Sample size in social contact surveys for epidemic modelling

This study analyzes existing social contact surveys and uses simulations to demonstrate that while small samples yield highly variable reproduction number estimates, a minimum sample size of approximately 1,200–1,300 participants is sufficient to achieve reliable precision for epidemic modeling, with diminishing returns observed beyond 3,000 individuals.

The Gist

Imagine you are trying to predict how fast a rumor will spread through a giant school. To do this, you need to know: Who talks to whom?

This paper is about figuring out the perfect number of students you need to interview to get a clear picture of that rumor-spreading network, without wasting time or money.

Here is the breakdown of the research in simple terms:

1. The Problem: Guessing the Size of the Crowd

Scientists use "social contact surveys" to map out who touches, talks to, or sits near whom. These maps are crucial for predicting how diseases (like the flu or COVID) will spread.

However, researchers have been guessing how many people to ask. Some surveys asked just 30 people; others asked 10,000. It was like trying to guess the weather by looking at one cloud versus looking at the whole sky. There was no standard rule, and often, the surveys were too small to be reliable, or too big and wasteful.

2. The Experiment: The "Subsampling" Game

The authors took two massive, real-world datasets (one from the UK and one from across Europe) that had thousands of participants. They treated these huge datasets like a giant jar of mixed jellybeans.

Then, they played a game:

• They took out a tiny handful (200 people) and tried to guess the "spread potential" (how fast a disease would move).
• Then they took a medium handful (1,000 people).
• Then a huge handful (5,000 people).

They did this hundreds of times to see how much their answers changed based on the size of the handful.

3. The Results: The "Goldilocks" Zone

The results were very clear, and they found a "Goldilocks" zone for the sample size:

• Too Small (Under 200 people): This is like trying to guess the average height of a basketball team by measuring just two people. The results were all over the place. Sometimes the disease looked like it would die out; other times, it looked like it would explode. The data was too shaky to trust.
• The Sweet Spot (Around 1,200–1,300 people): Once they reached about 1,300 people, the answers started to settle down. The "noise" disappeared, and the picture became clear. Adding more people after this point didn't change the answer very much.
• Too Big (Over 3,000 people): Asking 5,000 or 10,000 people gave slightly more precise answers, but the improvement was tiny. It was like adding a drop of water to a full bucket. It's a lot of extra work for almost no extra benefit.

4. The Analogy: The Concert Crowd

Think of a social contact survey like trying to figure out the vibe of a massive concert crowd.

• If you ask 5 people, you might just happen to ask a group of friends who are all standing in the corner. You'd think the whole crowd is quiet.
• If you ask 1,300 people scattered all over the venue, you get a true mix of the mosh pit, the VIP section, and the back row. You get a reliable picture of the whole event.
• If you ask 10,000 people, you are still just getting that same picture, but you've spent hours interviewing people who didn't add any new information.

5. The Conclusion: What Should We Do?

The authors are saying: "Stop guessing."

If you are a government or health official planning a study to track disease risks, you don't need to interview 10,000 people, but you definitely shouldn't stop at 200.

The Rule of Thumb: Aim for 1,200 to 1,300 participants.

• This is enough to give you a reliable map of how people mix.
• It saves money and time.
• It prevents panic caused by bad data (like thinking a disease is spreading fast when it's actually just a fluke in a tiny sample).

In short, this paper gives scientists a ruler to measure their surveys, ensuring that when they predict the next epidemic, they are looking at the whole picture, not just a blurry snapshot.

Technical Summary

1. Problem Statement

Social contact surveys are critical for estimating the basic reproduction number ($R_0$) and informing infectious disease transmission models. These surveys measure "who-contacts-whom," providing the empirical data necessary to parameterize age-structured mixing matrices.

However, a significant gap exists in the design of these surveys:

• Lack of Standardization: Sample sizes in published surveys are typically determined by pragmatic constraints (budget, logistics, recruitment channels) rather than formal statistical power calculations.
• Inapplicability of Traditional Methods: Standard epidemiological sample size calculations (based on detecting effect sizes between groups) do not apply here because these surveys are observational and aim to characterize complex, high-dimensional contact patterns rather than test a single hypothesis.
• Uncertainty in Estimates: It is unclear how small sample sizes impact the precision of derived epidemic metrics (specifically $R$), potentially leading to unreliable policy decisions. Conversely, excessively large samples may be inefficient and burdensome.

