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

Gene expression of PMP22 is an independent prognostic factor for disease-free and overall survival in breast cancer patients

<p>Abstract</p> <p>Background</p> <p>Gene expression of peripheral myelin protein 22 (<it>PMP22</it>) and the epithelial membrane proteins (<it>EMPs</it>) was found to be differentially expressed in invasive and non-invasive breast cell lines in a previous study. We want to evaluate the prognostic impact of the expression of these genes on breast cancer.</p> <p>Methods</p> <p>In a retrospective multicenter study, gene expression of <it>PMP22 </it>and the <it>EMPs </it>was measured in 249 primary breast tumors by real-time PCR. Results were statistically analyzed together with clinical data.</p> <p>Results</p> <p>In univariable Cox regression analyses PMP22 and the EMPs were not associated with disease-free survival or tumor-related mortality. However, multivariable Cox regression revealed that patients with higher than median <it>PMP22 </it>gene expression have a 3.47 times higher risk to die of cancer compared to patients with equal values on clinical covariables but lower <it>PMP22 </it>expression. They also have a 1.77 times higher risk to relapse than those with lower <it>PMP22 </it>expression. The proportion of explained variation in overall survival due to <it>PMP22 </it>gene expression was 6.5% and thus PMP22 contributes equally to prognosis of overall survival as nodal status and estrogen receptor status. Cross validation demonstrates that 5-years survival rates can be refined by incorporating <it>PMP22 </it>into the prediction model.</p> <p>Conclusions</p> <p><it>PMP22 </it>gene expression is a novel independent prognostic factor for disease-free survival and overall survival for breast cancer patients. Including it into a model with established prognostic factors will increase the accuracy of prognosis.</p

Different competing risks models applied to data from the Australian Orthopaedic Association National Joint Replacement Registry

Purpose: Here we describe some available statistical models and illustrate their use for analysis of arthroplasty registry data in the presence of the competing risk of death, when the influence of covariates on the revision rate may be different to the influence on the probability (that is, risk) of the occurrence of revision. Patients and methods: Records of 12,525 patients aged 75–84 years who had received hemiarthroplasty for fractured neck of femur were obtained from the Australian Orthopaedic Association National Joint Replacement Registry. The covariates whose effects we investigated were: age, sex, type of prosthesis, and type of fixation (cementless or cemented). Extensions of competing risk regression models were implemented, allowing the effects of some covariates to vary with time. Results: The revision rate was significantly higher for patients with unipolar than bipolar prostheses (HR = 1.38, 95% CI: 1.01–1.89) or with monoblock than bipolar prostheses (HR = 1.45, 95% CI: 1.08–1.94). It was significantly higher for the younger age group (75–79 years) than for the older one (80–84 years) (HR = 1.28, 95% CI: 1.05–1.56) and higher for males than for females (HR = 1.37, 95% CI: 1.09–1.71). The probability of revision, after correction for the competing risk of death, was only significantly higher for unipolar prostheses than for bipolar prostheses, and higher for the younger age group. The effect of fixation type varied with time; initially, there was a higher probability of revision for cementless prostheses than for cemented prostheses, which disappeared after approximately 1.5 years. Interpretation: When accounting for the competing risk of death, the covariates type of prosthesis and sex influenced the rate of revision differently to the probability of revision. We advocate the use of appropriate analysis tools in the presence of competing risks and when covariates have time-dependent effects.Marianne H Gillam, Amy Salter, Philip Ryan, and Stephen E Grave

