In statistics, stratified randomization is a method of sampling which first stratifies the whole study population into subgroups with same attributes or characteristics, known as strata, then followed by simple random sampling from the stratified groups, where each element within the same subgroup are selected unbiasedly during any stage of the sampling process, randomly and entirely by chance. Stratified randomization is considered a subdivision of stratified sampling, and should be adopted when shared attributes exist partially and vary widely between subgroups of the investigated population, so that they require special considerations or clear distinctions during sampling. This sampling method should be distinguished from cluster sampling, where a simple random sample of several entire clusters is selected to represent the whole population, or stratified systematic sampling, where a systematic sampling is carried out after the stratification process.
Steps for stratified random sampling Stratified randomization is extremely useful when the target population is heterogeneous and effectively displays how the trends or characteristics under study differ between strata. When performing a stratified randomization, the following 8 steps should be taken:
Define a target population. Define stratification variables and decide the number of strata to be created. The criteria for defining variables for stratification include age, socioeconomic status, nationality, race, education level and others and should be in line with the research objective. Ideally, 4-6 strata should be employed, as any increase in stratification variables will raise the probability for some of them to cancel out the impact of other variables. Use a sampling frame to evaluate all the elements in the target population. Make changes afterwards based on coverage and grouping. List all the elements and consider the sampling result. Each stratum should be mutually exclusive and add up to cover all members of the population, whilst each member of the population should fall into unique stratum, along with other members with minimum differences. Make decisions over the random sampling selection criteria. This can be done manually or with a designed computer program. Assign a random and unique number to all the elements followed by sorting these elements according to their number assigned. Review the size of each stratum and numerical distribution of all elements in every strata. Determine the type of sampling, either proportional or disproportional stratified sampling. Carry out the selected random sampling as defined in step 5. At minimum, one element must be chosen from each stratum so that the final sample includes representatives from every stratum. If two or more elements from each stratum are selected, error margins of the collected data can be calculated.
Stratified random assignment Stratified randomization may also refer to the random assignment of treatments to subjects, in addition to referring to random sampling of subjects from a population, as described above.
In this context, stratified randomization uses one or multiple prognostic factors to make subgroups, on average, that have similar entry characteristics. The patient factor can be accurately decided by examining the outcome in previous studies. The number of subgroups can be calculated by multiplying the number of strata for each factor. Factors are measured before or at the time of randomization and experimental subjects are divided into several subgroups or strata according to the results of measurements. Within each stratum, several randomization strategies can be applied, which involves simple randomization, blocked randomization, and minimization.
Simple randomization within strata Simple randomization is considered as the easiest method for allocating subjects in each stratum. Subjects are assigned to each group purely randomly for every assignment. Even though it is easy to conduct, simple randomization is commonly applied in strata that contain more than 100 samples since a small sampling size would make assignment unequal.
Block randomization within strata Block randomization, sometimes called permuted block randomization, applies blocks to allocate subjects from the same strata equally to each group in the study. In block randomization, allocation ratio (ratio of the number of one specific group over other groups) and group sizes are specified. The block size must be multiples of the number of treatments so that samples in each stratum can be assigned to treatment groups with the intended ratio. For instance, there should be 4 or 8 strata in a clinical trial concerning breast cancer where age and nodal statuses are two prognostic factors and each factor is split into two-level. The different blocks can be assigned to samples in multiple ways including random list and computer programming. Block randomization is commonly used in the experiment with a relatively big sampling size to avoid the imbalance allocation of samples with important characteristics. In certain fields with strict requests of randomization such as clinical trials, the allocation would be predictable when there is no blinding process for conductors and the block size is limited. The blocks permuted randomization in strata could possibly cause an imbalance of samples among strata as the number of strata increases and the sample size is limited, For instance, there is a possibility that no sample is found meeting the characteristic of certain strata.
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