An evaluation of inferential procedures for adaptive clinical trial designs with pre-specified rules for modifying the sample size.

Many papers have introduced adaptive clinical trial methods that allow modifications to the sample size based on interim estimates of treatment effect. There has been extensive commentary on type I error control and efficiency considerations, but little research on estimation after an adaptive hypothesis test. We evaluate the reliability and precision of different inferential procedures in the presence of an adaptive design with pre-specified rules for modifying the sampling plan. We extend group sequential orderings of the outcome space based on the stage at stopping, likelihood ratio statistic, and sample mean to the adaptive setting in order to compute median-unbiased point estimates, exact confidence intervals, and P-values uniformly distributed under the null hypothesis. The likelihood ratio ordering is found to average shorter confidence intervals and produce higher probabilities of P-values below important thresholds than alternative approaches. The bias adjusted mean demonstrates the lowest mean squared error among candidate point estimates. A conditional error-based approach in the literature has the benefit of being the only method that accommodates unplanned adaptations. We compare the performance of this and other methods in order to quantify the cost of failing to plan ahead in settings where adaptations could realistically be pre-specified at the design stage. We find the cost to be meaningful for all designs and treatment effects considered, and to be substantial for designs frequently proposed in the literature.

Estimating mean annual 25-hydroxyvitamin D concentrations from single measurements: the Multi-Ethnic Study of Atherosclerosis.

BACKGROUND: The seasonal variation in circulating 25-hydroxyvitamin D [25(OH)D] concentrations is large relative to mean values. Single measurements may misclassify annual exposure, which may lead to bias in research and complicate clinical decision making. OBJECTIVE: We aimed to develop and validate a model for adjusting a single measurement of a serum 25(OH)D concentration to the time of year it was measured. DESIGN: We measured serum 25(OH)D concentrations by using mass spectrometry in 6476 participants from the Multi-Ethnic Study of Atherosclerosis at baseline and again in a subset of 368 participants at a median of 17 mo later. We estimated a cosinor model to describe the seasonal variability in 25(OH)D concentrations and evaluated this model by using follow-up 25(OH)D measurements. RESULTS: The mean age of subjects was 62.1 y, 61.2% of participants were nonwhite, and 53.3% of participants were women. The cosinor model predicted follow-up 25(OH)D concentrations better than a single measurement [difference in root mean squared error (RMSE): 1.3 ng/mL; P< 0.001]. The cosinor model also better predicted the measured annual mean 25(OH)D concentration (difference in RMSE: 1.0 ng/mL; P< 0.001). Annual mean 25(OH)D concentrations estimated from the cosinor model reclassified 7.1% of participants with regard to 25(OH)D deficiency, which was defined as <20 ng/mL. An estimated annual mean 25(OH)D concentration <20 ng/mL was significantly associated with lower bone mineral density, whereas an untransformed 25(OH)D concentration <20 ng/mL was not. CONCLUSIONS: Cross-sectional data can be used to estimate subject-specific mean annual 25(OH)D concentrations from single values by using a cosinor model. The tool we developed by using this approach may assist research and clinical care of adults in North America by reducing the misclassification of 25(OH)D deficiency.

Adaptive clinical trial designs with pre-specified rules for modifying the sample size: understanding efficient types of adaptation.

Adaptive clinical trial design has been proposed as a promising new approach that may improve the drug discovery process. Proponents of adaptive sample size re-estimation promote its ability to avoid 'up-front' commitment of resources, better address the complicated decisions faced by data monitoring committees, and minimize accrual to studies having delayed ascertainment of outcomes. We investigate aspects of adaptation rules, such as timing of the adaptation analysis and magnitude of sample size adjustment, that lead to greater or lesser statistical efficiency. Owing in part to the recent Food and Drug Administration guidance that promotes the use of pre-specified sampling plans, we evaluate alternative approaches in the context of well-defined, pre-specified adaptation. We quantify the relative costs and benefits of fixed sample, group sequential, and pre-specified adaptive designs with respect to standard operating characteristics such as type I error, maximal sample size, power, and expected sample size under a range of alternatives. Our results build on others' prior research by demonstrating in realistic settings that simple and easily implemented pre-specified adaptive designs provide only very small efficiency gains over group sequential designs with the same number of analyses. In addition, we describe optimal rules for modifying the sample size, providing efficient adaptation boundaries on a variety of scales for the interim test statistic for adaptation analyses occurring at several different stages of the trial. We thus provide insight into what are good and bad choices of adaptive sampling plans when the added flexibility of adaptive designs is desired.

