimensional penalized spline approach in net survival trend analysis

Cancer survival trend analyses are essential to describe accurately the way medical practices impact patients' survival according to the year of diagnosis. To this end, survival models should be able to account simultaneously for non-linear and non-proportional effects and for complex interactions between continuous variables. However, in the statistical literature, there is no consensus yet on how to build such models that should be flexible but still provide smooth estimates of survival. In this article, we tackle this challenge by smoothing the complex hypersurface (time since diagnosis, age at diagnosis, year of diagnosis, and mortality hazard) using a multidimensional penalized spline built from the tensor product of the marginal bases of time, age, and year. Considering this penalized survival model as a Poisson model, we assess the performance of this approach in estimating the net survival with a comprehensive simulation study that reflects simple and complex realistic survival trends. The bias was generally small and the root mean squared error was good and often similar to that of the true model that generated the data. This parametric approach offers many advantages and interesting prospects (such as forecasting) that make it an attractive and efficient tool for survival trend analyses.

Assessing the time dependence of prognostic values of cytology and human papillomavirus testing in cervical cancer screening

Accurate assessment of risks for developing cervical intraepithelial neoplasia of grade 2 or worse (CIN2+) after a given set of screening test results is instrumental to reaching valid conclusions and informing cervical cancer screening recommendations. Using data from the Canadian Cervical Cancer Screening Trial (CCCaST), we assessed prognostic values of enrollment screening test results to predict CIN2+ among women attending routine cervical screening using multivariable Cox proportional hazards (PH) regression and its flexible extension during each of two follow-up periods (protocol-defined and extended). Nonproportional (time-dependent (TD)) and/or nonlinear effects were modeled, as appropriate. Women with abnormal cytology had hazard ratios (HRs) for CIN2+ detection of 17.61 (95% CI: 11.25-27.57) and 10.46 (95% CI: 5.41-20.24) relative to women with normal cytology during the protocol-defined and extended follow-up periods, respectively. High-risk human papillomavirus (HR-HPV) positivity was an even stronger predictor of CIN2+ risk, with significant TD effects during both follow-up periods (p <0.001 for both TD effects). Risks among women co-testing HR-HPV+ with and without abnormal cytology (relative to women co-testing negative) were highest immediately after baseline, and decreased significantly thereafter (p <0.001 for both TD effects). HRs for HPV16+ and HPV18+ women (relative to those testing HR-HPV-) did not vary significantly over time (HR = 182.96; 95% CI: 95.16-351.77 and HR = 111.81; 95% CI: 44.60-280.31, respectively). Due to TD effects, conventional Cox model estimates considerably underestimated adjusted HRs associated with positive HR-HPV testing results early on in the follow-up periods.

On the use of flexible excess hazard regression models for describing long-term breast cancer survival: a case-study using population-based cancer registry data

BACKGROUND

Breast cancer prognosis has dramatically improved over 40 years. There is, however, no proof of population 'cure'. This research aimed to examine the pattern of long-term excess mortality due to breast cancer and evaluate its determinants in the context of cancer registry data.

METHODS

We used data from the Geneva Cancer Registry to identify women younger than 75 years diagnosed with invasive, localised and operated breast cancer between 1995 and 2002. Flexible modelling of excess mortality hazard, including time-dependent (TD) regression parameters, was used to estimate mortality related to breast cancer. We derived a single "final" model using a backward selection procedure and evaluated its stability through sensitivity analyses using a bootstrap technique.

RESULTS

We analysed data from 1574 breast cancer women including 351 deaths (22.3%). The model building strategy retained age at diagnosis (TD), tumour size and grade (TD), chemotherapy and hormonal treatment (TD) as prognostic factors, while the sensitivity analysis on bootstrap samples identified nodes involvement and hormone receptors (TD) as additional long-term prognostic factors but did not identify chemotherapy and hormonal treatment as important prognostic factors.

