Sample size clinical trials

In clinical research it is of particular interest to estimate a population mean on the basis of data collected from a sample of subjects employed in a randomized clinical trial. Sampling and statistical procedures facilitate the estimation of the population mean based on the sample mean and sample SD that are precisely calculated from the data collected in the trial. If we take a sample of 100 numbers from a population of 100,000 numbers and calculate the mean of those 100 numbers, this sample mean, which is precisely known, provides an estimate of the unknown population mean. If we then took another sample of 100 numbers, or indeed many samples, it is extremely unlikely that the numbers in any subsequent sample would be identical to those in the first sample, and it is unlikely that the calculated sample means would be identical to that of the first sample. Therefore, in a randomized clinical trial, a situation in which only one sample is taken from a population, a question that arises is What degree of certainty is there that the mean of that sample represents the mean of the population This question can be answered using statistical theory in conjunction with knowledge of the number of subjects participating in the trial, i.e., the sample size. 

The number of subjects planned to be enrolled, if more than one site the numbers of enrolled subjects projected for each trial site should be specified. Reason for choice of sample size include calculations of the statistical power of the trial, the level of significance to be used and the clinical justification. 

In pharmaceutical and medical device development, clinical trials are classified into four main phases designated with Roman numerals 1,11, III and lY The various phases of development trials differ in purpose, length and number of subjects involved. Phase I trials are conducted to determine safe dose levels of a medication, treatment or product (National Institutes of Health, 2002). The main purpose is often to determine an acceptable single dosage - how much can be given without causing serious side-effects. Phase I trials will also involve studies of metabolism and bioavailabity (Pocock, 1983). The sample size of a Phase 1 clinical trial is usually small, ranging from 10-80 subjects (National Institutes of Health, 2002 Pocock, 1983). 

Statistical methods are often employed to determine the study sample size and optimize power. Outlining the methods for calculating sample size and power for clinical trials is beyond the scope of this chapter. Interested readers are referred to texts by Chow and Liu (1998), Hulley and Cummings (1988), and Shuster (1990) for specific information on sample size and power estimation methods. 

Clinical trials are costly to conduct, and results are often critical to the commercial viability of a phytochemical product. Seemingly minor decisions, such as which measurement tool to use or a single entry criterion, can produce thousands of dollars in additional costs. Likewise, a great deal of time, effort and money can be saved by having experts review the study protocol to provide feedback regarding ways to improve efficiency, reduce subject burden and insure that the objectives are being met in the most scientifically sound and cost-effective manner possible. In particular, I recommend that an expert statistician is consulted regarding sample size and power and that the assumptions used in these calculations are reviewed carefully with one or more clinicians. It is not uncommon to see two studies with very similar objectives, which vary by two-fold in the number of subjects under study. Often this can be explained by differences in the assumptions employed in the sample size calculations. 

SHUSTER J J (1990) CRC handbook of sample size guidelines for clinical trials, Boston, CRC Press. 

Unfortunately, clinical trials in human volunteers usually have small sample sizes and adverse reactions are poorly documented. Also, adverse effects that have a long latency period such as carcinogenicity are difficult to account for. 

All drugs will pose some degree of risk, and completed clinical trials are the primary source of information in this subject. Clinical trials do, of course, have limitations. The principal one concerns the everpresent problem of sample size. Rare side effects, if they exist, cannot generally be detected in clinical trials involving limited numbers of patients. Adverse drug reports and case-reports provide early clues to such effects so-called pharmacoepidemiology studies may be mounted to evaluate such risks. 

The impact of these considerations on study subject selection, sample size and endpoint measures will need to figure in future clinical trial designs. 

Clinical trials generate vast quantities of data, most of which are processed by the sponsor. Assessments should be kept to the minimum that is compatible with the safety and comfort of the subject. Highest priority needs to be given to assessment and recording of primary endpoints, as these will determine the main outcome of the study. The power calculation for sample size should be based on the primary critical endpoint. Quite frequently, trials have two or more evaluable endpoints. It must be stated clearly in the protocol whether the secondary endpoints are to be statistically evaluated, in which case power statements will need to be given, or are simply... 

The aim of any clinical trial is to have low risk of Type I and II errors and sufficient power to detect a difference between treatments, if it exists. Of the three factors in determining sample size, the power (probability of detecting a true difference) is arbitrarily chosen. The magnitude of the drug s effect can be estimated with more or less accuracy from previous experience with drugs of the same or similar action, and the variability of the measurements is often known from published experiments on the primary endpoint, with or without the drug. These data will, however, not be available for novel substances in a new class and frequently the sample size in the early phase of development has to be chosen on an arbitrary basis. 

To illustrate the use of the formula suppose we are designing a trial to compare treatments for the reduction of blood pressure. We determine that a clinically relevant difference is 5 mmHg and that the between-patient standard deviation 0 is 10 mmHg. At)q)e-1 error is set at 0.05 and the type-11 error at 0.20. Then the required sample size, per group, is... 

