Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression

ArticleinAmerican Journal of Epidemiology 165(6):710-8 · April 2007with99 Reads
DOI: 10.1093/aje/kwk052 · Source: PubMed
Abstract
The rule of thumb that logistic and Cox models should be used with a minimum of 10 outcome events per predictor variable (EPV), based on two simulation studies, may be too conservative. The authors conducted a large simulation study of other influences on confidence interval coverage, type I error, relative bias, and other model performance measures. They found a range of circumstances in which coverage and bias were within acceptable levels despite less than 10 EPV, as well as other factors that were as influential as or more influential than EPV. They conclude that this rule can be relaxed, in particular for sensitivity analyses undertaken to demonstrate adequate control of confounding.
    • "All PS methods rely on the validity of estimates of individual exposure probability, and thus on the validity of the logistic regression fitted for these estimations. A classical rule when fitting a logistic model is to have an adequate number of outcomes per predictor (at least five or ten outcomes per predictor [49, 50]). This explains why we chose to limit the number of confounding factors in our simulations: in case of small prevalence of exposure, the number of exposed subjects, and therefore the number of variables that could be included in the logistic model, is limited. "
    [Show abstract] [Hide abstract] ABSTRACT: Background: Observational post-marketing assessment studies often involve evaluating the effect of a rare treatment on a time-to-event outcome, through the estimation of a marginal hazard ratio. Propensity score (PS) methods are the most used methods to estimate marginal effect of an exposure in observational studies. However there is paucity of data concerning their performance in a context of low prevalence of exposure. Methods: We conducted an extensive series of Monte Carlo simulations to examine the performance of the two preferred PS methods, known as PS-matching and PS-weighting to estimate marginal hazard ratios, through various scenarios. Results: We found that both PS-weighting and PS-matching could be biased when estimating the marginal effect of rare exposure. The less biased results were obtained with estimators of average treatment effect in the treated population (ATT), in comparison with estimators of average treatment effect in the overall population (ATE). Among ATT estimators, PS-weighting using ATT weights outperformed PS-matching. These results are illustrated using a real observational study. Conclusions: When clinical objectives are focused on the treated population, applied researchers are encouraged to estimate ATT with PS-weighting for studying the relative effect of a rare treatment on time-to-event outcomes.
    Full-text · Article · Dec 2016
    • "A study published by Hoogendam et al. however reported that changing the tested b-value combinations did not influence the ADC-based differentiation of benign tissue from malignant tissue and so it is not clear if this impacted the results of this study [30]. Also, we limited the number of adjusted variables in the confirmatory multivariate model in order to avoid an over fitting due to the relative small number of events [31]. Hence, we decided to use well-known prognostic factors as adjusted variables such as FIGO stage for DSS and DFS and GTV for LRC. "
    [Show abstract] [Hide abstract] ABSTRACT: Background Diffusion Weighted (DW) Magnetic Resonance Imaging (MRI) has been studed in several cancers including cervical cancer. This study was designed to investigate the association of DW-MRI parameters with baseline clinical features and clinical outcomes (local regional control (LRC), disease free survival (DFS) and disease specific survival (DSS)) in cervical cancer patients treated with definitive chemoradiation. Methods This was a retrospective study approved by an institutional review board that included 66 women with cervical cancer treated with definitive chemoradiation who underwent pre-treatment MRI at our institution between 2012 and 2013. A region of interest (ROI) was manually drawn by one of three radiologists with experience in pelvic imaging on a single axial CT slice encompassing the widest diameter of the cervical tumor while excluding areas of necrosis. The following apparent diffusion coefficient (ADC) values (×10−3 mm2/s) were extracted for each ROI: Minimum - ADCmin, Maximum - ADCmax, Mean - ADCmean, and Standard Deviation of the ADC - ADCdev. Receiver operating characteristic (ROC) curves were built to choose the most accurate cut off value for each ADC value. Correlation between imaging metrics and baseline clinical features were evaluated using the Mann Whitney test. Confirmatory multi-variate Cox modeling was used to test associations with LRC (adjusted by gross tumor volume – GTV), DFS and DSS (both adjusted by FIGO stage). Kaplan Meyer curves were built for DFS and DSS. A p-value < 0.05 was considered significant. Women median age was 52 years (range 23–90). 