Genetic variants and associations of 25-hydroxyvitamin D concentrations with major clinical outcomes.

CONTEXT: Lower serum 25-hydroxyvitamin D concentrations are associated with greater risks of many chronic diseases across large, prospective community-based studies. Substrate 25-hydroxyvitamin D must be converted to 1,25-dihydroxyvitamin D for full biological activity, and complex metabolic pathways suggest that interindividual variability in vitamin D metabolism may alter the clinical consequences of measured serum 25-hydroxyvitamin D. OBJECTIVE: To investigate whether common variation within genes encoding the vitamin D-binding protein, megalin, cubilin, CYP27B1, CYP24A1, and the vitamin D receptor (VDR) modify associations of low 25-hydroxyvitamin D with major clinical outcomes. DESIGN, SETTING, AND PARTICIPANTS: Examination of 141 single-nucleotide polymorphisms in a discovery cohort of 1514 white participants (who were recruited from 4 US regions) from the community-based Cardiovascular Health Study. Participants had serum 25-hydroxyvitamin D measurements in 1992-1993 and were followed up for a median of 11 years (through 2006). Replication meta-analyses were conducted across the independent, community-based US Health, Aging, and Body Composition (n = 922; follow-up: 1998-1999 through 2005), Italian Invecchiare in Chianti (n = 835; follow-up: 1998-2000 through 2006), and Swedish Uppsala Longitudinal Study of Adult Men (n = 970; follow-up: 1991-1995 through 2008) cohort studies. MAIN OUTCOME MEASURE: Composite outcome of incident hip facture, myocardial infarction, cancer, and mortality over long-term follow-up. RESULTS: Interactions between 5 single-nucleotide polymorphisms and low 25-hydroxyvitamin D concentration were identified in the discovery phase and 1 involving a variant in the VDR gene replicated in independent meta-analysis. Among Cardiovascular Health Study participants, low 25-hydroxyvitamin D concentration was associated with hazard ratios for risk of the composite outcome of 1.40 (95% CI, 1.12-1.74) for those who had 1 minor allele at rs7968585 and 1.82 (95% CI, 1.31-2.54) for those with 2 minor alleles at rs7968585. In contrast, there was no evidence of an association (estimated hazard ratio, 0.93 [95% CI, 0.70-1.24]) among participants who had 0 minor alleles at this single-nucleotide polymorphism. CONCLUSION: Known associations of low 25-hydroxyvitamin D with major health outcomes may vary according to common genetic differences in the vitamin D receptor.

Allopurinol and mortality in hyperuricaemic patients.

OBJECTIVES: While studies have suggested that gout and hyperuricaemia are associated with the risk of premature death, none has investigated the role of urate-lowering therapy on this critical outcome. We examined the impact of allopurinol, the most commonly used urate-lowering drug, on the risk of mortality in hyperuricaemic patients. METHODS: From a population of hyperuricaemic veterans of [serum urate level >416 micromol/l (7.0 mg/dl)] at least 40 years of age, we compared the risk of death between incident allopurinol users (n = 2483) and non-users (n = 7441). We estimated the multivariate mortality hazard ratio (HR) of allopurinol use with Cox proportional hazards models. RESULTS: Of the 9924 veterans (males, 98% and mean age 62.7 years), 1021 died during the follow-up. Patients who began treatment with allopurinol had worse prognostic factors for mortality, including higher BMI and comorbidities. After adjusting for baseline urate levels, allopurinol treatment was associated with a lower risk of all-cause mortality (HR 0.78; 95% CI 0.67, 0.91). Further adjustment with other prognostic factors did not appreciably alter this estimate (HR 0.77; 95% CI 0.65, 0.91). The mean change from baseline in serum urate within the allopurinol group was -111 micromol/l (-1.86 mg/dl). Adjusting for baseline urate level, allopurinol users had a 40 micromol/l (0.68 mg/dl) lower follow-up serum urate value than controls (95% CI -0.55, -0.81). CONCLUSION: Our findings indicate that allopurinol treatment may provide a survival benefit among patients with hyperuricaemia.