10. Study size

What to write

Explain how the study size was arrived at.

Explanation

A study should be large enough to obtain a point estimate with a sufficiently narrow confidence interval to meaningfully answer a research question. Large samples are needed to distinguish a small association from no association. Small studies often provide valuable information, but wide confidence intervals may indicate that they contribute less to current knowledge in comparison with studies providing estimates with narrower confidence intervals. Also, small studies that show ‘interesting’ or ‘statistically significant’ associations are published more frequently than small studies that do not have ‘significant’ findings. While these studies may provide an early signal in the context of discovery, readers should be informed of their potential weaknesses.

The importance of sample size determination in observational studies depends on the context. If an analysis is performed on data that were already available for other purposes, the main question is whether the analysis of the data will produce results with sufficient statistical precision to contribute substantially to the literature, and sample size considerations will be informal. Formal, a priori calculation of sample size may be useful when planning a new study1,2. Such calculations are associated with more uncertainty than implied by the single number that is generally produced. For example, estimates of the rate of the event of interest or other assumptions central to calculations are commonly imprecise, if not guesswork3. The precision obtained in the final analysis can often not be determined beforehand because it will be reduced by inclusion of confounding variables in multivariable analyses4, the degree of precision with which key variables can be measured5, and the exclusion of some individuals.

Few epidemiological studies explain or report deliberations about sample size6,7. We encourage investigators to report pertinent formal sample size calculations if they were done. In other situations they should indicate the considerations that determined the study size (e.g., a fixed available sample, as in the first example above). If the observational study was stopped early when statistical significance was achieved, readers should be told. Do not bother readers with post hoc justifications for study size or retrospective power calculations3. From the point of view of the reader, confidence intervals indicate the statistical precision that was ultimately obtained. It should be realized that confidence intervals reflect statistical uncertainty only, and not all uncertainty that may be present in a study (see 20. Interpretation).

Examples

“The number of cases in the area during the study period determined the sample size”8.

“A survey of postnatal depression in the region had documented a prevalence of 19.8%. Assuming depression in mothers with normal weight children to be 20% and an odds ratio of 3 for depression in mothers with a malnourished child we needed 72 case-control sets (one case to one control) with an 80% power and 5% significance”9.

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References

1.
Carlin J, Doyle L. Sample size. Journal of Paediatrics and Child Health. 2002;38(3):300-304. doi:10.1046/j.1440-1754.2002.00855.x
2.
Rigby AS, Vail A. Statistical methods in epidemiology. II: A commonsense approach to sample size estimation. Disability and Rehabilitation. 1998;20(11):405-410. doi:10.3109/09638289809166102
3.
Schulz KF, Grimes DA. Sample size calculations in randomised trials: Mandatory and mystical. The Lancet. 2005;365(9467):1348-1353. doi:10.1016/s0140-6736(05)61034-3
4.
Drescher K, Timm J, Jöckel K. The design of case‐control studies: The effect of confounding on sample size requirements. Statistics in Medicine. 1990;9(7):765-776. doi:10.1002/sim.4780090706
5.
Devine OJ, Smith JM. Estimating sample size for epidemiologic studies: The impact of ignoring exposure measurement uncertainty. Statistics in Medicine. 1998;17(12):1375-1389. doi:10.1002/(sici)1097-0258(19980630)17:12<1375::aid-sim857>3.0.co;2-d
6.
Pocock SJ, Collier TJ, Dandreo KJ, et al. Issues in the reporting of epidemiological studies: A survey of recent practice. BMJ. 2004;329(7471):883. doi:10.1136/bmj.38250.571088.55
7.
Tooth L. Quality of reporting of observational longitudinal research. American Journal of Epidemiology. 2005;161(3):280-288. doi:10.1093/aje/kwi042
8.
YADON ZE, RODRIGUES LC, DAVIES CR, QUIGLEY MA. INDOOR AND PERIDOMESTIC TRANSMISSION OF AMERICAN CUTANEOUS LEISHMANIASIS IN NORTHWESTERN ARGENTINA: A RETROSPECTIVE CASE-CONTROL STUDY. The American Journal of Tropical Medicine and Hygiene. 2003;68(5):519-526. doi:10.4269/ajtmh.2003.68.519
9.
Anoop S. Maternal depression and low maternal intelligence as risk factors for malnutrition in children: A community based case-control study from south india. Archives of Disease in Childhood. 2004;89(4):325-329. doi:10.1136/adc.2002.009738

Citation

For attribution, please cite this work as:
von Elm E, Altman DG, Egger M, Pocock SJ, Gøtzsche PC, Vandenbroucke JP. The STROBE reporting guideline for writing up observational studies in epidemiology. The EQUATOR Network guideline dissemination platform. doi:10.1234/equator/1010101

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Who reads research?

