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Direct Standardisation is a way to make event rates (often mortality rates) comparable across two or more cohorts whose demographic characteristics (often age-sex-year distributions) are not the same.
Say we want to compare death rates between cohort A and cohort B. Cohort A is substantially younger on average than cohort B, so naturally the death rate in cohort A is lower. But cohort B is more affluent and has better access to healthcare services. If the age distribution of the two cohorts was the same would we still see that cohort A had a lower death rate than cohort B? To answer this question, we can standardise the age distributions so that they match a reference population, the population of England for example, and then compare rates.
Essentially, direct standardisation answers the question: "if each cohort had the same number of people in each demographic strata as the reference population, but the event rates stayed the same in each strata, what would the overall event rate be?".
Often the comparator cohort is the reference population itself. The standardisation procedure remains the same.
This idea can be extended to other cohort characteristics, such as sex, region, ethnicity, as long as the number of people in each stratum is known in the reference population.
A reference population is usually a real distribution, such as the population of England or Europe, but can be anything.
Unstandardised event rates can be calculated as R = events/people or events/timeatrisk. This can be decomposed into strata-specific rates R_i = events_i/people_i, where people_i is the number of people in stratum i, and event_i is the number of events in stratum i.
E.g. The stratum in age standardisation would be age band. How many events occurred in individuals aged between 20 -29 etc? This would need to be computed for all age bands in each cohort to match the age banding within your reference set.
This in turn can be used to recover the overall rate: R = sum(R_i * people_i)/sum(people_i) = sum((events_i/people_i)*people_i)/sum(people_i) = sum(events_i)/sum(people_i) = events/people. But instead of recovering the original rate R using the size of each stratum in the cohort, people_i, we can recover an alternative rate using any other population with different stratum sizes. This leads us to standardised event rates: R = sum(R_i * reference_i)/sum(reference_i), where reference_i is the number of people in each stratum of the reference population.
E.g. For age standardisation, your alternative age standardised rate would be the sum of how many events would have happened in each of your age bands if the population was the same distribution as reference, divided by the total reference population.