Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines

Background: Multiple imputation (MI) provides an effective approach to handle missing covariate data within prognostic modelling studies, as it can properly account for the missing data uncertainty. The multiply imputed datasets are each analysed using standard prognostic modelling techniques to obtain the estimates of interest. The estimates from each imputed dataset are then combined into one overall estimate and variance, incorporating both the within and between imputation variability. Rubin's rules for combining these multiply imputed estimates are based on asymptotic theory. The resulting combined estimates may be more accurate if the posterior distribution of the population parameter of interest is better approximated by the normal distribution. However, the normality assumption may not be appropriate for all the parameters of interest when analysing prognostic modelling studies, such as predicted survival probabilities and model performance measures. Methods: Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies. Results: Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated. Conclusion: The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies

Suitability of PSA-detected localised prostate cancers for focal therapy: Experience from the ProtecT study

This article is available through a Creative Commons Attribution-NonCommercial-Share Alike 3.0 Unported License. Copyright @ 2011 Cancer Research UK.Background: Contemporary screening for prostate cancer frequently identifies small volume, low-grade lesions. Some clinicians have advocated focal prostatic ablation as an alternative to more aggressive interventions to manage these lesions. To identify which patients might benefit from focal ablative techniques, we analysed the surgical specimens of a large sample of population-detected men undergoing radical prostatectomy as part of a randomised clinical trial. Methods: Surgical specimens from 525 men who underwent prostatectomy within the ProtecT study were analysed to determine tumour volume, location and grade. These findings were compared with information available in the biopsy specimen to examine whether focal therapy could be provided appropriately. Results: Solitary cancers were found in prostatectomy specimens from 19% (100 out of 525) of men. In addition, 73 out of 425 (17%) men had multiple cancers with a solitary significant tumour focus. Thus, 173 out of 525 (33%) men had tumours potentially suitable for focal therapy. The majority of these were small, well-differentiated lesions that appeared to be pathologically insignificant (38–66%). Criteria used to select patients for focal prostatic ablation underestimated the cancer's significance in 26% (34 out of 130) of men and resulted in overtreatment in more than half. Only 18% (24 out of 130) of men presumed eligible for focal therapy, actually had significant solitary lesions. Conclusion: Focal therapy appears inappropriate for the majority of men presenting with prostate-specific antigen-detected localised prostate cancer. Unifocal prostate cancers suitable for focal ablation are difficult to identify pre-operatively using biopsy alone. Most lesions meeting criteria for focal ablation were either more aggressive than expected or posed little threat of progression.National Institute for Health Researc

Prediction of two month modified Rankin Scale with an ordinal prediction model in patients with aneurysmal subarachnoid haemorrhage

Background. Aneurysmal subarachnoid haemorrhage (aSAH) is a devastating event with a frequently disabling outcome. Our aim was to develop a prognostic model to predict an ordinal clinical outcome at two months in patients with aSAH. Methods. We studied patients enrolled in the International Subarachnoid Aneurysm Trial (ISAT), a randomized multicentre trial to compare coiling and clipping in aSAH patients. Several models were explored to estimate a patient's outcome according to the modified Rankin Scale (mRS) at two months after aSAH. Our final model was validated internally with bootstrapping techniques. Results. The study population comprised of 2,128 patients of whom 159 patients died within 2 months (8%). Multivariable proportional odds analysis identified World Federation of Neurosurgical Societies (WFNS) grade as the most important predictor, followed by age, sex, lumen size of the aneurysm, Fisher grade, vasospasm on angiography, and treatment modality. The model discriminated moderately between those with poor and good mRS scores (c statistic = 0.65), with minor optimism according to bootstrap re-sampling (optimism corrected c statistic = 0.64). Conclusion. We presented a calibrated and internally validated ordinal prognostic model to predict two month mRS in aSAH patients who survived the early stage up till a treatment decision.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

<p>Abstract</p> <p>Background</p> <p>During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions.</p> <p>Methods</p> <p>Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations.</p> <p>Results</p> <p>We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001.</p> <p>Conclusion</p> <p>Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia.</p

External validation of the UK Prospective Diabetes Study (UKPDS) risk engine in patients with type 2 diabetes