CONCLUSIONS

Two main issues were observed when describing the determinants of long-term survival. First, the modelling strategy presented a lack of robustness, probably due to the limited number of events observed in our study. The second was the misspecification of the model, probably due to confounding by indication. Our results highlight the need for more detailed data and the use of causal inference methods.

Multiple imputation in Cox regression when there are time-varying effects of covariates

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time-varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a "complete-case" analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive-model-compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive-model-compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete-case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided.

Describing the association between socioeconomic inequalities and cancer survival: methodological guidelines and illustration with population-based data

BACKGROUND

Describing the relationship between socioeconomic inequalities and cancer survival is important but methodologically challenging. We propose guidelines for addressing these challenges and illustrate their implementation on French population-based data.

METHODS

We analyzed 17 cancers. Socioeconomic deprivation was measured by an ecological measure, the European Deprivation Index (EDI). The Excess Mortality Hazard (EMH), ie, the mortality hazard among cancer patients after accounting for other causes of death, was modeled using a flexible parametric model, allowing for nonlinear and/or time-dependent association between the EDI and the EMH. The model included a cluster-specific random effect to deal with the hierarchical structure of the data.

RESULTS

We reported the conventional age-standardized net survival (ASNS) and described the changes of the EMH over the time since diagnosis at different levels of deprivation. We illustrated nonlinear and/or time-dependent associations between the EDI and the EMH by plotting the excess hazard ratio according to EDI values at different times after diagnosis. The median excess hazard ratio quantified the general contextual effect. Lip-oral cavity-pharynx cancer in men showed the widest deprivation gap, with 5-year ASNS at 41% and 29% for deprivation quintiles 1 and 5, respectively, and we found a nonlinear association between the EDI and the EMH. The EDI accounted for a substantial part of the general contextual effect on the EMH. The association between the EDI and the EMH was time dependent in stomach and pancreas cancers in men and in cervix cancer.

CONCLUSION

The methodological guidelines proved efficient in describing the way socioeconomic inequalities influence cancer survival. Their use would allow comparisons between different health care systems.

A log-rank-type test to compare net survival distributions

In population-based cancer studies, it is often interesting to compare cancer survival between different populations. However, in such studies, the exact causes of death are often unavailable or unreliable. Net survival methods were developed to overcome this difficulty. Net survival is the survival that would be observed if the disease under study was the only possible cause of death. The Pohar-Perme estimator (PPE) is a nonparametric consistent estimator of net survival. In this article, we present a log-rank-type test for comparing net survival functions (as estimated by PPE) between several groups. We put the test within the counting process framework to introduce the inverse probability weighting procedure as required by the PPE. We built a stratified version to control for categorical covariates that affect the outcome. We performed simulation studies to evaluate the performance of this test and worked an application on real data.

Changes in dynamics of excess mortality rates and net survival after diagnosis of follicular lymphoma or diffuse large B-cell lymphoma: comparison between European population-based data (EUROCARE-5)

BACKGROUND

Since 2001, the World Health Organization classification of tumours of haematopoietic and lymphoid tissues and the International Classification of Diseases for Oncology (third edition) have improved data collection for lymphoma subtypes in most European cancer registries and allowed reporting on the major non-Hodgkin lymphoma subtypes. Treatment of non-Hodgkin lymphoma has changed profoundly, benefiting patients with follicular lymphoma or diffuse large B-cell lymphoma. We aimed to compare dynamics of cancer mortality in patients with follicular lymphoma or diffuse large B-cell lymphoma in five large European areas using data for survival from the largest number of collaborative European population-based cancer registries (EUROCARE).

METHODS

We considered follicular lymphoma and diffuse large B-cell lymphoma cases in patients aged older than 15 years diagnosed between Jan 1, 1996, and Dec 31, 2004, and recorded in 43 cancer registries in five areas: Scotland and Wales, and northern, central, eastern, and southern Europe. We excluded cases incidentally diagnosed at autopsy or known from death certificates only. The vital status could be updated on Dec 31, 2008, in all registries but the French ones (Dec 31, 2007). We obtained changes in net survival with the Pohar-Perme estimator and excess mortality rate with a flexible parametric model according to age and year of diagnosis.