There are of course practical considerations in clinical research. We may find patient recruitment difficult in single centre studies and this is one of the major drivers to multicentre and multinational trials. Alternatively, we may need to relax the inclusion/exclusion criteria or lengthen the recruitment period. Unfortunately, while each of these may indeed increase the supply of patients they may also lead to increased variability that in turn will require more patients. A second issue is the size of the CRD which, if it is too small, will require a large number of patients. In such circumstances we may need to consider the use of surrogate endpoints (Section S.3.3.2). Finally, the standard deviation may be large and this can have a considerable impact on the sample size - for example, a doubling of the standard deviation leads to a four times increase in the... 

Sample sizes for clinical trials are discussed more fully elsewhere in this book and should be established in discussion with a statistician. Sample sizes should, however, be sufficient to be 90% certain of detecting a statistically significant difference between treatments, based on a set of predetermined primary variables. This means that trials utilising an active control will generally be considerably larger than placebo-controlled studies, in order to exclude a Type II statistical error (i.e. the failure to demonstrate a difference where one exists). Thus, in areas where a substantial safety database is required, for example, hypertension, it may be appropriate to have in the programme a preponderance of studies using a positive control. 

The size required of the sample to identify a meaningful economic difference is frequently problematic. Often those setting up clinical trials focus on the primary clinical question when developing sample-size estimates. They fail to consider the fact that the sample required to address the economic questions posed in the trial may differ from that needed for the primary clinical question. In some cases the sample size required for the economic analysis is smaller than that required to address the clinical question. More often, however, the opposite is true, in that the variances in cost and patient preference data are larger than those for clinical data. Then one needs to confront the question of whether it is either ethical... 

The types of data available at the end of a clinical trial will depend upon the trial s sample size, duration, and clinical endpoint. There are two categories of clinical endpoints considered in pharmacoeco-nomic analysis intermediate endpoints and final endpoints. An intermediate endpoint is a clinical parameter, such as systolic blood pressure, which varies as a result of therapy. A final endpoint is an outcome variable, such as change in survival, or quality-adjusted survival, that is common to several economic trials, which allows for comparisons of economic data across clinical studies and is of relevance to policy makers. 

Willan AR. Analysis, sample size, and power for estimating incremental net health benefit for clinical trial data. Control Clin Trials 2001 22 228-37. 

Imagine that this is a real clinical trial setting and our objective is to find out the value of the mean diastolic blood pressure in the population (but remember because this is a computer simulation we know the answer ). So let s take a sample of size 50. 

In large trials and with events that are rare the OR and RR give very similar values. In fact we can see this in the trastuzumab example where the OR was 1.51 and the RR was 1.47. In smaller trials and with more common events, however, this wHl not be the case. Comparable values for the OR and the RR arise more frequently in cohort studies where generally the sample sizes are large and the events being investigated are often rare, and these measures tend to be used interchangeably. As a result there seems to be some confusion as to the distinction and it is my experience that the OR and RR are occasionally labelled incorrectly in clinical research papers, so take care. 

Suppose now that the trial in the example were a trial in which a difference of 0.5 mmol/1 was viewed as an important difference. Maybe this reflects the clinical relevance of such a difference or perhaps from a commercial standpoint it would be a worthwhile difference to have. Under such circumstances only having 62.3 per cent power to detect such a difference would be unacceptable this corresponds to a 37.7 per cent type II error, an almost 40 per cent chance of failing to declare significant differences. Well, there is only one thing you can do, and that is to increase the sample size. The recalculated values for power are given in Table 8.3 with a doubling of the sample size to 100 patients per group. 

In a placebo-controlled hypertension trial, the primary endpoint is the fall in diastolic blood pressure. It is required to detect a clinically relevant difference of 8 mmHg in a 5 per cent level test. Fiistorical data suggests that CT= 10 mmHg. Table 8.4 provides sample sizes for various levels of power and differences around 8 mmHg the sample sizes are per group. 

The CONSORT statement (Moher et al. (2001)) sets down standards for the reporting of clinical trials and their recommendations in relation to the sample size calculation are in line with these points. 

Clearly the main advantage of a non-parametric method is that it makes essentially no assumptions about the underlying distribution of the data. In contrast, the corresponding parametric method makes specific assumptions, for example, that the data are normally distributed. Does this matter Well, as mentioned earlier, the t-tests, even though in a strict sense they assume normality, are quite robust against departures from normality. In other words you have to be some way off normality for the p-values and associated confidence intervals to be become invalid, especially with the kinds of moderate to large sample sizes that we see in our trials. Most of the time in clinical studies, we are within those boundaries, particularly when we are also able to transform data to conform more closely to normality. 

---