PU520 Unit 2 Asthma Frequency Measures Problem Set Example

Eighteen Thousand Pupils, One School Year and Six Denominators: An Epidemiology Problem Set Working Point Prevalence, Cumulative Incidence, Period Prevalence and an Incidence Rate for Asthma in a Composite School District, With Each Denominator Explained

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Purdue University Global

PU520: Principles of Epidemiology

Unit 2 Epidemiology Problem Set

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[Date]

The district and every figure are composite and bracketed for the writer's own data; the methods cited are real.

The Data

Pupils enrolled on September 1: [18,000]. Pupils with active asthma on September 1: [1,530]. New asthma diagnoses during the school year among pupils free of asthma at the start: [214]. Pupils enrolled at any time during the year, including [600] who transferred in: [18,600]. Child-years at risk among pupils free of asthma, after accounting for transfers in and out: [15,900].

Problem 1: Point Prevalence

Question: what proportion of pupils had active asthma on September 1? Formula: cases existing at a point in time divided by the population at that time. Substitution: [1,530] / [18,000]. Answer: [8.5] percent. Meaning: about one pupil in twelve began the year with asthma, which sizes the number of inhalers and action plans school nurses must manage.

Problem 2: Cumulative Incidence

Question: what proportion of pupils free of asthma at the start developed it during the year? Formula: pupils newly diagnosed, over the pupils who were asthma-free when the year began. Substitution: [214] / ([18,000] minus [1,530]) = [214] / [16,470]. Answer: [13.0] per [1,000] pupils over the school year. Meaning: the denominator excludes pupils who already had asthma, because they could not become new cases.

Problem 3: Period Prevalence

Question: what proportion of pupils had asthma at any time during the year? Formula: existing plus new cases during the period divided by everyone enrolled at any time during the period. Substitution: ([1,530] + [214]) / [18,600] = [1,744] / [18,600]. Answer: [9.4] percent. Meaning: the denominator now includes transfers in, since they were part of the population during the period. Each problem changes the denominator, and each change is the point of the problem.

Problem 4: Incidence Rate

Question: how fast did new cases occur, per unit of time at risk? Formula: new cases divided by person-time at risk. Substitution: [214] / [15,900] child-years. Answer: [13.5] per [1,000] child-years. Meaning: person-time accounts for pupils who were enrolled for only part of the year, so the rate reflects actual time observed.

Problem 5: Why Problems 2 and 4 Differ

Question: why are cumulative incidence and the incidence rate close but not equal? Answer: cumulative incidence assumes everyone at risk at the start was observed for the whole year. Transfers out shortened some pupils' time at risk and transfers in added others for part of the year. The rate uses the actual time observed, which here is slightly less than one full year per pupil at risk, so the rate is a little higher. When follow-up is complete and short, the two measures converge (Rothman, 2012).

Problem 6: Prevalence, Incidence and Duration

Question: what average duration of asthma is implied by the prevalence and incidence? Formula: in a steady state, prevalence divided by one minus prevalence approximately equals incidence rate times average duration (Freeman & Hutchison, 1980). Substitution: ([0.085] / [0.915]) / [0.0135] per year. Answer: about [6.9] years. Meaning: childhood asthma lasts many years for many pupils, which is why prevalence is several times the yearly incidence. The steady-state assumption is approximate, since enrollment changes and many children outgrow asthma.

What the District Should Take From the Set

Prevalence measures the burden nurses manage each day; incidence measures how quickly new cases arise and is the better target for prevention, such as reducing triggers in school buildings. Reporting both, with clear denominators, avoids confusing the two (Celentano & Szklo, 2019).

Why the District Asked for These Figures

The district's nursing supervisor wanted to know two things: how many children nurses would be caring for on any given day, and whether new cases were rising after the district replaced the ventilation in several older buildings. The first question is about burden and calls for prevalence. The second is about the speed at which healthy children become ill and calls for incidence. Answering the wrong question with the right arithmetic is a common failure, so the set states which question each figure answers.

Presenting the Figures to the School Board

A board member will not want six formulas. The summary for the board would say that about one pupil in twelve started the year with asthma, that about thirteen of every thousand asthma-free pupils were newly diagnosed during the year, and that these figures will serve as a baseline for judging whether building improvements reduce new cases over the next three years. Each figure would carry its denominator in plain words, such as pupils free of asthma at the start, so no one mistakes one measure for another.

Common Errors to Avoid

Using the whole enrollment as the denominator for cumulative incidence, which includes pupils who could not become new cases. Reporting a rate without its unit of person-time. Comparing period prevalence from one year with point prevalence from another.

References

Celentano, D. D., & Szklo, M. (2019). Gordis epidemiology (6th ed.). Elsevier.

Freeman, J., & Hutchison, G. B. (1980). Prevalence, incidence and duration. American Journal of Epidemiology, 112(5), 707-723. https://doi.org/10.1093/oxfordjournals.aje.a113043

Rothman, K. J. (2012). Epidemiology: An introduction (2nd ed.). Oxford University Press.