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

Immortal-time bias in older vs younger age groups: a simulation study with application to a population-based cohort of patients with colon cancer

BACKGROUND: In observational studies, the risk of immortal-time bias (ITB) increases with the likelihood of early death, itself increasing with age. We investigated how age impacts the magnitude of ITB when estimating the effect of surgery on 1-year overall survival (OS) in patients with Stage IV colon cancer aged 50–74 and 75–84 in England. METHODS: Using simulations, we compared estimates from a time-fixed exposure model to three statistical methods addressing ITB: time-varying exposure, delayed entry and landmark methods. We then estimated the effect of surgery on OS using a population-based cohort of patients from the CORECT-R resource and conducted the analysis using the emulated target trial framework. RESULTS: In simulations, the magnitude of ITB was larger among older patients when their probability of early death increased or treatment was delayed. The bias was corrected using the methods addressing ITB. When applied to CORECT-R data, these methods yielded a smaller effect of surgery than the time-fixed exposure approach but effects were similar in both age groups. CONCLUSION: ITB must be addressed in all longitudinal studies, particularly, when investigating the effect of exposure on an outcome in different groups of people (e.g., age groups) with different distributions of exposure and outcomes

Explained variation of excess hazard models.

The availability of longstanding collection of detailed cancer patient information makes multivariable modelling of cancer-specific hazard of death appealing. We propose to report variation in survival explained by each variable that constitutes these models. We adapted the ranks explained (RE) measure to the relative survival data setting, ie, when competing risks of death are accounted for through life tables from the general population. RE is calculated at each event time. We introduce weights for each death reflecting its probability to be a cancer death. RE varies between -1 and +1 and can be reported at given times in the follow-up and as a time-varying measure from diagnosis onward. We present an application for patients diagnosed with colon or lung cancer in England. The RE measure shows reasonable properties and is comparable in both relative and cause-specific settings. One year after diagnosis, RE for the most complex excess hazard models reaches 0.56, 95% CI: 0.54 to 0.58 (0.58 95% CI: 0.56-0.60) and 0.69, 95% CI: 0.68 to 0.70 (0.67, 95% CI: 0.66-0.69) for lung and colon cancer men (women), respectively. Stage at diagnosis accounts for 12.4% (10.8%) of the overall variation in survival among lung cancer patients whereas it carries 61.8% (53.5%) of the survival variation in colon cancer patients. Variables other than performance status for lung cancer (10%) contribute very little to the overall explained variation. The proportion of the variation in survival explained by key prognostic factors is a crucial information toward understanding the mechanisms underpinning cancer survival. The time-varying RE provides insights into patterns of influence for strong predictors

Impact of national cancer policies on cancer survival trends and socioeconomic inequalities in England, 1996-2013: population based study.

OBJECTIVE: To assess the effectiveness of the NHS Cancer Plan (2000) and subsequent national cancer policy initiatives in improving cancer survival and reducing socioeconomic inequalities in survival in England. DESIGN: Population based cohort study. SETTING: England. POPULATION: More than 3.5 million registered patients aged 15-99 with a diagnosis of one of the 24 most common primary, malignant, invasive neoplasms between 1996 and 2013. MAIN OUTCOME MEASURES: Age standardised net survival estimates by cancer, sex, year, and deprivation group. These estimates were modelled using regression model with splines to explore changes in the cancer survival trends and in the socioeconomic inequalities in survival. RESULTS: One year net survival improved steadily from 1996 for 26 of 41 sex-cancer combinations studied, and only from 2001 or 2006 for four cancers. Trends in survival accelerated after 2006 for five cancers. The deprivation gap observed for all 41 sex-cancer combinations among patients with a diagnosis in 1996 persisted until 2013. However, the gap slightly decreased for six cancers among men for which one year survival was more than 65% in 1996, and for cervical and uterine cancers, for which survival was more than 75% in 1996. The deprivation gap widened notably for brain tumours in men and for lung cancer in women. CONCLUSIONS: Little evidence was found of a direct impact of national cancer strategies on one year survival, and no evidence for a reduction in socioeconomic inequalities in cancer survival. These findings emphasise that socioeconomic inequalities in survival remain a major public health problem for a healthcare system founded on equity

On models for the estimation of the excess mortality hazard in case of insufficiently stratified life tables.

In cancer epidemiology using population-based data, regression models for the excess mortality hazard is a useful method to estimate cancer survival and to describe the association between prognosis factors and excess mortality. This method requires expected mortality rates from general population life tables: each cancer patient is assigned an expected (background) mortality rate obtained from the life tables, typically at least according to their age and sex, from the population they belong to. However, those life tables may be insufficiently stratified, as some characteristics such as deprivation, ethnicity, and comorbidities, are not available in the life tables for a number of countries. This may affect the background mortality rate allocated to each patient, and it has been shown that not including relevant information for assigning an expected mortality rate to each patient induces a bias in the estimation of the regression parameters of the excess hazard model. We propose two parametric corrections in excess hazard regression models, including a single-parameter or a random effect (frailty), to account for possible mismatches in the life table and thus misspecification of the background mortality rate. In an extensive simulation study, the good statistical performance of the proposed approach is demonstrated, and we illustrate their use on real population-based data of lung cancer patients. We present conditions and limitations of these methods and provide some recommendations for their use in practice

Multivariable flexible modelling for estimating complete, smoothed life tables for sub-national populations.