Treatment guidelines recommend the UK Prospective Diabetes Study (UKPDS) risk engine for predicting cardiovascular risk in patients with type 2 diabetes, although validation studies showed moderate performance. The methods used in these validation studies were diverse, however, and sometimes insufficient. Hence, we assessed the discrimination and calibration of the UKPDS risk engine to predict 4, 5, 6 and 8 year cardiovascular risk in patients with type 2 diabetes. The cohort included 1,622 patients with type 2 diabetes. During a mean follow-up of 8 years, patients were followed for incidence of CHD and cardiovascular disease (CVD). Discrimination and calibration were assessed for 4, 5, 6 and 8 year risk. Discrimination was examined using the c-statistic and calibration by visually inspecting calibration plots and calculating the Hosmer-Lemeshow χ(2) statistic. The UKPDS risk engine showed moderate to poor discrimination for both CHD and CVD (c-statistic of 0.66 for both 5 year CHD and CVD risks), and an overestimation of the risk (224% and 112%). The calibration of the UKPDS risk engine was slightly better for patients with type 2 diabetes who had been diagnosed with diabetes more than 10 years ago compared with patients diagnosed more recently, particularly for 4 and 5 year predicted CVD and CHD risks. Discrimination for these periods was still moderate to poor. We observed that the UKPDS risk engine overestimates CHD and CVD risk. The discriminative ability of this model is moderate, irrespective of various subgroup analyses. To enhance the prediction of CVD in patients with type 2 diabetes, this model should be update

Pretreatment CD4 Cell Slope and Progression to AIDS or Death in HIV-Infected Patients Initiating Antiretroviral Therapy—The CASCADE Collaboration: A Collaboration of 23 Cohort Studies

Analyzing data from several thousand cohort study participants, Marcel Wolbers and colleagues find that the rate of CD4 T cell decline is not useful in deciding when to start HIV treatment

Risk-adjusted CUSUM control charts for shared frailty survival models with application to hip replacement outcomes: a study using the NJR dataset

Background:  Continuous monitoring of surgical outcomes after joint replacement is needed to detect which brands’ components have a higher than expected failure rate and are therefore no longer recommended to be used in surgical practice. We developed a monitoring method based on cumulative sum (CUSUM) chart specifically for this application.  Methods:  Our method entails the use of the competing risks model with the Weibull and the Gompertz hazard functions adjusted for observed covariates to approximate the baseline time-to-revision and time-to-death distributions, respectively. The correlated shared frailty terms for competing risks, corresponding to the operating unit, are also included in the model. A bootstrap-based boundary adjustment is then required for risk-adjusted CUSUM charts to guarantee a given probability of the false alarm rates. We propose a method to evaluate the CUSUM scores and the adjusted boundary for a survival model with the shared frailty terms. We also introduce a unit performance quality score based on the posterior frailty distribution. This method is illustrated using the 2003-2012 hip replacement data from the UK National Joint Registry (NJR). Results:  We found that the best model included the shared frailty for revision but not for death. This means that the competing risks of revision and death are independent in NJR data. Our method was superior to the standard NJR methodology. For one of the two monitored components, it produced alarms four years before the increased failure rate came to the attention of the UK regulatory authorities. The hazard ratios of revision across the units varied from 0.38 to 2.28. Conclusions:  An earlier detection of failure signal by our method in comparison to the standard method used by the NJR may be explained by proper risk-adjustment and the ability to accommodate time-dependent hazards. The continuous monitoring of hip replacement outcomes should include risk adjustment at both the individual and unit level

Methodology of a novel risk stratification algorithm for patients with multiple myeloma in the relapsed setting

Introduction Risk stratification tools provide valuable information to inform treatment decisions. Existing algorithms for patients with multiple myeloma (MM) were based on patients with newly diagnosed disease, and these have not been validated in the relapsed setting or in routine clinical practice. We developed a risk stratification algorithm (RSA) for patients with MM at initiation of second-line (2L) treatment, based on data from the Czech Registry of Monoclonal Gammopathies. Methods Predictors of overall survival (OS) at 2L treatment were identified using Cox proportional hazards models and backward selection. Risk scores were obtained by multiplying the hazard ratios for each predictor. The K-adaptive partitioning for survival (KAPS) algorithm defined four groups of stratification based on individual risk scores. Results Performance of the RSA was assessed using Nagelkerke’s R2 test and Harrell’s concordance index through Kaplan–Meier analysis of OS data. Prognostic groups were successfully defined based on real-world data. Use of a multiplicative score based on Cox modeling and KAPS to define cut-off values was effective. Conclusion Through innovative methods of risk assessment and collaboration between physicians and statisticians, the RSA was capable of stratifying patients at 2L treatment by survival expectations. This approach can be used to develop clinical decision-making tools in other disease areas to improve patient management