FINDINGS

We identified 13,988 follicular lymphoma and 25,320 diffuse large B-cell lymphoma cases. We noted improvements in 5-year net survival for all ages between the 1999-2001 and 2002-04 periods for both cancers (except for follicular lymphoma in Scotland and Wales and diffuse large B-cell lymphoma in eastern Europe). For follicular lymphoma, 5-year net survival in northern Europe was 64% (95% CI 58-71) in 1999-2001 versus 75% (69-80) for 2002-04, for Scotland and Wales, it was 71% (66-76) versus 68% (64-72), for central Europe, it was 64% (61-67) versus 72% (70-75), for southern Europe, it was 67% (63-70) versus 73% (70-76), and for eastern Europe, it was 50% (43-57) versus 61% (54-69). For diffuse large B-cell lymphoma, 5-year net survival in northern Europe was 41% (35-49) versus 58% (54-62), in Scotland and Wales, it was 44% (41-48) versus 52% (49-54), in central Europe, it was 46% (44-47) versus 50% (48-51), in southern Europe, it was 44% (42-47) versus 50% (48-52), and in eastern Europe, it was 47% (41-54) versus 46% (43-50). We noted the largest area disparity during the 2002-04 period between eastern and northern Europe. We noted a significant effect of the year of diagnosis on the excess mortality rate for all ages in all areas, except for diffuse large B-cell lymphoma in eastern Europe. The excess mortality rate was not constant during the follow-up period: we noted a high rate early for both lymphomas, except for follicular lymphoma in northern Europe.

INTERPRETATION

Although survival for follicular lymphoma and diffuse large B-cell lymphoma is improving, the results from this study should foster the search for more and better means of improvement of access to adequate care than that at present, as there remains variation in survival between European regions. Study of the dynamics of the excess mortality rate seems to be a useful clinical indicator to help the practitioner's choice of optimum management of patients.

FUNDING

Compagnia di San Paolo, Fondazione Cariplo Italy, Italian Ministry of Health, European Commission, Registre des Hémopathies Malignes de Côte d'Or, and French Agence Nationale de la Recherche.

Flexible modeling of disease activity measures improved prognosis of disability progression in relapsing-remitting multiple sclerosis

OBJECTIVES

To illustrate the advantages of updating time-varying measures of disease activity and flexible modeling in prognostic clinical studies using the example of the association between the frequency of past relapses and occurrence of ambulation-related disability in multiple sclerosis (MS).

STUDY DESIGN AND SETTING

Longitudinal population-based study of 288 patients from Burgundy, France, diagnosed with relapsing-remitting MS in 1990-2003. The end point was a nonreversible moderate MS disability (European Database for Multiple Sclerosis score ≥ 3.0 derived from Extended Disability Status Scale). Alternative time-varying measures of attacks frequency included (1) conventional number of early MS attacks in the first 2 years after diagnosis; and two new measures, continuously updated during the follow-up; (2) cumulative number of past attacks; and (3) number of recent attacks, during the past 2 years. Multivariate analyses used Cox proportional hazards model and its flexible generalization, which accounted for time-dependent changes in the hazard ratios (HRs) for different attack frequency measures.

RESULTS

HRs for all measures decreased significantly with increasing follow-up time. The proposed updated number of recent attacks improved model's fit to data, relative to alternative measures of attack frequency, and was associated with a statistically significantly increased hazard of developing ambulation-related MS disability in the next 2 years during the entire follow-up period.

CONCLUSION

Updated measures of recent disease activity, such as frequency of recent attacks and modeling of their time-dependent effects, may substantially improve prognosis of clinical outcomes, such as development of MS disability.