You work will be read by different people, for different reasons, around the world, and for decades to come. Reporting guidelines help you consider all of your potential audiences. For example, your research may be read by researchers from different fields, by clinicians, patients, evidence synthesisers, peer reviewers, or editors. Your readers will need information to understand, to replicate, apply, appraise, synthesise, and use your work.

Cohort studies

A cohort study is an observational study in which a group of people with a particular exposure (e.g. a putative risk factor or protective factor) and a group of people without this exposure are followed over time. The outcomes of the people in the exposed group are compared to the outcomes of the people in the unexposed group to see if the exposure is associated with particular outcomes (e.g. getting cancer or length of life).

Source.

Case-control studies

A case-control study is a research method used in healthcare to investigate potential risk factors for a specific disease. It involves comparing individuals who have been diagnosed with the disease (cases) to those who have not (controls). By analysing the differences between the two groups, researchers can identify factors that may contribute to the development of the disease.

An example would be when researchers conducted a case-control study examining whether exposure to diesel exhaust particles increases the risk of respiratory disease in underground miners. Cases included miners diagnosed with respiratory disease, while controls were miners without respiratory disease. Participants' past occupational exposures to diesel exhaust particles were evaluated to compare exposure rates between cases and controls.

Source.

Cross-sectional studies

A cross-sectional study (also sometimes called a "cross-sectional survey") serves as an observational tool, where researchers capture data from a cohort of participants at a singular point. This approach provides a 'snapshot'— a brief glimpse into the characteristics or outcomes prevalent within a designated population at that precise point in time. The primary aim here is not to track changes or developments over an extended period but to assess and quantify the current situation regarding specific variables or conditions. Such a methodology is instrumental in identifying patterns or correlations among various factors within the population, providing a basis for further, more detailed investigation.

Source

Systematic reviews

A systematic review is a comprehensive approach designed to identify, evaluate, and synthesise all available evidence relevant to a specific research question. In essence, it collects all possible studies related to a given topic and design, and reviews and analyses their results.

The process involves a highly sensitive search strategy to ensure that as much pertinent information as possible is gathered. Once collected, this evidence is often critically appraised to assess its quality and relevance, ensuring that conclusions drawn are based on robust data. Systematic reviews often involve defining inclusion and exclusion criteria, which help to focus the analysis on the most relevant studies, ultimately synthesising the findings into a coherent narrative or statistical synthesis. Some systematic reviews will include a meta-analysis.

Source

Systematic review protocols

TODO

Meta analyses of Observational Studies

TODO

Randomised Trials

A randomised controlled trial (RCT) is a trial in which participants are randomly assigned to one of two or more groups: the experimental group or groups receive the intervention or interventions being tested; the comparison group (control group) receive usual care or no treatment or a placebo. The groups are then followed up to see if there are any differences between the results. This helps in assessing the effectiveness of the intervention.

Source

Randomised Trial Protocols

TODO

Qualitative research

Research that aims to gather and analyse non-numerical (descriptive) data in order to gain an understanding of individuals' social reality, including understanding their attitudes, beliefs, and motivation. This type of research typically involves in-depth interviews, focus groups, or field observations in order to collect data that is rich in detail and context. Qualitative research is often used to explore complex phenomena or to gain insight into people's experiences and perspectives on a particular topic. It is particularly useful when researchers want to understand the meaning that people attach to their experiences or when they want to uncover the underlying reasons for people's behavior. Qualitative methods include ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis.

Source

Case Reports

TODO

Diagnostic Test Accuracy Studies

Diagnostic accuracy studies focus on estimating the ability of the test(s) to correctly identify subjects with a predefined target condition, or the condition of interest (sensitivity) as well as to clearly identify those without the condition (specificity).

Prediction Models

Prediction model research is used to test the accurarcy of a model or test in estimating an outcome value or risk. Most models estimate the probability of the presence of a particular health condition (diagnostic) or whether a particular outcome will occur in the future (prognostic). Prediction models are used to support clinical decision making, such as whether to refer patients for further testing, monitor disease deterioration or treatment effects, or initiate treatment or lifestyle changes. Examples of well known prediction models include EuroSCORE II for cardiac surgery, the Gail model for breast cancer, the Framingham risk score for cardiovascular disease, IMPACT for traumatic brain injury, and FRAX for osteoporotic and hip fractures.

Source

Animal Research

TODO

Quality Improvement in Healthcare

Quality improvement research is about finding out how to improve and make changes in the most effective way. It is about systematically and rigourously exploring "what works" to improve quality in healthcare and the best ways to measure and disseminate this to ensure positive change. Most quality improvement effectiveness research is conducted in hospital settings, is focused on multiple quality improvement interventions, and uses process measures as outcomes. There is a great deal of variation in the research designs used to examine quality improvement effectiveness.