BACKGROUND: The methods currently available to estimate age- and sex-specific mortality rates for sub-populations are subject to a number of important limitations. We propose two alternative multivariable approaches: a relational model and a Poisson model both using restricted cubic splines. METHODS: We evaluated a flexible Poisson and flexible relational model against the Elandt-Johnson approach in a simulation study using 100 random samples of population and death counts, with different sampling proportions and data arrangements. Estimated rates were compared to the original mortality rates using goodness-of-fit measures and life expectancy. We further investigated an approach for determining optimal knot locations in the Poisson model. RESULTS: The flexible Poisson model outperformed the flexible relational and Elandt-Johnson methods with the smallest sample of data (1%). With the largest sample of data (20%), the flexible Poisson and flexible relational models performed comparably, though the flexible Poisson model displayed a slight advantage. Both approaches tended to underestimate infant mortality and thereby overestimate life expectancy at birth. The flexible Poisson model performed much better at young ages when knots were fixed a priori. For ages 30 and above, results were similar to the model with no fixed knots. CONCLUSIONS: The flexible Poisson model is recommended because it derives robust and unbiased estimates for sub-populations without making strong assumptions about age-specific mortality profiles. Fixing knots a priori in the final model greatly improves fit at the young ages

Data-Adaptive Estimation for Double-Robust Methods in Population-Based Cancer Epidemiology: Risk Differences for Lung Cancer Mortality by Emergency Presentation.

In this paper, we propose a structural framework for population-based cancer epidemiology and evaluate the performance of double-robust estimators for a binary exposure in cancer mortality. We conduct numerical analyses to study the bias and efficiency of these estimators. Furthermore, we compare 2 different model selection strategies based on 1) Akaike's Information Criterion and the Bayesian Information Criterion and 2) machine learning algorithms, and we illustrate double-robust estimators' performance in a real-world setting. In simulations with correctly specified models and near-positivity violations, all but the naive estimators had relatively good performance. However, the augmented inverse-probability-of-treatment weighting estimator showed the largest relative bias. Under dual model misspecification and near-positivity violations, all double-robust estimators were biased. Nevertheless, the targeted maximum likelihood estimator showed the best bias-variance trade-off, more precise estimates, and appropriate 95% confidence interval coverage, supporting the use of the data-adaptive model selection strategies based on machine learning algorithms. We applied these methods to estimate adjusted 1-year mortality risk differences in 183,426 lung cancer patients diagnosed after admittance to an emergency department versus persons with a nonemergency cancer diagnosis in England (2006-2013). The adjusted mortality risk (for patients diagnosed with lung cancer after admittance to an emergency department) was 16% higher in men and 18% higher in women, suggesting the importance of interventions targeting early detection of lung cancer signs and symptoms

Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.

BACKGROUND: In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. METHODS: We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. RESULTS: All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. CONCLUSION: We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion

Reflection on modern methods: trial emulation in the presence of immortal-time bias. Assessing the benefit of major surgery for elderly lung cancer patients using observational data.

Acquiring real-world evidence is crucial to support health policy, but observational studies are prone to serious biases. An approach was recently proposed to overcome confounding and immortal-time biases within the emulated trial framework. This tutorial provides a step-by-step description of the design and analysis of emulated trials, as well as R and Stata code, to facilitate its use in practice. The steps consist in: (i) specifying the target trial and inclusion criteria; (ii) cloning patients; (iii) defining censoring and survival times; (iv) estimating the weights to account for informative censoring introduced by design; and (v) analysing these data. These steps are illustrated with observational data to assess the benefit of surgery among 70-89-year-old patients diagnosed with early-stage lung cancer. Because of the severe unbalance of the patient characteristics between treatment arms (surgery yes/no), a naïve Kaplan-Meier survival analysis of the initial cohort severely overestimated the benefit of surgery on 1-year survival (22% difference), as did a survival analysis of the cloned dataset when informative censoring was ignored (17% difference). By contrast, the estimated weights adequately removed the covariate imbalance. The weighted analysis still showed evidence of a benefit, though smaller (11% difference), of surgery among older lung cancer patients on 1-year survival. Complementing the CERBOT tool, this tutorial explains how to proceed to conduct emulated trials using observational data in the presence of immortal-time bias. The strength of this approach is its transparency and its principles that are easily understandable by non-specialists