67 % had FIGO stage I-II disease while 33 % had FIGO stage III-IV disease. Eighty-two percent had squamous cell cancer. Eighty-eight percent received concurrent cisplatin chemotherapy with radiation. Median EQD2 of external beam and brachytherapy was 82.2 Gy (range 74–84). Results Women with disease staged III-IV (FIGO) had significantly higher mean ADCmax values compared with those with stage I-II (1.806 (0.4) vs 1.485 (0.4), p = 0.01). Patients with imaging defined positive nodes also had significantly higher mean (±SD) ADCmax values compared with lymph node negative patients (1.995 (0.3) vs 1.551 (0.5), p = 0.03). With a median follow-up of 32 months (range 5–43) 11 patients (17 %) have developed recurrent disease and 8 (12 %) have died because of cervical cancer. ROC curves based on DSS showed optimal cutoffs for ADCmin (0.488 × 10−3), ADCmean (0.827 × 10−3), ADCmax (1.838 × 10−3) and ADCdev (0.148 × 10−3). ADCmin higher than the cutoff was significantly associated with worse DFS (HR = 3.632–95 % CI: 1.094–12.054; p = 0.035) and DSS (HR = 4.401–95 % CI: 1.048–18.483; p = 0.043). Conclusion Pre-treatment ADCmax measured in the primary tumor may be associated with FIGO stage and lymph node status. Pre-treatment ADCmin may be a prognostic factor associated with disease-free survival and disease-specific survival in cervical cancer patients treated with definitive chemoradiation. Prospective validation of these findings is currently ongoing.
    Full-text · Article · Dec 2016
    • "The resulting 2.6 events-per-variable (EPV) ratio is well below the EPV of 10 often recommended as the minimum to avoid biased OR estimates [41]. Even though more recent statistical evaluations show that this rule often can be relaxed [42] and that other considerations (e.g., number of predictors, correlations among predictors, clustering, magnitudes of regression coefficients, selection rules used in building the model) are in many cases more important than EPV in determining model performance [43][44][45], caution is nonetheless needed in interpreting model results because of the low EPV. Despite these limitations, our results are valuable in providing the first large-scale cross-national data on prevalence and predictors of MVC-related PTSD. "
    [Show abstract] [Hide abstract] ABSTRACT: Background Motor vehicle collisions (MVCs) are a substantial contributor to the global burden of disease and lead to subsequent post-traumatic stress disorder (PTSD). However, the relevant literature originates in only a few countries, and much remains unknown about MVC-related PTSD prevalence and predictors. Methods Data come from the World Mental Health Survey Initiative, a coordinated series of community epidemiological surveys of mental disorders throughout the world. The subset of 13 surveys (5 in high income countries, 8 in middle or low income countries) with respondents reporting PTSD after life-threatening MVCs are considered here. Six classes of predictors were assessed: socio-demographics, characteristics of the MVC, childhood family adversities, MVCs, other traumatic experiences, and respondent history of prior mental disorders. Logistic regression was used to examine predictors of PTSD. Mental disorders were assessed with the fully-structured Composite International Diagnostic Interview using DSM-IV criteria. Results Prevalence of PTSD associated with MVCs perceived to be life-threatening was 2.5 % overall and did not vary significantly across countries. PTSD was significantly associated with low respondent education, someone dying in the MVC, the respondent or someone else being seriously injured, childhood family adversities, prior MVCs (but not other traumatic experiences), and number of prior anxiety disorders. The final model was significantly predictive of PTSD, with 32 % of all PTSD occurring among the 5 % of respondents classified by the model as having highest PTSD risk. Conclusion Although PTSD is a relatively rare outcome of life-threatening MVCs, a substantial minority of PTSD cases occur among the relatively small proportion of people with highest predicted risk. This raises the question whether MVC-related PTSD could be reduced with preventive interventions targeted to high-risk survivors using models based on predictors assessed in the immediate aftermath of the MVCs.
    Full-text · Article · Dec 2016
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