Sample size in clinical and experimental trials

Investigative clinical-epidemiological or experimental studies have the objectives of describing phenomena or comparing the behavior of variables in subgroups of a population. To accomplish those objectives, the population universe is not studied in its entirety, usually because it is not accessible or viable, but mainly because it is not necessary, when a representative sample is available for correlations with the target population1,2. The sample planning of a study determines the numerical dimension and also the sampling technique (collection/selection) of the elements of the study. It is essential in the elaboration of the project, and problems with such planning may compromise the final data analysis and interpretation of its results. A proper sample planning depends on basic knowledge of the study statistics and deep knowledge of the problem under investigation, in order to combine the statistical significance of the tests with the clinical meaning of the results1,3,4. Most biostatistical tests assume that the study sample is probabilistically representative of the population. Some samples of convenience, e.g. like choosing consecutive patients of a specific outpatient clinic, may not properly represent all the study population. The investigator should be alert to possible selection biases resulting from the availability of patients in consecutive sampling, because increasing sample size would not correct the effect of biased samples. In addition, strategies of non-probability stratified sampling, by using sample quotas, complex sampling (conglomerates, multi-levels), voluntary response, saturation of variables, “snowball” type or by using non-randomized methods of data collection should be designed, sized and analyzed with expert statistical support. This paper discusses the principles of simple random sample size calculations4. The selection of a population fraction that makes up the study sample implies the investigator will assume a certain degree of error for the estimated values of population parameters to each variable; such sample error is quantifiable, and inversely proportional to the sample size4,5. In order to describe the population estimate represented by a quantitative variable (discrete or continuous), one should obtain the population standard deviation of that variable and determine the significance level of the estimate and the maximum tolerable sample error (in units of mean value) (Chart 1)2. In order to describe the population estimate represented by a qualitative variable (nominal or ordinal), one should obtain the population frequency of the variable results and determine the significance level of the estimate and the maximum tolerable sample error (in percentage) (Chart 1). When a qualitative variable is not dichotomic, sample sizing should be considered for the proportion of each category that constitutes the variable4. When the population standard deviation or frequencies of the variable are unknown, and the literature does not present any similar data, a pre-test should be conducted with 30-40 subjects and the behavior of this subgroup should be considered as the population estimate2.