2. Methodology

The authors employed a two-pronged approach combining a systematic review with simulation-based sensitivity analysis.

A. Rapid Review of Current Practice

• Search Strategy: A PubMed search (Jan 2008 – March 2025) for English-language articles using keywords related to "social contact," "survey," and "infectious disease."
• Inclusion Criteria: Primary reports of human social contact data specifically for infectious disease transmission.
• Data Extraction: Extracted sample sizes and survey settings from 57 studies, representing 107 unique surveys.

B. Simulation of Sample Size Impact

To quantify the relationship between sample size and the precision of $R$ estimates, the authors used two large, established datasets:

1. POLYMOD: A 2005 survey of 7,290 individuals across 8 European countries.
2. UK Social Contact Survey (UKSCS): A 2010 survey of 5,861 individuals in the UK.

Simulation Protocol:

• Resampling: Repeated random subsamples (without replacement) were drawn from the full datasets, ranging from $N=100$ to the full dataset size.
• Replication: 200 random samples were generated for each target sample size.
• Estimation Methods: Two distinct methods were used to calculate the reproduction number to test robustness:
  1. Dominant Eigenvalue Method (POLYMOD): Used to calculate the population reproduction number from an age-specific contact matrix (10-year age bands).
  2. Sum of Squared Individual $R$ (UKSCS): Used to calculate heterogeneity in individual reproduction numbers (since age of contact was not recorded in UKSCS).
• Metrics: For each sample size, the authors calculated the mean, standard deviation (SD), range, and the Kolmogorov-Smirnov (KS) statistic (measuring the distance between the cumulative distribution of the subsample $R$ and the full dataset $R$).

3. Key Contributions

• First Quantitative Assessment: This is the first study to systematically evaluate how sample size affects the uncertainty of reproduction number estimates derived from social contact data.
• Identification of a "Sweet Spot": The study moves beyond arbitrary sample sizes to propose a data-driven target range (1,200–1,300 participants) that balances precision with logistical feasibility.
• Methodological Comparison: It highlights how survey design (e.g., recording groups vs. individuals) and analysis methods (matrix eigenvalues vs. individual sums) influence the required sample size and the resulting variance.

4. Key Results

Current Practice Analysis

• Sample Size Variability: The review of 107 surveys revealed a massive range in sample sizes, from 30 (pilot studies) to >10,000 (embedded in national censuses).
• Median Size: The median sample size was 1,438.
• Prevalence of Small Samples: 25% of surveys had fewer than 1,000 participants, and 75% had fewer than 2,500.

Simulation Findings

• High Variability at Low $N$: Sample sizes below 200 resulted in highly variable $R$ estimates.
  • POLYMOD (Eigenvalue): $R$ ranged from 0.87 to 1.3.
  • UKSCS (Sum of Squares): $R$ ranged from 0 to 6.8 (indicating extreme instability).
• Diminishing Returns:
  • 1,200–1,300 Participants: This range represents the point of maximum meaningful gain in precision. The KS statistic (distributional difference) dropped significantly below this threshold.
  • >3,000 Participants: Increasing the sample size beyond 3,000 yielded only marginal improvements in precision (small reductions in SD).
• Method Sensitivity: The UKSCS method (sum of squares) showed higher variability and required larger samples to stabilize compared to the POLYMOD matrix approach, likely due to the heavy-tailed nature of contact distributions and the ability to report contact groups.

5. Significance and Implications

• Guidance for Public Health: The authors recommend a minimum target sample size of 1,200–1,300 participants for general-purpose social contact surveys used in epidemic modelling. This ensures sufficient confidence in the derived $R$ estimates without incurring the diminishing returns of larger samples.
• Policy and Reporting: The study advocates for the inclusion of sample size justifications in the design and reporting of future surveys. Surveys with fewer than 1,000 participants should be interpreted with caution when used for policy decisions.
• Pandemic Preparedness: Reliable early estimates of $R$ are crucial for pandemic response (e.g., assessing the impact of non-pharmaceutical interventions). Establishing a standard minimum sample size improves the comparability of data across different settings and time periods, strengthening the evidence base for coordinated public health decisions.
• Limitations Acknowledged: The authors note that while sample size is critical, it cannot fix data quality issues such as survey fatigue, underreporting, or demographic bias. Furthermore, the 1,300 target is based on 10-year age bands; finer-grained models may require larger samples.