Bayesian sample size for exploratory clinical trials incorporating historical data

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored. Copyright (C) 2007 John Wiley & Sons, Ltd.

The Role of Cell Sterilization in Population Based Studies of Radiogenic Second Cancers Following Radiation Therapy

Advances in radiotherapy have generated increased interest in comparative studies of treatment techniques and their effectiveness. In this respect, pediatric patients are of specific interest because of their sensitivity to radiation induced second cancers. However, due to the rarity of childhood cancers and the long latency of second cancers, large sample sizes are unavailable for the epidemiological study of contemporary radiotherapy treatments. Additionally, when specific treatments are considered, such as proton therapy, sample sizes are further reduced due to the rareness of such treatments. We propose a method to improve statistical power in micro clinical trials. Specifically, we use a more biologically relevant quantity, cancer equivalent dose (DCE), to estimate risk instead of mean absorbed dose (DMA). Our objective was to demonstrate that when DCE is used fewer subjects are needed for clinical trials. Thus, we compared the impact of DCE vs. DMA on sample size in a virtual clinical trial that estimated risk for second cancer (SC) in the thyroid following craniospinal irradiation (CSI) of pediatric patients using protons vs. photons. Dose reconstruction, risk models, and statistical analysis were used to evaluate SC risk from therapeutic and stray radiation from CSI for 18 patients. Absorbed dose was calculated in two ways: with (1) traditional DMA and (2) with DCE. DCE and DMA values were used to estimate relative risk of SC incidence (RRCE and RRMA, respectively) after proton vs. photon CSI. Ratios of RR for proton vs. photon CSI (RRRCE and RRRMA) were then used in comparative estimations of sample size to determine the minimal number of patients needed to maintain 80% statistical power when using DCE vs. DMA. For all patients, we found that protons substantially reduced the risk of developing a second thyroid cancer when compared to photon therapy. Mean RRR values were 0.052±0.014 and 0.087±0.021 for RRRMA and RRRCE, respectively. However, we did not find that use of DCE reduced the number of patents needed for acceptable statistical power (i.e, 80%). In fact, when considerations were made for RRR values that met equipoise requirements and the need for descriptive statistics, the minimum number of patients needed for a micro-clinical trial increased from 17 using DMA to 37 using DCE. Subsequent analyses revealed that for our sample, the most influential factor in determining variations in sample size was the experimental standard deviation of estimates for RRR across the patient sample. Additionally, because the relative uncertainty in dose from proton CSI was so much larger (on the order of 2000 times larger) than the other uncertainty terms, it dominated the uncertainty in RRR. Thus, we found that use of corrections for cell sterilization, in the form of DCE, may be an important and underappreciated consideration in the design of clinical trials and radio-epidemiological studies. In addition, the accurate application of cell sterilization to thyroid dose was sensitive to variations in absorbed dose, especially for proton CSI, which may stem from errors in patient positioning, range calculation, and other aspects of treatment planning and delivery.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.

Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Sample size in orthodontic randomized controlled trials: are numbers justified?

Sample size calculations are advocated by the Consolidated Standards of Reporting Trials (CONSORT) group to justify sample sizes in randomized controlled trials (RCTs). This study aimed to analyse the reporting of sample size calculations in trials published as RCTs in orthodontic speciality journals. The performance of sample size calculations was assessed and calculations verified where possible. Related aspects, including number of authors; parallel, split-mouth, or other design; single- or multi-centre study; region of publication; type of data analysis (intention-to-treat or per-protocol basis); and number of participants recruited and lost to follow-up, were considered. Of 139 RCTs identified, complete sample size calculations were reported in 41 studies (29.5 per cent). Parallel designs were typically adopted (n = 113; 81 per cent), with 80 per cent (n = 111) involving two arms and 16 per cent having three arms. Data analysis was conducted on an intention-to-treat (ITT) basis in a small minority of studies (n = 18; 13 per cent). According to the calculations presented, overall, a median of 46 participants were required to demonstrate sufficient power to highlight meaningful differences (typically at a power of 80 per cent). The median number of participants recruited was 60, with a median of 4 participants being lost to follow-up. Our finding indicates good agreement between projected numbers required and those verified (median discrepancy: 5.3 per cent), although only a minority of trials (29.5 per cent) could be examined. Although sample size calculations are often reported in trials published as RCTs in orthodontic speciality journals, presentation is suboptimal and in need of significant improvement.

