chapt 2

crude rates, direct and indirect standardisation, CMF, SMR, and internal versus external standardisation

Disease map

Provides instant visual information on the variation of a disease throughout space.

Pitfalls of mapping health indicators

Naive mapping can mislead: shadings, scaling of the mapped quantity, number of risk classes and their delimitation must be chosen with care (depends on range of variation, precision of estimates, comparability across maps); regions in observational data are not necessarily comparable.

Pennsylvania lung cancer data (pennLC)

R package SpatialEpi: population (2000 census), lung cancer cases (2002) and smoking proportions for Pennsylvania counties; list with geo (centroids), data (cases/population by county, race, gender, age), smoking, spatial.polygon.

Issues with crude counts

Interpretation is limited: population density is not accounted for (dense at-risk populations yield more cases), so counts cannot express increased risk in a region.

Incidence rate (IR, crude rate)

Number of new cases in a population of disease-free individuals over a specific period: IR = total cases observed in study period / total number of people at risk; often reported per 1,000, 10,000, 100,000.

Why are regions not comparable (age)?

Most diseases affect certain age groups disproportionately (cancer incidence rises with age); regions can differ in age distribution.

Why is the crude rate 'crude'?

It does not take the composition (e.g. age distribution) of the population into account; differences between regions may reflect different age distributions rather than different age-specific risk.

Standardization

Mechanism to adjust summary rates to remove the effect of known risk factors (e.g. age) so rates of different populations are comparable; needed because populations are heterogeneous (age, gender, education, religion, genetics, diet, …).

Standard population

Reference population used to minimize the influence of age (or other factors); can be a superpopulation containing the study population (Belgian, European, world population) or the total subpopulation of interest.

Notation for standardization

G age groups g; ygi = cases in group g for study population i; ngi = people at risk; rgi = ygi/ngi = age-specific incidence proportion; yi = Σg ygi; ni = Σg ngi; superscript S denotes the same quantities for the standard population.

Direct standardisation: question

How many cases would we observe in the standard population if the observed age-specific rates of the study population applied?

Direct standardisation: expected cases

E^S_gi = rgi · n^S_g = (ygi/ngi) · n^S_g for each age group g.

Directly standardised rate

Σg E^S_gi / Σg n^S_g = Σg (ygi/ngi)·n^S_g / Σg n^S_g: a weighted average of the study population's age-specific rates, with weights = numbers at risk per group in the standard population.

Comparative mortality figure (CMF)

CMFi = Σg E^S_gi / Σg y^S_g: expected cases in the standard population under the study area's age-specific rates over the actually observed cases in the standard population.

Relation CMF and directly standardised rate

Directly standardised rate = CMFi × crude incidence proportion of the standard population (Σg y^S_g / Σg n^S_g).

Data required for direct standardisation

Age-specific rates of the study population rgi = ygi/ngi; numbers at risk in the standard population n^S_g; total cases in the standard population Σg y^S_g.

Motivation for direct standardisation

Gives one summary measure per area; easier to interpret than many age-specific rates; makes rates comparable across areas.

Issues with direct standardisation

Needs accurate age-specific rates rgi, which are unstable for rare diseases/small ngi (one extra case changes rgi a lot); age-specific counts may be unavailable (confidentiality); information is lost by summarizing across age groups; results depend on the chosen standard population (weights).

Indirect standardisation: question

How many cases would be expected in the study population if it contracted the disease at the same rate as the standard population?

Indirect standardisation: expected cases

Egi = r^S_g · ngi = (y^S_g / n^S_g) · ngi; overall Ei = Σg Egi.

Standardised mortality ratio (SMR)

SMRi = yi / Ei = Σg ygi / Σg Egi: observed over expected cases. SMR > 1 means more cases than expected from the standard population's age-specific rates.

SMR vs SIR / standardised morbidity ratio

When referring to incidence rather than mortality it is called standardised morbidity ratio or standardised incidence ratio (SIR); SMRs are often the basis of disease risk atlases.

Indirectly standardised rate

SMRi × crude rate in the standard population (Σg y^S_g / Σg n^S_g).

Data required for indirect standardisation

Age-specific rates of the standard population r^S_g = y^S_g/n^S_g; numbers at risk in the study population ngi; total observed cases in the study population yi. Does NOT use age-specific rates of the study population.

Internal standardisation

Standard rates taken from the data itself (aggregate/marginal standard: r_g = Σi yig / Σi nig, so Eig = r_g·nig). Somewhat 'cheating' because a degree of freedom is lost by estimating the rate from the same data.

External standardisation

Using an existing standard table of age-adjusted rates for the disease (available for many cancers).

Motivation for indirect standardisation

Works when group-specific counts per area are small (small city) where direct standardisation is unsatisfactory; avoids imprecise group-specific rates; usable when group-specific rates of the study population are unknown.

Issues with indirect standardisation

Each rate is based on its own population distribution, so comparing indirectly standardised rates across areas can be problematic if age distributions differ; interpretation is relative to the standard population (higher/lower than standard).

Direct vs indirect standardisation (data)

Direct: needs age-specific rates in the study population (unstable for small areas). Indirect: needs study-population sizes per age group and total cases; uses the standard's age-specific rates; preferred for small areas.

Pennsylvania lung cancer SMR (R workflow)

Compute age-specific rates over all counties (rate = Y/N by age); Ei = rate × county-age population; E = Σ Ei per county; SMR = Y/E. Examples: Adams 0.785, Allegheny 1.08, Armstrong 0.717.

Remarks on SMR maps

A map of SMRs gives a sense of disease risk but can be misleading/unreliable in small-population counties; model-based approaches add covariates and borrow information from neighbors to smooth extreme values.

Age-area interaction

If age-area interactions are present, any summary measure (standardized rate, SMR) masks the underlying pattern.

When are rate comparisons fully valid? (Doll & Smith, 1982)

Difficulties comparing populations with different age distributions are completely overcome only by comparing individual age-specific rates.