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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.

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

Three-state model.Living individuals of the population aged a at calendar time t are either in state A or state B. The respective numbers are S(t, a) and C(t, a). Individuals may change states according to the transition rates.
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pone.0118955.g001: Three-state model.Living individuals of the population aged a at calendar time t are either in state A or state B. The respective numbers are S(t, a) and C(t, a). Individuals may change states according to the transition rates.

Mentions: Most modelling approaches in public health and epidemiology divide the population under consideration into a number of compartments that contain individuals who are identical in terms of their status in question. Famous examples like the SIR-model come from infectious disease epidemiology [1]. The transitions from one compartment to another are described by rates that may depend on calendar time t, and in case of age-structured models also on the age a [2]. The model we are dealing with is shown in Fig. 1. It consists of the states A, B and an additional state Dead. The transition rates are denoted as in Fig. 1: the rates between states A and B are the incidence rate i and the remission rate r. Mortality rates from the respective states are denoted mA and mB. All rates may depend on calendar time t and age a.


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

Brinks R, Landwehr S - PLoS ONE (2015)

Three-state model.Living individuals of the population aged a at calendar time t are either in state A or state B. The respective numbers are S(t, a) and C(t, a). Individuals may change states according to the transition rates.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4352043&req=5

pone.0118955.g001: Three-state model.Living individuals of the population aged a at calendar time t are either in state A or state B. The respective numbers are S(t, a) and C(t, a). Individuals may change states according to the transition rates.
Mentions: Most modelling approaches in public health and epidemiology divide the population under consideration into a number of compartments that contain individuals who are identical in terms of their status in question. Famous examples like the SIR-model come from infectious disease epidemiology [1]. The transitions from one compartment to another are described by rates that may depend on calendar time t, and in case of age-structured models also on the age a [2]. The model we are dealing with is shown in Fig. 1. It consists of the states A, B and an additional state Dead. The transition rates are denoted as in Fig. 1: the rates between states A and B are the incidence rate i and the remission rate r. Mortality rates from the respective states are denoted mA and mB. All rates may depend on calendar time t and age a.

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