Sample size in studies on diagnostic accuracy in ophthalmology:A literature survey

Aim: To assess the sample sizes used in studies on diagnostic accuracy in ophthalmology. Design and sources: A survey literature published in 2005. Methods: The frequency of reporting calculations of sample sizes and the samples' sizes were extracted from the published literature. A manual search of five leading clinical journals in ophthalmology with the highest impact (Investigative Ophthalmology and Visual Science, Ophthalmology, Archives of Ophthalmology, American Journal of Ophthalmology and British Journal of Ophthalmology) was conducted by two independent investigators. Results: A total of 1698 articles were identified, of which 40 studies were on diagnostic accuracy. One study reported that sample size was calculated before initiating the study. Another study reported consideration of sample size without calculation. The mean (SD) sample size of all diagnostic studies was 172.6 (218.9). The median prevalence of the target condition was 50.5%. Conclusion: Only a few studies consider sample size in their methods. Inadequate sample sizes in diagnostic accuracy studies may result in misleading estimates of test accuracy. An improvement over the current standards on the design and reporting of diagnostic studies is warranted.

Personalised and Precision Medicine in Cancer Clinical Trials: Panacea for Progress or Pandora's Box?

Cancer clinical trials have been one of the key foundations for significant advances in oncology. However, there is a clear recognition within the academic, care delivery and pharmaceutical/biotech communities that our current model of clinical trial discovery and development is no longer fit for purpose. Delivering transformative cancer care should increasingly be our mantra, rather than maintaining the status quo of, at best, the often miniscule incremental benefits that are observed with many current clinical trials. As we enter the era of precision medicine for personalised cancer care (precision and personalised medicine), it is important that we capture and utilise our greater understanding of the biology of disease to drive innovative approaches in clinical trial design and implementation that can lead to a step change in cancer care delivery. A number of advances have been practice changing (e.g. imatinib mesylate in chronic myeloid leukaemia, Herceptin in erb-B2-positive breast cancer), and increasingly we are seeing the promise of a number of newer approaches, particularly in diseases like lung cancer and melanoma. Targeting immune checkpoints has recently yielded some highly promising results. New algorithms that maximise the effectiveness of clinical trials, through for example a multi-stage, multi-arm type design are increasingly gaining traction. However, our enthusiasm for the undoubted advances that have been achieved are being tempered by a realisation that these new approaches may have significant cost implications. This article will address these competing issues, mainly from a European perspective, highlight the problems and challenges to healthcare systems and suggest potential solutions that will ensure that the cost/value rubicon is addressed in a way that allows stakeholders to work together to deliver optimal cost-effective cancer care, the benefits of which can be transferred directly to our patients.

Postoperative pain control in cats: clinical trials with pre-emptive lidocaine epidural co-administered with morphine or methadone

To evaluate the effectiveness of epidural lidocaine in combination with either methadone or morphine for postoperative analgesia in cats undergoing ovariohysterectomy. Under general anesthesia, 24 cats that underwent ovariohysterectomy were randomly allocated into three treatments groups of eight each. Treatment 1 included 2% lidocaine (4.0 mg/kg); treatment 2 included lidocaine and methadone (4.0 mg/kg and 0.3 mg/kg, respectively); and treatment 3 included lidocaine and morphine (4.0 mg/kg and 0.1 mg/kg, respectively). All drugs were injected in a total volume of 0.25 ml/kg via the lumbosacral route in all cats. During the anesthetic and surgical periods, the physiological variables (respiratory and heart rate, arterial blood pressure and rectal temperature) were measured at intervals of time zero, 10 mins, 20 mins, 30 mins, 60 mins and 120 mins. After cats had recovered from anesthesia, a multidimensional composite pain scale was used to assess postoperative analgesia at 2, 4, 8, 12, 18, and 24 h after epidural. The time to first rescue analgesic was significantly (P <0.05) prolonged in cats that received both lidocaine and methadone or lidocaine and morphine treatments compared with those that received the lidocaine treatment. All cats that received lidocaine treatment alone required rescue analgesic within 2 h of epidural injections. All treatments had significant cardiovascular and respiratory changes but they were within acceptable range for healthy animals during the surgical period. The two combinations administered via epidural allowed ovariohysterectomy with sufficient analgesia in cats, and both induced prolonged postoperative analgesia.

Addressing missing participant outcome data in dental clinical trials

Missing outcome data are common in clinical trials and despite a well-designed study protocol, some of the randomized participants may leave the trial early without providing any or all of the data, or may be excluded after randomization. Premature discontinuation causes loss of information, potentially resulting in attrition bias leading to problems during interpretation of trial findings. The causes of information loss in a trial, known as mechanisms of missingness, may influence the credibility of the trial results. Analysis of trials with missing outcome data should ideally be handled with intention to treat (ITT) rather than per protocol (PP) analysis. However, true ITT analysis requires appropriate assumptions and imputation of missing data. Using a worked example from a published dental study, we highlight the key issues associated with missing outcome data in clinical trials, describe the most recognized approaches to handling missing outcome data, and explain the principles of ITT and PP analysis.

A study of sample size in making decisions about instructional materials /

Project No. 711151.01.