Why Sample Size Matters in Medical Research
In medical research, we face a fundamental challenge: testing an entire population is rarely feasible or practical. As illustrated in many clinical trials (cohort and randomized controlled trials), it is necessary to deal with samples that are manageable and critically valid. This creates a delicate balance between resource allocation and statistical reliability.
The heart of good research resides in identifying the best number of subjects that is required to draw consequential conclusions. This optimization process is contingent upon consideration of several issues, such as, study design, anticipated results and current resources.
Just as we saw in recent clinical trials, where each participant can represent a significant investment of time and money, getting this calculation right from the start is crucial.
The Cost of Getting It Wrong
One of the most devastating realizations in research is discovering retrospectively that your study lacked sufficient statistical power due to inadequate sample size. Consider the real-world example from the CRASH trial, where each patient cost approximately $100 to study. At 2,000 patients, explained by an additional 8,000 patients not analyzed in the final analysis, the financial costs associated with decision on sample size are evident.
Outcomes of inaccurate sample size calculations go beyond monetary issues. Understaffed studies may fail to detect significant effects, while oversized studies waste valuable resources and potentially expose more participants than necessary to experimental conditions. This renders sample size calculation more than just a statistical task instead an unethical obligation.
Setting Up for Success: Prerequisites for Sample Size Calculation
Before calculating a sample size of a study, researchers must first establish a number of essential aspects of the study. The first step is identifying whether you’re working with qualitative data (like the presence or absence of a condition) or quantitative data (such as survival time in months). This irreducible difference will dictate which formulas and methods are appropriate.
Additionally, researchers need to consider:
| Prerequisite Factor | Key Considerations | Impact on Sample Size |
| Study Design | Cohort, Case-control, RCT | Affects calculation method |
| Primary Outcome | Continuous, Binary, Time-to-event | Determines formula choice |
| Expected Effect Size | Minimal clinically important difference | Influences required numbers |
| Resource Availability | Budget, time, personnel | Sets practical constraints |
Understanding the Core Components
Significance Level (α): Making Sense of Type I Error
The value of significance level, conventionally denoted as α, is one of the critical input parameters for sample size calculation. When we talk about a 95% confidence level, we’re actually working with an α of 0.05, meaning we’re willing to accept a 5% chance of incorrectly rejecting the null hypothesis. This decision has direct implications for sample size requirements.
Also its important to understand how modifying the confidence level changes the required sample size. Shifting from 95% confidence (α=0.05) to 99% confidence (α=0.01) can significantly augment the required sample size. This association demonstrates the rationale behind carefully balancing statistical rigor, when deciding on a significance level, and practical constraints.
Statistical Power: The Role of Type II Error (β)
Consider a scenario in which an HIV test gives a false negative result when the patient in fact has HIV. This false negative (Type II error) is accounted for by our power computation, which reduces the risk of such false negatives. Power, defined as 1-β, represents our ability to detect a true effect.
The relationship between power and sample size is direct but not linear. Consider the following typical power levels and their implications:
| Power Level | Sample Size Impact | Common Applications |
| 80% | Baseline standard | Most clinical trials |
| 90% | ~25% increase in N | Critical safety studies |
| 95% | ~50% increase in N | Regulatory submissions |
Effect Size: Determining Meaningful Differences
what constitutes a meaningful difference in sample size calculation is one of the most important factors a research must grasp always. In biomedical research, this is usually to identify the smallest change that would be at least minimally clinically important. For instance, in a survival studies example with GBM patients, we can consider a difference of 3 months between treatment groups to be meaningful this isnot an arbitrary recommendation but based on clinical significance in brain tumor treatment outcomes (from past studies).
The relationship between effect size and sample size is inverse: smaller effect sizes require larger sample sizes to detect with statistical confidence. This relationship can be demonstrated through a practical example from the table below:
| Effect Size | Required Sample Size* | Clinical Context |
| Large (0.8) | ~26 per group | Major symptom changes |
| Medium (0.5) | ~64 per group | Moderate therapeutic effects |
| Small (0.2) | ~393 per group | Subtle but important changes |
| *Based on 80% power and α=0.05 | ||
Population Variability: Working with Standard Deviations
Population variability, generally assessed by standard deviation, is an important factor in sample size calculation. In medical research the variability can be as useful as knowing a drug’s standard deviation of 8 months or 12 months and thus knowledge of such variability is particularly important for making reliable estimates.
The impact of variability on sample size follows a squared relationship – doubling the standard deviation quadruples the required sample size, assuming all other factors remain constant. Because of this relationship, well estimated variability must be obtained from pilot studies or previous work on an analogous population.
Calculating Sample Size for Quantitative Data
Single Population Studies
When studying a single population the main parameters are the target confidence level (Z-score), standard deviation, and the maximum allowable error margin.
For example, based on our example (99% confidence (Z 2.58):
n = (Z²σ²)/E²
n = (2.58² × 46²)/4²
n = 880
This computation provides us the necessary sample size to work with, it is, however, common to up this number in a practical setting, due to considerations other than just statistical sample size.
Comparing Two Groups
In a comparison between two groups, as we often do in survival studies, the evaluation is more intricate since we should take into account the variance of the two groups. Based on example with standard deviations of 8 and 12 months, with a goal sensitivity of 3-month interval, here is how to determine the sample:
| Component | Value | Rationale |
| Combined SD | 10.2 | Pooled from both groups |
| Effect Size | 3 months | Clinically meaningful difference |
| Power | 80% | Standard for clinical trials |
| Required N | 243 per group | Calculated total |
The used formula also considers variability of both groups, but with a maintained sufficient power to identify the required difference.
