Change rates and prevalence of a dichotomous variable: simulations and applications. Brinks R, Landwehr S - PLoS ONE (2015) Bottom Line: The transitions between the states are described by change rates, which depend on calendar time and on age.We develop a partial differential equation (PDE) that simplifies the use of the three-state model.In two further applications, the PDE may provide insights into smoking behaviour of males in Germany and the knowledge about the ovulatory cycle in Egyptian women. View Article: PubMed Central - PubMed Affiliation: Institute for Biometry and Epidemiology, German Diabetes Center, Duesseldorf, Germany. ABSTRACTA common modelling approach in public health and epidemiology divides the population under study into compartments containing persons that share the same status. Here we consider a three-state model with the compartments: A, B and Dead. States A and B may be the states of any dichotomous variable, for example, Healthy and Ill, respectively. The transitions between the states are described by change rates, which depend on calendar time and on age. So far, a rigorous mathematical calculation of the prevalence of property B has been difficult, which has limited the use of the model in epidemiology and public health. We develop a partial differential equation (PDE) that simplifies the use of the three-state model. To demonstrate the validity of the PDE, it is applied to two simulation studies, one about a hypothetical chronic disease and one about dementia in Germany. In two further applications, the PDE may provide insights into smoking behaviour of males in Germany and the knowledge about the ovulatory cycle in Egyptian women. No MeSH data available. Related in: MedlinePlus © Copyright Policy Related In: Results  -  Collection License getmorefigures.php?uid=PMC4352043&req=5 .flowplayer { width: px; height: px; } pone.0118955.g002: Difference stratified by age.Mean (top) and standard deviation (bottom) of the difference D between the left and the right-hand side of Equation (3) stratified by age a. Mentions: The upper part of Fig. 2 shows the mean of D for each of the age groups a* = 5, 6, …, 85. The values vary around the zero line, again indicating an unbiased estimator. But as the age increases, the variation increases. This increase is also illustrated in the lower part of Fig. 2, where the standard deviation of the difference D is depicted versus age a*. Obviously, for higher ages the difference D has a higher variation. The reason for the variation comes from a higher uncertainty of the rate estimation in the higher age groups. For example, in year t = 115, there are 1576 and 88 death cases (with or without the disease) as opposed to 7375.5 and 273.5 person-years at risk in the age groups 70–79 and 80–89, respectively. Calculating the standard error of the person-years method [p. 237, 17] yields a more than 6-fold higher standard error for the (overall) mortality rate in the age-group 80–89 than in the age group 70–79. As a consequence, the difference D has a higher variation as the age increases.

Change rates and prevalence of a dichotomous variable: simulations and applications.

Brinks R, Landwehr S - PLoS ONE (2015)

Related In: Results  -  Collection

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pone.0118955.g002: Difference stratified by age.Mean (top) and standard deviation (bottom) of the difference D between the left and the right-hand side of Equation (3) stratified by age a.
Mentions: The upper part of Fig. 2 shows the mean of D for each of the age groups a* = 5, 6, …, 85. The values vary around the zero line, again indicating an unbiased estimator. But as the age increases, the variation increases. This increase is also illustrated in the lower part of Fig. 2, where the standard deviation of the difference D is depicted versus age a*. Obviously, for higher ages the difference D has a higher variation. The reason for the variation comes from a higher uncertainty of the rate estimation in the higher age groups. For example, in year t = 115, there are 1576 and 88 death cases (with or without the disease) as opposed to 7375.5 and 273.5 person-years at risk in the age groups 70–79 and 80–89, respectively. Calculating the standard error of the person-years method [p. 237, 17] yields a more than 6-fold higher standard error for the (overall) mortality rate in the age-group 80–89 than in the age group 70–79. As a consequence, the difference D has a higher variation as the age increases.

Bottom Line: The transitions between the states are described by change rates, which depend on calendar time and on age.We develop a partial differential equation (PDE) that simplifies the use of the three-state model.In two further applications, the PDE may provide insights into smoking behaviour of males in Germany and the knowledge about the ovulatory cycle in Egyptian women.

View Article: PubMed Central - PubMed

Affiliation: Institute for Biometry and Epidemiology, German Diabetes Center, Duesseldorf, Germany.

ABSTRACT
A common modelling approach in public health and epidemiology divides the population under study into compartments containing persons that share the same status. Here we consider a three-state model with the compartments: A, B and Dead. States A and B may be the states of any dichotomous variable, for example, Healthy and Ill, respectively. The transitions between the states are described by change rates, which depend on calendar time and on age. So far, a rigorous mathematical calculation of the prevalence of property B has been difficult, which has limited the use of the model in epidemiology and public health. We develop a partial differential equation (PDE) that simplifies the use of the three-state model. To demonstrate the validity of the PDE, it is applied to two simulation studies, one about a hypothetical chronic disease and one about dementia in Germany. In two further applications, the PDE may provide insights into smoking behaviour of males in Germany and the knowledge about the ovulatory cycle in Egyptian women.

No MeSH data available.

Related in: MedlinePlus