Analysis and design of randomised clinical trials involving competing risks endpoints

<p>Abstract</p> <p>Background</p> <p>In randomised clinical trials involving time-to-event outcomes, the failures concerned may be events of an entirely different nature and as such define a classical competing risks framework. In designing and analysing clinical trials involving such endpoints, it is important to account for the competing events, and evaluate how each contributes to the overall failure. An appropriate choice of statistical model is important for adequate determination of sample size.</p> <p>Methods</p> <p>We describe how competing events may be summarised in such trials using cumulative incidence functions and Gray's test. The statistical modelling of competing events using proportional cause-specific and subdistribution hazard functions, and the corresponding procedures for sample size estimation are outlined. These are illustrated using data from a randomised clinical trial (SQNP01) of patients with advanced (non-metastatic) nasopharyngeal cancer.</p> <p>Results</p> <p>In this trial, treatment has no effect on the competing event of loco-regional recurrence. Thus the effects of treatment on the hazard of distant metastasis were similar via both the cause-specific (unadjusted <it>csHR </it>= 0.43, 95% CI 0.25 - 0.72) and subdistribution (unadjusted <it>subHR </it>0.43; 95% CI 0.25 - 0.76) hazard analyses, in favour of concurrent chemo-radiotherapy followed by adjuvant chemotherapy. Adjusting for nodal status and tumour size did not alter the results. The results of the logrank test (<it>p </it>= 0.002) comparing the cause-specific hazards and the Gray's test (<it>p </it>= 0.003) comparing the cumulative incidences also led to the same conclusion. However, the subdistribution hazard analysis requires many more subjects than the cause-specific hazard analysis to detect the same magnitude of effect.</p> <p>Conclusions</p> <p>The cause-specific hazard analysis is appropriate for analysing competing risks outcomes when treatment has no effect on the cause-specific hazard of the competing event. It requires fewer subjects than the subdistribution hazard analysis for a similar effect size. However, if the main and competing events are influenced in opposing directions by an intervention, a subdistribution hazard analysis may be warranted.</p

Outcome-Oriented Cutpoints in Analysis of Quantitative Exposures

In the analysis of epidemiologic data in which exposure has been measured on a continuous scale, cutpoints can be defined to delineate categories or exposure can be modeled as a continuous covariate by assuming a special functional shape of the effect on disease status. Rules for classifying exposure into two or more categories range from a priori selection of cutpoints to data-oriented rules. The risk estimates may vary, however, with the choice of cutpoint. If the cutpoint selected is that for which the most impressive effect of exposure on outcome is observed, the final result must be qualified by adjustment. In this paper, the authors propose a method for adjusting results which are derived by varying the cutpoint on a specified selection interval. Adjustment is derived from the null distribution of the maximally selected test statistic. The method should be applied to correct p values if the cutpoint used to define different levels of exposure is selected in such a way that the measure of difference between two risk groups, such as the odds ratio or relative risk, is maximized. No method is yet available for adjusting the resulting risk estimate and the corresponding confidence limits. The authors illustrate the statistical method by applying it to data from a case-control study of the association between exposure to magnetic fields and risk of cancer in children which was conducted recently in Denmark

The time-dependent bias and its effect on extra length of stay due to nosocomial infection

AbstractObjectivesMany studies disregard the time dependence of nosocomial infection when examining length of hospital stay and the associated financial costs. This leads to the “time-dependent bias,” which biases multiplicative hazard ratios. We demonstrate the time-dependent bias on the additive scale of extra length of stay.MethodsTo estimate the extra length of stay due to infection, we used a multistate model that accounted for the time of infection. For comparison we used a generalized linear model assuming a gamma distribution, a commonly used model that ignores the time of infection. We applied these two methods to a large prospective cohort of hospital admissions from Argentina, and compared the methods' performance using a simulation study.ResultsFor the Argentina data the extra length of stay due to nosocomial infection was 11.23 days when ignoring time dependence and only 1.35 days after accounting for the time of infection. The simulations showed that ignoring time dependence consistently overestimated the extra length of stay. This overestimation was similar for different rates of infection and even when an infection prolonged or shortened stay. We show examples where the time-dependent bias remains unchanged for the true discharge hazard ratios, but the bias for the extra length of stay is doubled because length of stay depends on the infection hazard.ConclusionsIgnoring the timing of nosocomial infection gives estimates that greatly overestimate its effect on the extra length of hospital stay