Working with Survival Data
In survival analysis research, such as treatment comparison, we must take into account not only the endpoint measurements, but also the time-to-event nature of the data. The calculation becomes more complex since we have to take into consideration not only the survival time for which we expect a certain value but also its uncertainty.
In survival data analysis we also have to take into account censoring where patients stop attending or the study is over before the event occurs. In an empirical strategy, the estimated number of subjects in the sample can be increased by a supposed censoring rate. For instance, if we expect 20% censoring in our GBM study, our base calculation of 243 patients per group should be adjusted:.
Adjusted N = Base N / (1 – censoring rate)
Adjusted N = 243 / (1 – 0.20) = 304 per group
Understanding Confidence Intervals and Their Impact
The dependence of confidence intervals on sample size is nicely described in our previous article on size determination, here however we do a breakdown of how the confidence intervals changed:
| Sample Size | Relative Risk | 95% CI | Interpretation |
| 10 | 1.5 | 0.4 – 5.4 | Very wide, inconclusive |
| 100 | 1.5 | 0.9 – 2.5 | Narrower, but still includes 1.0 |
| 1000 | 1.5 | 1.2 – 1.9 | Narrow, clearly significant |
This shows that larger sample sizes lead to narrower confidence intervals, allowing us to provide more accurate estimates of the actual effect.
Sample Size for Qualitative Data
Working with Proportions
In the case of qualitative data (e.g., anemia in lymphoma patients [30% prevalence], which are use case scenarios) the formulas change. We deal, rather than means and standard deviations, with proportions and with their expected difference. For a given margin of error (e.g., 4% and confidence level (95%, Z=1.96) the equation is:.
n = Z² × p(1-p) / d²
where:
p = expected proportion
d = desired precision
Calculating Size for Single Group Studies
In single group proportion studies (e.g., our anemia in lymphoma example), the estimation is based on precision of a single point estimate. The crux is to appreciate the dependence of the required sample size from the level of the desired precision:.
| Desired Precision | Confidence Level | Required Sample Size |
| ±4% | 95% | 504 |
| ±4% | 99% | 871 |
| ±2% | 95% | 2016 |
Two-Group Comparisons
When comparing two proportions, as in our diabetes and hypertension example (70% vs 40%, we need a more sophisticated approach. The calculation must account for both proportions and the desired detectable difference. Our example showed that detecting a 4% difference between these groups required 2,400 patients per group – a number that might surprise many researchers.
For example, to get an idea of how many such large numbers are required, one needs to consider the contribution of the baseline proportions to the sample size needs:
| Group 1 Proportion | Group 2 Proportion | Minimum Detectable Difference | Sample Size per Group |
| 70% | 40% | 4% | 2,400 |
| 50% | 40% | 4% | 2,892 |
| 20% | 10% | 4% | 1,891 |
The greater the proportion of specified target, the greater the sample size required to show a specified difference, and that is why 50% vs 40% is larger than 20% vs 10%.
Accounting for Expected Response Rates
In real-world studies, we must consider that, for a sample, not all potential subjects will actually contribute to the study and/or its completion. Our experience with clinical trials teaches us that response rates can significantly impact final sample sizes. In survey-based investigations and clinical trials that require continuous participation we are normally forced to recompute the sample size based on the estimated response rate:.
Final Sample Size = Calculated Sample Size / Expected Response Rate
For instance, if we require 500 final responses and assume a 70% response rate:.
Final Sample Size = 500 / 0.70 = 714 participants needed
Real-World Considerations
Adjusting for Attrition
Loss to follow-up (attrition) is a significant factor that should be taken into account in the sample size planning. From our clinical experience, it is known to us that dropouts can happen for various reasons, e.g., geographical change, loss of interest, or due to complicating factors that could result in dropout from the study. The CRASH trial example demonstrated this reality, where significant numbers of potential participants couldn’t be included in the final analysis.
In a practical scenario, it is reasonable to augment your calculated sample size by your estimated attrition rate and a small margin:
| Expected Attrition | Calculation Method | Example (base N=100) |
| 10% | N/(1-0.10) | 111 |
| 20% | N/(1-0.20) | 125 |
| 30% | N/(1-0.30) | 143 |
Accounting for Multiple Outcomes
When a study has several endpoints or outcomes the effect of these on our sample size calculation must be acknowledged. The idea is to estimate the sample size required for each outcome and to apply the larger value to guarantee sufficient power for all the analyses. Despite being conservative, this method can prevent underfitting to each of your key outcomes.
For example, if we were logging survival time (quantitative) as well as treatment response (qualitative), we would calculate:
- Sample size for survival time comparison
- Sample size for response rate comparison
- Use the larger of the two numbers
Learning from Previous Studies
Based on review of the existing literature, valuable data can be derived for sample size calculation. As discussed in so far, existing studies related to the past similar studies help us to estimate:
- Expected effect sizes
- Likely standard deviations
- Typical attrition rates
- Common challenges and pitfalls
This data may have a profound impact on the accuracy of our calculations as well as help avoid a very frequent and costly fare, the underpowered study.
Making Practical Adjustments
Additionally, we must address practical constraints while maintaining scientific rigor. Especially when limited by financial, e.g., $100 per patient, considerations, it is also necessary to assess statistical needs. Some practical approaches include:
- Using pilot studies to refine estimates
- Planning interim analyses to check assumptions
- Building in flexibility for sample size re-estimation
Although other design approaches, which could subsequently reduce the number of participants needed, are also available.
Just remember, the objective is not only to reach statistical significance, but to do valuable research that promotes medical knowledge, all the while minimizing resource consumption and complying with ethical guidelines.
This guide has provided a practical approach to sample determination calculation grounded in real-world setting and through illustrative examples. The key is how to reconcile statistical rigor and efficiency, and the key point of view is that with all the time being that the true goal is high quality research to make valuable contribution to the patient care.
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