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We present a method for computing sample size for cluster-randomized studies involving a large number of clusters with relatively small numbers of observations within each cluster. For multivariate survival data, only the marginal bivariate distribution is assumed to be known. The validity of this assumption is also discussed.
Many clinical trials involve the collection of data on the time to occurrence of the same type of multiple events within sample units, in which ordering of events is arbitrary and times are usually correlated. To design a clinical trial with this type of clustered survival times as the primary endpoint, estimating the number of subjects (sampling units) required for a given power to detect a specified treatment difference is an important issue. In this paper we derive a sample size formula for clustered survival data via Lee, Wei and Amato's marginal model. It can be easily used to plan a clinical trial in which clustered survival times are of primary interest. Simulation studies demonstrate that the formula works very well. We also discuss and compare cluster survival time design and single survival time design (for example, time to the first event) in different scenarios.
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Safety equivalence studies may be required to demonstrate that a new procedure or process is at least as safe as a previous one. They usually involve low or very low outcome rates that are often not precisely determined, making patient-based sample sizing uncertain. Using a reverse sampling approach, a method is derived from standard equations to estimate the number of events that need to be observed to demonstrate equivalence using the confidence interval approach. For instance, for a one-sided (nonsuperiority) hypothesis, 5% alpha risk, and 80% power, almost 100 events need to be observed in each study arm to demonstrate equivalence within 30%, or 250 events for 20% equivalence. The number of patients to be included can be derived directly from expected event rates.
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We propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome. The procedure is based on a chi-square goodness-of-fit test as applied to a model frequently used for clustered binary data. The procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures. The procedure also has use for significance-testing and the planning of corresponding sample size requirements.
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BACKGROUND: Identification of stroke risk genes in humans has relied on case-control methods to determine the association between candidate genes and disease. Alternative approaches include linkage analysis using affected sibling pairs, transmission disequilibrium testing (TDT), and sibling TDT (S-TDT). Despite theoretical benefits, the feasibility of these methods in stroke remains unknown. METHODS: Family history was determined in 727 patients with ischemic stroke and 623 control subjects. These data were used to estimate the number of stroke patients required for the different study designs. RESULTS: A family history of any stroke occurring at < or =65 years was an independent risk factor for ischemic stroke at all ages (OR 1.47, 95% CI 1.02 to 2.12, p = 0.04) and a stronger risk factor for young (< or =65 years) ischemic stroke (OR 2.25, 95% CI 1.43 to 3.55, p < 0.0001). For early-onset ischemic stroke, the sibling risk ratio was estimated to be 3.08. Assuming three major stroke loci, collection of 953 affected sibling pairs (both < or =65 years) would be needed for a linkage study, and 115,472 ischemic stroke patients would have to be screened to achieve this sample size from the authors' population. The predicted sample sizes for association studies to detect a gene conferring an OR of 2.0 were case-control methodology (414), TDT (414), and S-TDT (617), which would require screening of 820, 31,680, and 3,062 cases. CONCLUSION: Alternative genetic approaches are feasible, but TDT and linkage studies using the affected sib-pair methodology may require large multicenter collaborations. S-TDT approaches appear more practical. These estimates will aid in planning of such studies.
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BACKGROUND: Risk factors for short-term progression in early relapsing remitting MS have been identified recently. Previously we determined potential risk factors for rapid progression of early relapsing remitting MS and identified three groups of high-risk patients. These non-mutually exclusive groups of patients were drawn from a consecutively studied sample of 98 patients with newly diagnosed MS. High-risk patients had a history of either poor recovery from initial attacks, more than two attacks in the first two years of disease, or a combination of at least four other risk factors. OBJECTIVE: To determine differences in sample sizes required to show a meaningful treatment effect when using a high-risk sample versus a random sample of patients. METHODS: Power analyses were used to calculate the different sample sizes needed for hypothetical treatment trials. RESULTS: We found that substantially smaller numbers of patients should be needed to show a significant treatment effect by employing these high-risk groups of patients as compared to a random population of MS patients (e.g., 58% reduction in sample size in one model). CONCLUSION: The use of patients at higher risk of progression to perform drug treatment trials can be considered as a means to reduce the number of patients needed to show a significant treatment effect for patients with very early MS.
This paper contains a short generalization of a known method for sample size determination in the case of more than two parallel groups. The term 'set of allocation ratios' corresponding to the allocation ratio from the two-group design is defined. A formula using these ratios to determine the non-centrality parameter of the F distribution is deduced. It is shown that in case of more than two groups, equal group numbers does not constitute an optimal design. Two worked examples are presented.
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Two equations for calculating sample sizes that are required for power in testing differences in rates of change in repeated measurement designs have been presented by different authors. One equation provides support for the conclusion that increased frequency of measurements across a treatment period of fixed duration enhances power of the tests. The other equation supports the counterintuitive conclusion that increased frequency of measurements actually tends to decrease power in the presence of realistic serial dependencies in the data. Monte Carlo methods confirm that the equation providing support for the latter conclusion is accurate, whereas the alternative equation tends to underestimate sample sizes required for power in testing differences in slopes of regression lines fitted to changes in the repeated measurements across time when symmetry is absent from the covariance structure.
In the European Union, vaccination campaigns against Pseudorabies virus (PRV) in swine have been started to eradicate PRV. Specific sampling designs are needed to monitor PRV seroprevalence at a regional level. This paper demonstrates how sampling theory can be applied to design a disease seroprevalence survey, using PRV as an example. In the spring of 1994, the four regions in the Netherlands covered by the regional Animal Health Services were monitored with respect to PRV seroprevalence. Per region, blood samples from approximately 1400 herds, with two animals per herd, were collected. The sampling design accounted for stratification by fattening pig and sow population within each region. The regional PRV seroprevalence of swine in the Southern region was the highest (24.9%), closely followed by the PRV seroprevalence of swine in the Eastern region (20.5%). These regions have the highest density of swine in the Netherlands. The PRV seroprevalence in the Western and Central region (11.7%) was about half of the seroprevalence in the Southern and Eastern regions; the lowest regional PRV seroprevalence was observed in the Northern region (3.5%). The Northern part also has the lowest pig density. The PRV seroprevalence was approximately two times higher in sows than in fattening pigs.
Paired data occur in crossover trials and matched case-control studies, and it is rare to find studies reporting sample size calculations associated with these types of studies, despite recommendations from editors that sample size calculations should be justified. In this article we describe some simple formulas and strategies for calculating the number of patients that should be entered into a matched or paired study when the outcome measures are continuous, binary, or ordinal.