Cross-Sectional Design

Cross-Sectional Design in Health Economic Evidence

A cross-sectional study takes one look at each person in a sample, so everything it reports describes the population as it stands on the survey date. Health economists depend on this kind of evidence more than its modest standing in epidemiology suggests, because prevalence estimates for budget impact, the population health surveys behind age-specific EQ-5D norms, the public surveys used to value health states, and regressions of cost on patient characteristics are often built from single snapshots. A snapshot cannot settle questions about cause or change over time, and prevalent-case samples can mislead a model built for newly diagnosed patients. An illustrative worked example shows how much a baseline utility can shift when it is taken from prevalent rather than incident cases.

One measurement occasion per person

The defining feature is the timing of measurement, whatever the size of the sample or the length of the fieldwork. Each participant contributes data on one occasion, and exposures, outcomes and covariates are recorded together. The STROBE reporting guideline treats the design as one of the three main types of observational study, notes that "prevalence study" is used as a synonym, and describes investigators assessing all individuals in a sample at the same point in time, often to examine the prevalence of exposures, risk factors or disease.

STROBE also separates descriptive cross-sectional studies from analytical ones that aim to quantify potential causal associations. The distinction matters in health economics, because the same survey can supply a descriptive input (how many adults report a condition) and an analytical one (how much higher costs are among those who report it). A survey repeated each year with fresh samples, such as the Health Survey for England, is a series of cross-sections. It tracks the population over time but does not follow the same people, which is what a longitudinal design does.

Where snapshot evidence enters health economics

Cross-sectional data appear at several points in economic evaluation and health policy analysis. The uses below differ in what they take from the snapshot, and so in how exposed they are to its limits.

Prevalence and population size. Estimates of prevalence set the number of people eligible for a technology in a budget impact analysis. Uptake is a separate market-share assumption applied to that eligible population, and incidence is needed to add the new patients who become eligible each year.

Prevalence-based cost-of-illness studies. The prevalence-based approach to a cost-of-illness study, which the linked page contrasts with incidence-based costing, often rests on a cross-sectional design. A scoping review of cost-of-illness studies in rare diseases found that 59 of 63 studies (94%) used prevalence-based estimation, most often with a retrospective cross-sectional design. A review of cost-of-illness methods by Akobundu and colleagues found regression and matched-control methods among the four approaches used to estimate costs; both attribute cost to a condition by comparing people with and without it, usually in one period's data.

Health surveys and population utility norms. The Health Survey for England is a series of annual surveys of people living in private households in England. A report for the NICE Decision Support Unit estimated EQ-5D-3L values by age and sex from the 2014 wave, using 7,085 adult respondents with complete EQ-5D-3L responses, and took the survey's clustering, stratification and weighting into account. Ara and Brazier pooled four consecutive waves to compare the health state utility values of respondents with and without prevalent conditions.

Valuation studies. The value sets that turn EQ-5D descriptions into utilities come from one-off surveys of the public. The original UK EQ-5D-3L tariff was modelled from time trade-off valuations of 42 health states elicited from a representative sample of the UK population, and a regression model interpolated values for the remaining states to form the value set. The values therefore reflect one sample's preferences at the time of fieldwork, which is one reason value sets are re-estimated over time and for other populations.

Cost regressions. Analysts often regress annual cost on age, sex, comorbidity and condition status in a single year of survey or administrative data. Such cost data are skewed, contain many zeros and have heavy right tails, which is why a review of statistical methods for healthcare costs compared approaches such as generalised linear models and two-part models. That review focused on randomised trials, although it notes that the methods often apply more widely.

Analysing a sample taken at one time

Large health surveys rarely use simple random samples, so the analysis has to reflect how the sample was drawn. STROBE asks cross-sectional studies to describe analytical methods that take account of the sampling strategy, and the Health Survey for England supplies weights that adjust for selection, non-response and the population profile. A weighted prevalence estimate is calculated as follows.

$$\hat{P}_w = \frac{\sum_{i=1}^{n} w_i y_i}{\sum_{i=1}^{n} w_i}$$

where $\hat{P}_w$ is the weighted prevalence, $n$ is the number of respondents, $w_i$ is the survey weight of respondent $i$, and $y_i$ equals 1 if respondent $i$ has the condition and 0 otherwise.

Clustering and weighting usually widen confidence intervals compared with a simple random sample of the same size. The Health Survey for England methods report expresses this through the design factor, the ratio of the standard error under the complex design to that of a simple random sample of the same size, and STROBE describes the related design effect as a ratio measure of how much precision is gained or lost under a more complex sampling strategy. Associations from a cross-section are often reported as a prevalence ratio or a prevalence odds ratio, and STROBE notes that both may be useful in some situations.

Why a snapshot cannot settle causal or dynamic questions

Most limits of the design follow from the single time point. Exposure and outcome are observed together, and the sample contains only the people who are alive, reachable and still affected on the survey date. Where condition status is self-reported, misclassification adds a further source of error.

Temporality. STROBE notes that establishing that an exposure preceded the disease is particularly difficult in cross-sectional studies. The Health Survey for England methods report gives a concrete warning that associations do not necessarily imply causality, that current liver disease may reflect past heavy drinking by someone who no longer drinks, and that current behaviour may be a response to advice about an existing condition. A cross-sectional regression of cost or utility on a risk factor can therefore reflect reverse causation rather than an effect of the risk factor, which limits its use for causal inference.

