Estimating the correlation of bivariate failure times under censoring.

The analysis of correlations within pairs of survival times is of interest to many research topics in medicine, such as the correlation of survival-type endpoints of twins, the correlation of times till failure in paired organs, or the correlation of survival time with a surrogate endpoint. The dependence of such times is assumed monotonic and thus quantification by rank correlation coefficients appropriate. The typical censoring of such times requires more involved methods of estimation and inference as have been developed in recent years. The paper focuses on semiparametric approaches, and in particular on the normal copula-based estimation of Spearman correlation coefficients. The copula approach, often presented for a mathematically inclined readership, is reviewed from the viewpoint of an applied statistician. As an alternative to the maximum likelihood methodology for the normal copula approach (NCE) we introduce an iterative multiple imputation (IMI) method which requires only about 0.05% of the computing time of NCE, without sacrificing statistical performance. For IMI, survival probabilities at death or censoring times are first transformed to normal deviates. Then, those deviates that relate to censored times are iteratively augmented, by using conditional multiple imputation, until convergence is obtained for the normal scores rank correlation, which is similar to Spearman's rank correlation. Statistical properties of NCE and IMI are compared by means of a Monte Carlo study and by means of three real data sets, which also give an impression of the typical range of applications, and of their problems.

The estimation of average hazard ratios by weighted Cox regression.

Often the effect of at least one of the prognostic factors in a Cox regression model changes over time, which violates the proportional hazards assumption of this model. As a consequence, the average hazard ratio for such a prognostic factor is under- or overestimated. While there are several methods to appropriately cope with non-proportional hazards, in particular by including parameters for time-dependent effects, weighted estimation in Cox regression is a parsimonious alternative without additional parameters. The methodology, which extends the weighted k-sample logrank tests of the Tarone-Ware scheme to models with multiple, binary and continuous covariates, has been introduced in the nineties of the last century and is further developed and re-evaluated in this contribution. The notion of an average hazard ratio is defined and its connection to the effect size measure P(X

Prognosis in patients with congestive heart failure and subacute renal failure treated with hemodialysis.

BACKGROUND: Renal dysfunction confers a grave prognosis for patients with congestive heart failure (CHF); even small increases in plasma creatinine are associated with excess mortality. Little, however, is known about prognostic indices and outcome in patients with CHF who (sub-)acutely progress to dialysis dependency. DESIGN AND SETTING: We evaluated prognostic indices in a retrospective cohort analysis of non-critically ill patients with CHF who (sub-)acutely progressed to dialysis-dependent renal failure. PATIENTS AND METHODS: 46 patients (95% ischemic cardiomyopathy) with CHF (NYHA III-IV) with dialysis-dependent renal failure (acute and acute-to-chronic renal failure) were analyzed. Demographic factors and patient characteristics, of cardiac function parameters and renal parameters were recorded longitudinally. MAIN RESULTS: CHF patients progressing to dialysis- dependent renal failure had a grave prognosis: median survival time was 95 days, mean survival 444 days. None of the known factors except age was associated with a worse outcome in CHF patients. LV/RV dysfunction, high plasma NT-pro-BNP, C-reactive protein, low albumin and body-mass index did not turn out to be prognostic indicators. The only factors indicating improved survival were recovery of renal function and low hemoglobin. CONCLUSION: Non-critically ill CHF patients with (sub-)acute renal dysfunction progressing to dialysis dependency have a grave prognosis. Renal failure itself had such a strong prognostic impact that conventional factors such as poor myocardial function or inflammation were concealed. Recovery of renal function and, surprisingly, anemia were beneficial factors. Alternative treatment strategies must be designed to improve the devastating prognosis for this special subset of patients with CHF.

Non-parametric estimation of relative risk in survival and associated tests.

We extend the Tarone and Ware scheme of weighted log-rank tests to cover the associated weighted Mantel-Haenszel estimators of relative risk. Weighting functions previously employed are critically reviewed. The notion of an average hazard ratio is defined and its connection to the effect size measure P(Y > X) is emphasized. The connection makes estimation of P(Y > X) possible also under censoring. Two members of the extended Tarone-Ware scheme accomplish the estimation of intuitively interpretable average hazard ratios, also under censoring and time-varying relative risk which is achieved by an inverse probability of censoring weighting. The empirical properties of the members of the extended Tarone-Ware scheme are demonstrated by a Monte Carlo study. The differential role of the weighting functions considered is illustrated by a comparative analysis of four real data sets.