Source

Economic Evaluations in Healthcare

TODO

Meta Analyses

A meta-analysis is a statistical technique that amalgamates data from multiple studies to yield a single estimate of the effect size. This approach enhances precision and offers a more comprehensive understanding by integrating quantitative findings. Central to a meta-analysis is the evaluation of heterogeneity, which examines variations in study outcomes to ensure that differences in populations, interventions, or methodologies do not skew results. Techniques such as meta-regression or subgroup analysis are frequently employed to explore how various factors might influence the outcomes. This method is particularly effective when aiming to quantify the effect size, odds ratio, or risk ratio, providing a clearer numerical estimate that can significantly inform clinical or policy decisions.

How Meta-analyses and Systematic Reviews Work Together

Systematic reviews and meta-analyses function together, each complementing the other to provide a more robust understanding of research evidence. A systematic review meticulously gathers and evaluates all pertinent studies, establishing a solid foundation of qualitative and quantitative data. Within this framework, if the collected data exhibit sufficient homogeneity, a meta-analysis can be performed. This statistical synthesis allows for the integration of quantitative results from individual studies, producing a unified estimate of effect size. Techniques such as meta-regression or subgroup analysis may further refine these findings, elucidating how different variables impact the overall outcome. By combining these methodologies, researchers can achieve both a comprehensive narrative synthesis and a precise quantitative measure, enhancing the reliability and applicability of their conclusions. This integrated approach ensures that the findings are not only well-rounded but also statistically robust, providing greater confidence in the evidence base.

Why Don't All Systematic Reviews Use a Meta-Analysis?

Systematic reviews do not always have meta-analyses, due to variations in the data. For a meta-analysis to be viable, the data from different studies must be sufficiently similar, or homogeneous, in terms of design, population, and interventions. When the data shows significant heterogeneity, meaning there are considerable differences among the studies, combining them could lead to skewed or misleading conclusions. Furthermore, the quality of the included studies is critical; if the studies are of low methodological quality, merging their results could obscure true effects rather than explain them.

Protocol

A plan or set of steps that defines how something will be done. Before carrying out a research study, for example, the research protocol sets out what question is to be answered and how information will be collected and analysed.

Source

Cohort_studies

In cohort studies, the investigators follow people over time. They obtain information about people and their exposures at baseline, let time pass, and then assess the occurrence of outcomes. Investigators commonly make contrasts between individuals who are exposed and not exposed or among groups of individuals with different categories of exposure. Investigators may assess several different outcomes, and examine exposure and outcome variables at multiple points during follow-up. Closed cohorts (for example birth cohorts) enrol a defined number of participants at study onset and follow them from that time forward, often at set intervals up to a fixed end date. In open cohorts the study population is dynamic - people enter and leave the population at different points in time (for example inhabitants of a town). Open cohorts change due to deaths, births, and migration, but the composition of the population with regard to variables such as age and gender may remain approximately constant, especially over a short period of time. In a closed cohort cumulative incidences (risks) and incidence rates can be estimated; when exposed and unexposed groups are compared, this leads to risk ratio or rate ratio estimates. Open cohorts estimate incidence rates and rate ratios.

Case_control_studies

In case-control studies, investigators compare exposures between people with a particular disease outcome (cases) and people without that outcome (controls). Investigators aim to collect cases and controls that are representative of an underlying cohort or a cross-section of a population. That population can be defined geographically, but also more loosely as the catchment area of health care facilities. The case sample may be 100% or a large fraction of available cases, while the control sample usually is only a small fraction of the people who do not have the pertinent outcome. Controls represent the cohort or population of people from which the cases arose. Investigators calculate the ratio of the odds of exposures to putative causes of the disease among cases and controls (see Item 16c). Depending on the sampling strategy for cases and controls and the nature of the population studied, the odds ratio obtained in a case-control study is interpreted as the risk ratio, rate ratio or (prevalence) odds ratio [@pmed-0040297-b016; @pmed-0040297-b017]. The majority of published case-control studies sample open cohorts and so allow direct estimations of rate ratios.

Cross-sectional_studies

In cross-sectional studies, investigators assess all individuals in a sample at the same point in time, often to examine the prevalence of exposures, risk factors or disease. Some cross-sectional studies are analytical and aim to quantify potential causal associations between exposures and disease. Such studies may be analysed like a cohort study by comparing disease prevalence between exposure groups. They may also be analysed like a case-control study by comparing the odds of exposure between groups with and without disease. A difficulty that can occur in any design but is particularly clear in cross-sectional studies is to establish that an exposure preceded the disease, although the time order of exposure and outcome may sometimes be clear. In a study in which the exposure variable is congenital or genetic, for example, we can be confident that the exposure preceded the disease, even if we are measuring both at the same time.