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I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

Hi Christopher,

The recent (2024) 2nd edition of Stroup, Ptukhina and Garai: "Generalized Linear Mixed Models: Modern Concepts, Methods and Applications" presents state-of-the-art discussions on important issues associated with modeling of rates and proportions using a GLMM approach, including implementation and practical issues to contend with... several of these issues not obvious until recently, and thus commonly overlooked. E.g. non-trivial implications of using transformations and normal approximations. Specifically, Chapter 12 gets on the specifics of modeling rates and proportions using both binomial and beta distributions, depending on the case. There is much we are still learning about modeling of non-Gaussian responses, specifically in the context of studies characterized by data architecture.

Good luck! 

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.

I'm helping a colleague and his team of residents and medical students with a cross-sectional chart review study of hemoglobin A1c levels in patients with type 2 diabetes, and how (if at all) they relate to a variety of "social determinants of health": transportation problems, substance use, various measures of wealth/poverty, and so on.

For those unfamiliar with it, hemoglobin A1c is a measure of what percent of one's hemoglobin molecules are glycosolated---have glucose molecules hooked to them. It's a permanent bond, persisting for the life of that hemoglobin molecule---about 3 months. So it's a measure of long-term diabetes control: lower hemoglobin A1c = better diabetes control, and vice versa.

By rights, hemoglobin A1c is a percentage: can't be less than zero or greater than 100. In clinical reality, values less than about 4 or greater than about 16 are biologically implausible; in 25 years of practice I don't think I've never seen one outside that range. 

I've always been intrigued by the beta distribution and keep my eye out for opportunities to use it. It has a theoretical attraction for proportions/percentages. Any experience with, or thoughts about, modeling a percent outcome variable with the beta distribution, when the plausible range is narrow like this?

The log-normal also occurs to me. Using the fitdistrplus package in R, the observed data seem a tad closer to the lognormal theoretical CDF than to the beta or the normal. (I've attached two quick and dirty graphs. These are unconditional plots, or course, with no predictors, so might not be definitive.)

I'd welcome any thoughts. Thanks.