Variables with time-varying effects and the Cox model: Some statistical concepts illustrated with a prognostic factor study in breast cancer

Department of Clinical Epidemiology and Clinical Research, Institut Bergonié, Regional Comprehensive Cancer Centre, Bordeaux, France.
BMC Medical Research Methodology (Impact Factor: 2.17). 03/2010; 10:20. DOI: 10.1186/1471-2288-10-20
Source: PubMed

ABSTRACT The Cox model relies on the proportional hazards (PH) assumption, implying that the factors investigated have a constant impact on the hazard - or risk - over time. We emphasize the importance of this assumption and the misleading conclusions that can be inferred if it is violated; this is particularly essential in the presence of long follow-ups.
We illustrate our discussion by analyzing prognostic factors of metastases in 979 women treated for breast cancer with surgery. Age, tumour size and grade, lymph node involvement, peritumoral vascular invasion (PVI), status of hormone receptors (HRec), Her2, and Mib1 were considered.
Median follow-up was 14 years; 264 women developed metastases. The conventional Cox model suggested that all factors but HRec, Her2, and Mib1 status were strong prognostic factors of metastases. Additional tests indicated that the PH assumption was not satisfied for some variables of the model. Tumour grade had a significant time-varying effect, but although its effect diminished over time, it remained strong. Interestingly, while the conventional Cox model did not show any significant effect of the HRec status, tests provided strong evidence that this variable had a non-constant effect over time. Negative HRec status increased the risk of metastases early but became protective thereafter. This reversal of effect may explain non-significant hazard ratios provided by previous conventional Cox analyses in studies with long follow-ups.
Investigating time-varying effects should be an integral part of Cox survival analyses. Detecting and accounting for time-varying effects provide insights on some specific time patterns, and on valuable biological information that could be missed otherwise.

  • [Show abstract] [Hide abstract]
    ABSTRACT: While the addition of targeted therapy to neoadjuvant chemotherapy (NACT) dramatically increases the rate of pathological complete response in HER2-positive breast cancer, no reduction in the rate of mastectomy has been observed in randomised studies. A retrospective single centre analysis of all patients treated with anti HER2-based NACT for T2-4 breast cancer, focusing on patients treated with mastectomy. Among 165 patients treated between June 2005 and July 2012, surgery was performed immediately post-NACT in 152 cases (92%). Breast-conserving surgery could be performed for 108 of the patients (71%), with a 4-year local relapse-free survival of 97%. A mastectomy was performed in two cases following patients' wishes and in 37 cases based on pre-NACT findings (n=18) or post-NACT outcomes (n=19). For 21 out of the 37 cases, a good pathological response was observed, and multidisciplinary reanalysis suggests that breast-conserving surgery outright may have been sufficient for 12 patients. Finally, a salvage mastectomy based on post-lumpectomy pathological results was decided in five cases (11%). The 4-year metastasis-free survival was 84% for all patients operated on after NACT (n=152). Given the good efficacy of anti HER2-based NACT, breast-conserving surgery should be standard practice for most patients. Total mastectomy on the other hand should be restricted to a few patients, mainly those with positive margins on the lumpectomy specimen. Copyright © 2015 Elsevier Ltd. All rights reserved.
    European Journal of Cancer 02/2015; DOI:10.1016/j.ejca.2015.01.063 · 4.82 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The ever-growing volume of data routinely collected and stored in everyday life presents researchers with a number of opportunities to gain insight and make predictions. This study aimed to demonstrate the usefulness in a specific clinical context of a simulation-based technique called probabilistic sensitivity analysis (PSA) in interpreting the results of a discrete time survival model based on a large dataset of routinely collected dairy herd management data. Data from 12,515 dairy cows (from 39 herds) were used to construct a multilevel discrete time survival model in which the outcome was the probability of a cow becoming pregnant during a given two day period of risk, and presence or absence of a recorded lameness event during various time frames relative to the risk period amongst the potential explanatory variables. A separate simulation model was then constructed to evaluate the wider clinical implications of the model results (i.e. the potential for a herd's incidence rate of lameness to influence its overall reproductive performance) using PSA. Although the discrete time survival analysis revealed some relatively large associations between lameness events and risk of pregnancy (for example, occurrence of a lameness case within 14 days of a risk period was associated with a 25% reduction in the risk of the cow becoming pregnant during that risk period), PSA revealed that, when viewed in the context of a realistic clinical situation, a herd's lameness incidence rate is highly unlikely to influence its overall reproductive performance to a meaningful extent in the vast majority of situations. Construction of a simulation model within a PSA framework proved to be a very useful additional step to aid contextualisation of the results from a discrete time survival model, especially where the research is designed to guide on-farm management decisions at population (i.e. herd) rather than individual level.
    PLoS ONE 08/2014; 9(8):e103426. DOI:10.1371/journal.pone.0103426 · 3.53 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Although alcohol-stroke association is well known, the age-varying effect of alcohol drinking at midlife on subsequent stroke risk across older adulthood has not been examined. The effect of genetic/early-life factors is also unknown. We used cohort and twin analyses of data with 43 years of follow-up for stroke incidence to help address these gaps. All 11 644 members of the population-based Swedish Twin Registry born 1886 to 1925 with alcohol data aged ≤60 years were included. The interaction of midlife alcohol consumption by age at stroke was evaluated in Cox-regression and analyses of monozygotic twins were used. Covariates were baseline age, sex, cardiovascular diseases, diabetes mellitus, stress reactivity, depression, body mass index, smoking, and exercise. Altogether 29% participants developed stroke. Compared with very-light drinkers (<0.5 drink/d), heavy drinkers (>2 drinks/d) had greater risk of stroke (hazard ratio, 1.34; P=0.02) and the effect for nondrinkers approached significance (hazard ratio, 1.11; P=0.08). Age increased stroke risk for nondrinkers (P=0.012) and decreased it for heavy drinkers (P=0.040). Midlife heavy drinkers were at high risk from baseline until the age of 75 years when hypertension and diabetes mellitus grew to being the more relevant risk factors. In analyses of monozygotic twin-pairs, heavy drinking shortened time to stroke by 5 years (P=0.04). Stroke-risk associated with heavy drinking (>2 drinks/d) in midlife seems to predominate over well-known risk factors, hypertension and diabetes, until the age of ≈75 years and may shorten time to stroke by 5 years above and beyond covariates and genetic/early-life factors. Alcohol consumption should be considered an age-varying risk factor for stroke. © 2015 American Heart Association, Inc.

Full-text (2 Sources)

Available from
May 31, 2014