An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect

Background: Most randomized controlled trials with a time-to-event outcome are designed and analysed under the proportional hazards assumption, with a target hazard ratio for the treatment effect in mind. However, the hazards may be non-proportional. We address how to design a trial under such conditions, and how to analyse the results. Methods: We propose to extend the usual approach, a logrank test, to also include the Grambsch-Therneau test of proportional hazards. We test the resulting composite null hypothesis using a joint test for the hazard ratio and for time-dependent behaviour of the hazard ratio. We compute the power and sample size for the logrank test under proportional hazards, and from that we compute the power of the joint test. For the estimation of relevant quantities from the trial data, various models could be used; we advocate adopting a pre-specified flexible parametric survival model that supports time-dependent behaviour of the hazard ratio. Results: We present the mathematics for calculating the power and sample size for the joint test. We illustrate the methodology in real data from two randomized trials, one in ovarian cancer and the other in treating cellulitis. We show selected estimates and their uncertainty derived from the advocated flexible parametric model. We demonstrate in a small simulation study that when a treatment effect either increases or decreases over time, the joint test can outperform the logrank test in the presence of both patterns of non-proportional hazards. Conclusions: Those designing and analysing trials in the era of non-proportional hazards need to acknowledge that a more complex type of treatment effect is becoming more common. Our method for the design of the trial retains the tools familiar in the standard methodology based on the logrank test, and extends it to incorporate a joint test of the null hypothesis with power against non-proportional hazards. For the analysis of trial data, we propose the use of a pre-specified flexible parametric model that can represent a time-dependent hazard ratio if one is present

Long-term survival in patients undergoing cardiac resynchronization therapy: the importance of performing atrio-ventricular junction ablation in patients with permanent atrial fibrillation

AIMS: To investigate the effects of cardiac resynchronization therapy (CRT) on survival in heart failure (HF) patients with permanent atrial fibrillation (AF) and the role of atrio-ventricular junction (AVJ) ablation in these patients. METHODS AND RESULTS: Data from 1285 consecutive patients implanted with CRT devices are presented: 1042 patients were in sinus rhythm (SR) and 243 (19%) in AF. Rate control in AF was achieved by either ablating the AVJ in 118 patients (AVJ-abl) or prescribing negative chronotropic drugs (AF-Drugs). Compared with SR, patients with AF were significantly older, more likely to be non-ischaemic, with higher ejection fraction, shorter QRS duration, and less often received ICD back-up. During a median follow-up of 34 months, 170/1042 patients in SR and 39/243 in AF died (mortality: 8.4 and 8.9 per 100 person-year, respectively). Adjusted hazard ratios were similar for all-cause and cardiac mortality [0.9 (0.57-1.42), P = 0.64 and 1.00 (0.60-1.66) P = 0.99, respectively]. Among AF patients, only 11/118 AVJ-abl patients died vs. 28/125 AF-Drugs patients (mortality: 4.3 and 15.2 per 100 person-year, respectively, P < 0.001). Adjusted hazard ratios of AVJ-abl vs. AF-Drugs was 0.26 [95% confidence interval (CI) 0.09-0.73, P = 0.010] for all-cause mortality, 0.31 (95% CI 0.10-0.99, P = 0.048) for cardiac mortality, and 0.15 (95% CI 0.03-0.70, P = 0.016) for HF mortality. CONCLUSION: Patients with HF and AF treated with CRT have similar mortality compared with patients in SR. In AF, AVJ ablation in addition to CRT significantly improves overall survival compared with CRT alone, primarily by reducing HF death

Survival Analysis Part I: Basic concepts and first analyses

Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs. Because of censoring - the nonobservation of the event of interest after a period of follow-up - a proportion of the survival times of interest will often be unknown. It is assumed that those patients who are censored have the same survival prospects as those who continue to be followed, that is, the censoring is uninformative. Survival data are generally described and modelled in terms of two related functions, the survivor function and the hazard function. The survivor function represents the probability that an individual survives from the time of origin to some time beyond time t. It directly describes the survival experience of a study cohort, and is usually estimated by the KM method. The logrank test may be used to test for differences between survival curves for groups, such as treatment arms. The hazard function gives the instantaneous potential of having an event at a time, given survival up to that time. It is used primarily as a diagnostic tool or for specifying a mathematical model for survival analysis. In comparing treatments or prognostic groups in terms of survival, it is often necessary to adjust for patient-related factors that could potentially affect the survival time of a patient. Failure to adjust for confounders may result in spurious effects. Multivariate survival analysis, a form of multiple regression, provides a way of doing this adjustment, and is the subject the next paper in this series

Short-term outcome of 1,465 computer-navigated primary total knee replacements 2005–2008: A report from the Norwegian Arthroplasty Register

