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.Comment: 28 pages, 12 figures. For associated Supplementary material, see http://publicifsv.sund.ku.dk/~pka/STRATOSTG8

A reference relative time-scale as an alternative to chronological age for cohorts with long follow-up

Background: Epidemiologists have debated the appropriate time-scale for cohort survival studies; chronological age or time-on-study being two such time-scales. Importantly, assessment of risk factors may depend on the choice of time-scale. Recently, chronological or attained age has gained support but a case can be made for a ‘reference relative time-scale’ as an alternative which circumvents difficulties that arise with this and other scales. The reference relative time of an individual participant is the integral of a reference population hazard function between time of entry and time of exit of the individual. The objective here is to describe the reference relative time-scale, illustrate its use, make comparison with attained age by simulation and explain its relationship to modern and traditional epidemiologic methods. Results: A comparison was made between two models; a stratified Cox model with age as the time-scale versus an un-stratified Cox model using the reference relative time-scale. The illustrative comparison used a UK cohort of cotton workers, with differing ages at entry to the study, with accrual over a time period and with long follow-up. Additionally, exponential and Weibull models were fitted since the reference relative time-scale analysis need not be restricted to the Cox model. A simulation study showed that analysis using the reference relative time-scale and analysis using chronological age had very similar power to detect a significant risk factor and both were equally unbiased. Further, the analysis using the reference relative time-scale supported fully-parametric survival modelling and allowed percentile predictions and mortality curves to be constructed. Conclusions: The reference relative time-scale was a viable alternative to chronological age, led to simplification of the modelling process and possessed the defined features of a good time-scale as defined in reliability theory. The reference relative time-scale has several interpretations and provides a unifying concept that links contemporary approaches in survival and reliability analysis to the traditional epidemiologic methods of Poisson regression and standardised mortality ratios. The community of practitioners has not previously made this connection

Light smoking at base-line predicts a higher mortality risk to women than to men; evidence from a cohort with long follow-up

BACKGROUND: There is conflicting evidence as to whether smoking is more harmful to women than to men. The UK Cotton Workers’ Cohort was recruited in the 1960s and contained a high proportion of men and women smokers who were well matched in terms of age, job and length of time in job. The cohort has been followed up for 42 years. METHODS: Mortality in the cohort was analysed using an individual relative survival method and Cox regression. Whether smoking, ascertained at baseline in the 1960s, was more hazardous to women than to men was examined by estimating the relative risk ratio women to men, smokers to never smoked, for light (1–14), medium (15–24), heavy (25+ cigarettes per day) and former smoking. RESULTS: For all-cause mortality relative risk ratios were 1.35 for light smoking at baseline (95% CI 1.07-1.70), 1.15 for medium smoking (95% CI 0.89-1.49) and 1.00 for heavy smoking (95% CI 0.63-1.61). Relative risk ratios for light smoking at baseline for circulatory system disease was 1.42 (95% CI 1.01 to 1.98) and for respiratory disease was 1.89 (95% CI 0.99 to 3.63). Heights of participants provided no explanation for the gender difference. CONCLUSIONS: Light smoking at baseline was shown to be significantly more hazardous to women than to men but the effect decreased as consumption increased indicating a dose response relationship. Heavy smoking was equally hazardous to both genders. This result may help explain the conflicting evidence seen elsewhere. However gender differences in smoking cessation may provide an alternative explanation

Deriving stage at diagnosis from multiple population-based sources: colorectal and lung cancer in England.

BACKGROUND: Stage at diagnosis is a strong predictor of cancer survival. Differences in stage distributions and stage-specific management help explain geographic differences in cancer outcomes. Stage information is thus essential to improve policies for cancer control. Despite recent progress, stage information is often incomplete. Data collection methods and definition of stage categories are rarely reported. These inconsistencies may result in assigning conflicting stage for single tumours and confound the interpretation of international comparisons and temporal trends of stage-specific cancer outcomes. We propose an algorithm that uses multiple routine, population-based data sources to obtain the most complete and reliable stage information possible. METHODS: Our hierarchical approach derives a single stage category per tumour prioritising information deemed of best quality from multiple data sets and various individual components of tumour stage. It incorporates rules from the Union for International Cancer Control TNM classification of malignant tumours. The algorithm is illustrated for colorectal and lung cancer in England. We linked the cancer-specific Clinical Audit data (collected from clinical multi-disciplinary teams) to national cancer registry data. We prioritise stage variables from the Clinical Audit and added information from the registry when needed. We compared stage distribution and stage-specific net survival using two sets of definitions of summary stage with contrasting levels of assumptions for dealing with missing individual TNM components. This exercise extends a previous algorithm we developed for international comparisons of stage-specific survival. RESULTS: Between 2008 and 2012, 163 915 primary colorectal cancer cases and 168 158 primary lung cancer cases were diagnosed in adults in England. Using the most restrictive definition of summary stage (valid information on all individual TNM components), colorectal cancer stage completeness was 56.6% (from 33.8% in 2008 to 85.2% in 2012). Lung cancer stage completeness was 76.6% (from 57.3% in 2008 to 91.4% in 2012). Stage distribution differed between strategies to define summary stage. Stage-specific survival was consistent with published reports. CONCLUSIONS: We offer a robust strategy to harmonise the derivation of stage that can be adapted for other cancers and data sources in different countries. The general approach of prioritising good-quality information, reporting sources of individual TNM variables, and reporting of assumptions for dealing with missing data is applicable to any population-based cancer research using stage. Moreover, our research highlights the need for further transparency in the way stage categories are defined and reported, acknowledging the limitations, and potential discrepancies of using readily available stage variables

Spatial variation in prostate cancer survival in the Northern and Yorkshire region of England using Bayesian relative survival smoothing

Primary Care Trust (PCT) estimates of survival lack robustness as there are small numbers of deaths per year in each area, even when incidence is high. We assess PCT-level spatial variation in prostate cancer survival using Bayesian spatial models of excess mortality. We extracted data on men diagnosed with prostate cancer between 1990 and 1999 from the Northern and Yorkshire Cancer Registry and Information Service database. Models were adjusted for age at diagnosis, period of diagnosis and deprivation. All covariates had a significant association with excess mortality; men from more deprived areas, older age at diagnosis and diagnosed in 1990–1994 had higher excess mortality. The unadjusted relative excess risks (RER) of death by PCT ranged from 0.75 to 1.66. After adjustment, areas of high and low excess mortality were smoothed towards the mean, and the RERs ranged from 0.74 to 1.49. Using Bayesian smoothing techniques to model cancer survival by geographic area offers many advantages over traditional methods; estimates in areas with small populations or low incidence rates are stabilised and shrunk towards local and global risk estimates improving reliability and precision, complex models are easily handled and adjustment for covariates can be made