Length-biased sampling of prevalent cases. Prevalence reflects both how often a condition starts and how long it lasts. In a steady state, where incidence, duration and the size of the population are stable and there is no net migration of cases, the prevalence odds equal the incidence rate multiplied by the mean duration, as follows.

$$\frac{P}{1 - P} = I \times \bar{D} \quad \text{so} \quad P \approx I \times \bar{D} \ \text{when} \ P \ \text{is small}$$

where $P$ is the point prevalence, $I$ is the incidence rate in the population at risk and $\bar{D}$ is the mean duration of the condition, measured from diagnosis to recovery or death. The simpler form holds when $(1 - P)$ is close to 1, which is why the approximation is limited to prevalence below about 0.11. People with long-lasting forms are therefore over-represented among prevalent cases. Simon described this as length-biased sampling of living patients. The related Neyman bias, also called prevalence-incidence bias, arises when a risk factor affects mortality from the disease being studied, and so the duration of prevalent cases, making an association seen among prevalent cases spurious.

Survivor and coverage bias. People who died before the survey cannot appear in it, and those outside the sampling frame are missing too. The Health Survey for England excludes people living in institutions, and its methods report notes that this population is likely to be older and, on average, less healthy than people in private households.

No transitions. A single snapshot of different people cannot show how individuals move between health states. A Markov model needs transition probabilities, which are usually estimated from repeated observation of the same individuals. Cross-sectional data can inform them only indirectly, through calibration or back-calculation under strong assumptions.

Worked example of a utility baseline taken from prevalent cases

The figures below are illustrative. A chronic condition has an incidence of 2 per 1,000 person-years, and half of new cases are mild and half severe. Mild cases last 10 years on average, severe cases 2 years because of higher mortality, and the mean utility is 0.80 in mild cases and 0.50 in severe cases. Utility is assumed constant over the disease course within each subgroup. A modeller building a model for newly diagnosed patients finds a cross-sectional survey reporting the mean utility of everyone currently living with the condition.

1. Prevalence by subgroup. Using the steady-state approximation for each subgroup, with an incidence of 0.001 per person-year in each, prevalence is as follows.

$$P_{mild} = 0.001 \times 10 = 0.010, \quad P_{severe} = 0.001 \times 2 = 0.002$$

where $P_{mild}$ and $P_{severe}$ are the point prevalences of the two forms. Total prevalence is 0.012, or 1.2%, well below the 0.11 limit for the approximation.

2. Composition of the prevalent pool. Mild cases make up 0.010 / 0.012, or five sixths (83.3%), of people found in the survey, against half of new cases.

3. Mean utility in the survey. The cross-sectional mean weights each subgroup by incidence multiplied by duration, as follows.

$$\bar{u}_{prev} = \frac{0.010 \times 0.80 + 0.002 \times 0.50}{0.012} = \frac{0.009}{0.012} = 0.75$$

where $\bar{u}_{prev}$ is the mean utility among prevalent cases.

4. Mean utility at diagnosis. New cases are weighted by incidence alone, as follows.

$$\bar{u}_{inc} = \frac{0.001 \times 0.80 + 0.001 \times 0.50}{0.002} = \frac{0.0013}{0.002} = 0.65$$

where $\bar{u}_{inc}$ is the mean utility among incident cases.

5. Interpretation. Taking the survey mean as the starting utility overstates the health of the newly diagnosed cohort by 0.10, and the survey understates the share of severe cases at onset (one sixth against one half), which would also understate costs if severe cases cost more. Survey weights do not remove the gap, because it comes from who is alive and ill on the survey date, not from how the sample was drawn. Reweighting each prevalent case by the inverse of the mean duration of its subgroup restores the onset mix, since 0.833 divided by 10 and 0.167 divided by 2 both give about 0.083, an even split. The direction of the gap depends on the constant-utility assumption. If utility declines with time since diagnosis, long-duration cases are sampled late in their course and the prevalent-case bias can reverse.

Feeding cross-sectional estimates into decision models

Most cross-sectional inputs to a decision model are baselines and population quantities rather than treatment effects. The modelling question is whether the snapshot describes the same population, and the same point in the disease course, as the modelled cohort.

For baseline utilities, the NICE manual (PMG36) states that baseline values extrapolated over long time horizons should be adjusted for the decline in health-related quality of life seen in the general population, should not exceed general population values at a given age, should rest on a recent and robust source of population data, and that a multiplicative approach is generally preferred. Working with a cardiovascular disease model, Ara and Brazier found that assuming a baseline of perfect health ignores the natural decline in quality of life with age and overestimates treatment benefits. In a later analysis of pooled survey data they suggested that, if condition-specific data are not available, general population values would not be an appropriate baseline for cohorts with just one condition, for whom data from respondents reporting no prevalent condition may be more appropriate.

An age profile read across a cross-section compares different people at different ages, not the same people ageing, and it reflects conditions at the time of fieldwork. The Decision Support Unit report found a less clear relationship between age and EQ-5D in a survey whose fieldwork coincided with the early stages of the Covid-19 lockdown, driven by the anxiety or depression dimension and, to a lesser extent, self-care, and for consistency recommended the 2014 Health Survey for England values, which directly observe EQ-5D-3L.

Cross-sectional, cohort and case-control designs compared

The three designs covered by STROBE differ in how they sample people and in what they measure directly. The table summarises the contrasts most relevant to economic models.

Common misreadings of cross-sectional results

Errors with cross-sectional evidence usually come from asking it a longitudinal question. A cost difference between people with and without a condition is an association that may include confounding and reverse causation, so it is not automatically the cost a prevention programme would save. A falling age gradient in utility mixes ageing with differences between birth cohorts and with the circumstances of the survey year.

Utilities, costs and severity mixes measured in prevalent cases over-represent long-duration survivors and need adjustment before use in an incident cohort, as the worked example shows. Unweighted analyses of complex surveys can misstate prevalence and give confidence intervals that are too narrow. A series of annual cross-sections shows how the population changes but not which individuals moved between states, so it is no substitute for panel data.

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