Background and purpose: Improvement of positioning and alignment by the use of computer-assisted surgery (CAS) might improve longevity and function in total knee replacements, but there is little evidence. In this study, we evaluated the short-term results of computer-navigated knee replacements based on data from the Norwegian Arthroplasty Register. Patients and methods: Primary total knee replacements without patella resurfacing, reported to the Norwegian Arthroplasty Register during the years 2005–2008, were evaluated. The 5 most common implants and the 3 most common navigation systems were selected. Cemented, uncemented, and hybrid knees were included. With the risk of revision for any cause as the primary endpoint and intraoperative complications and operating time as secondary outcomes, 1,465 computer-navigated knee replacements (CAS) and 8,214 conventionally operated knee replacements (CON) were compared. Kaplan-Meier survival analysis and Cox regression analysis with adjustment for age, sex, prosthesis brand, fixation method, previous knee surgery, preoperative diagnosis, and ASA category were used. Results: Kaplan-Meier estimated survival at 2 years was 98% (95% CI: 97.5–98.3) in the CON group and 96% (95% CI: 95.0– 97.8) in the CAS group. The adjusted Cox regression analysis showed a higher risk of revision in the CAS group (RR = 1.7, 95% CI: 1.1–2.5; p = 0.02). The LCS Complete knee had a higher risk of revision with CAS than with CON (RR = 2.1, 95% CI: 1.3–3.4; p = 0.004)). The differences were not statistically significant for the other prosthesis brands. Mean operating time was 15 min longer in the CAS group. Interpretation: With the introduction of computer-navigated knee replacement surgery in Norway, the short-term risk of revision has increased for computer-navigated replacement with the LCS Complete. The mechanisms of failure of these implantations should be explored in greater depth, and in this study we have not been able to draw conclusions regarding causation

Prognostic significance of anti-p53 and anti-KRas circulating antibodies in esophageal cancer patients treated with chemoradiotherapy

<p>Abstract</p> <p>Background</p> <p>P53 mutations are an adverse prognostic factor in esophageal cancer. P53 and KRas mutations are involved in chemo-radioresistance. Circulating anti-p53 or anti-KRas antibodies are associated with gene mutations. We studied whether anti-p53 or anti-KRas auto-antibodies were prognostic factors for response to chemoradiotherapy (CRT) or survival in esophageal carcinoma.</p> <p>Methods</p> <p>Serum p53 and KRas antibodies (abs) were measured using an ELISA method in 97 consecutive patients treated at Saint Louis University Hospital between 1999 and 2002 with CRT for esophageal carcinoma (squamous cell carcinoma (SCCE) 57 patients, adenocarcinoma (ACE) 27 patients). Patient and tumor characteristics, response to treatment and the follow-up status of 84 patients were retrospectively collected. The association between antibodies and patient characteristics was studied. Univariate and multivariate survival analyses were conducted.</p> <p>Results</p> <p>Twenty-four patients (28%) had anti-p53 abs. Abs were found predominantly in SCCE (p = 0.003). Anti-p53 abs were associated with a shorter overall survival in the univariate analysis (HR 1.8 [1.03-2.9], p = 0.04). In the multivariate analysis, independent prognostic factors for overall and progression-free survival were an objective response to CRT, the CRT strategy (alone or combined with surgery [preoperative]) and anti-p53 abs. None of the long-term survivors had p53 abs. KRas abs were found in 19 patients (23%, no difference according to the histological type). There was no significant association between anti-KRas abs and survival neither in the univariate nor in the multivariate analysis. Neither anti-p53 nor anti-KRas abs were associated with response to CRT.</p> <p>Conclusions</p> <p>Anti-p53 abs are an independent prognostic factor for esophageal cancer patients treated with CRT. Individualized therapeutic approaches should be evaluated in this population.</p

Intestinal ischemia after cardiac surgery: analysis of a large registry.

Intestinal ischemia after cardiac surgery is a rare but severe complication with a high mortality. Early surgery can be lifesaving. The aim was to analyze the incidence, outcome, and risk factors for these patients