Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration

Uchechukwu Marius Okeh; Theophilus Sunday Igwe; Patrick Agwu Okpara

doi:doi:10.11648/j.ijtam.20251106.11

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Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration

Uchechukwu Marius Okeh^*

, Theophilus Sunday Igwe, Patrick Agwu Okpara

Published in International Journal of Theoretical and Applied Mathematics (Volume 11, Issue 6)

Received: 10 September 2025 Accepted: 23 September 2025 Published: 20 December 2025

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Abstract

Dummy variable regression model assumes a linear relationship between the categorical variables and outcome variable. Also its coefficients of regression might not be directly interpretable in terms of probability changes or odds ratios, which may potentially limit the usefulness of the model. This might not hold true if the gestation length is dichotomous. This study explores an alternative method of using dummy variable regression in estimating probabilities, odds and odds ratios in gestational outcomes if the outcome variable is continuous rather than the use of logistic regression. This involves first partitioning each of the parent independent variables into a set of mutually exclusive categories or subgroups and then use dummy variables to represent these categories in a regression model. In such a regression model, each parent independent variable is represented by one dummy variable of 1’s and 0’s less than the number of its categories. Any level of a parent independent variable that is not specifically represented by a dummy variable is referred to as the excluded level of that parent variable while the others are termed the included levels in the regression model. This study is limited as follows: there is need to ensure that the model assumptions of linearity and independence of observations, continuity of the outcome variable as well as categorical nature of the predictor variables are met. A pilot cross sectional study design was carried out at Alex Ekwueme Federal University Teaching Hospital Abakaliki where data on age, parity and sex of last births were collected from 41 anti-natal women. The overall results of analysis showed that R2 = 0.066; 95% CL = 1.234-2.765, p - value = 0.780 indicating an insignificant relationship between the outcome variable and the categorical predictor variables, signaling the end of analysis. For illustration purposes only, we estimated probabilities and used it to estimate any desired odds and odds ratios like the odds that the randomly selected mother has a male and female births with gestation length of more than 39.5 weeks gave 0.636 and 0.639 as odds for male and female respectively while odds ratio was 0.995 implying that for every 1000 female births with a gestation length of more than 39.5 weeks, there are 995 males’ births with the same gestation length of 39.5 weeks. We concluded that dummy variable regression enables one to estimate probabilities and odds ratios of continuous outcome variable and so compares favorably with logistic regression.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 11, Issue 6)
DOI	10.11648/j.ijtam.20251106.11
Page(s)	86-100
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Odds, Odds Ratio, Continuous Outcome, Dummy Variable Regression, Probabilities, Maternal Age

References

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APA Style

Okeh, U. M., Igwe, T. S., Okpara, P. A. (2025). Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration. International Journal of Theoretical and Applied Mathematics, 11(6), 86-100. https://doi.org/10.11648/j.ijtam.20251106.11

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ACS Style

Okeh, U. M.; Igwe, T. S.; Okpara, P. A. Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration. Int. J. Theor. Appl. Math. 2025, 11(6), 86-100. doi: 10.11648/j.ijtam.20251106.11

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AMA Style

Okeh UM, Igwe TS, Okpara PA. Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration. Int J Theor Appl Math. 2025;11(6):86-100. doi: 10.11648/j.ijtam.20251106.11

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@article{10.11648/j.ijtam.20251106.11,
  author = {Uchechukwu Marius Okeh and Theophilus Sunday Igwe and Patrick Agwu Okpara},
  title = {Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {11},
  number = {6},
  pages = {86-100},
  doi = {10.11648/j.ijtam.20251106.11},
  url = {https://doi.org/10.11648/j.ijtam.20251106.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20251106.11},
  abstract = {Dummy variable regression model assumes a linear relationship between the categorical variables and outcome variable. Also its coefficients of regression might not be directly interpretable in terms of probability changes or odds ratios, which may potentially limit the usefulness of the model. This might not hold true if the gestation length is dichotomous. This study explores an alternative method of using dummy variable regression in estimating probabilities, odds and odds ratios in gestational outcomes if the outcome variable is continuous rather than the use of logistic regression. This involves first partitioning each of the parent independent variables into a set of mutually exclusive categories or subgroups and then use dummy variables to represent these categories in a regression model. In such a regression model, each parent independent variable is represented by one dummy variable of 1’s and 0’s less than the number of its categories. Any level of a parent independent variable that is not specifically represented by a dummy variable is referred to as the excluded level of that parent variable while the others are termed the included levels in the regression model. This study is limited as follows: there is need to ensure that the model assumptions of linearity and independence of observations, continuity of the outcome variable as well as categorical nature of the predictor variables are met. A pilot cross sectional study design was carried out at Alex Ekwueme Federal University Teaching Hospital Abakaliki where data on age, parity and sex of last births were collected from 41 anti-natal women. The overall results of analysis showed that R2 = 0.066; 95% CL = 1.234-2.765, p - value = 0.780 indicating an insignificant relationship between the outcome variable and the categorical predictor variables, signaling the end of analysis. For illustration purposes only, we estimated probabilities and used it to estimate any desired odds and odds ratios like the odds that the randomly selected mother has a male and female births with gestation length of more than 39.5 weeks gave 0.636 and 0.639 as odds for male and female respectively while odds ratio was 0.995 implying that for every 1000 female births with a gestation length of more than 39.5 weeks, there are 995 males’ births with the same gestation length of 39.5 weeks. We concluded that dummy variable regression enables one to estimate probabilities and odds ratios of continuous outcome variable and so compares favorably with logistic regression.},
 year = {2025}
}

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TY  - JOUR
T1  - Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration
AU  - Uchechukwu Marius Okeh
AU  - Theophilus Sunday Igwe
AU  - Patrick Agwu Okpara
Y1  - 2025/12/20
PY  - 2025
N1  - https://doi.org/10.11648/j.ijtam.20251106.11
DO  - 10.11648/j.ijtam.20251106.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 86
EP  - 100
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20251106.11
AB  - Dummy variable regression model assumes a linear relationship between the categorical variables and outcome variable. Also its coefficients of regression might not be directly interpretable in terms of probability changes or odds ratios, which may potentially limit the usefulness of the model. This might not hold true if the gestation length is dichotomous. This study explores an alternative method of using dummy variable regression in estimating probabilities, odds and odds ratios in gestational outcomes if the outcome variable is continuous rather than the use of logistic regression. This involves first partitioning each of the parent independent variables into a set of mutually exclusive categories or subgroups and then use dummy variables to represent these categories in a regression model. In such a regression model, each parent independent variable is represented by one dummy variable of 1’s and 0’s less than the number of its categories. Any level of a parent independent variable that is not specifically represented by a dummy variable is referred to as the excluded level of that parent variable while the others are termed the included levels in the regression model. This study is limited as follows: there is need to ensure that the model assumptions of linearity and independence of observations, continuity of the outcome variable as well as categorical nature of the predictor variables are met. A pilot cross sectional study design was carried out at Alex Ekwueme Federal University Teaching Hospital Abakaliki where data on age, parity and sex of last births were collected from 41 anti-natal women. The overall results of analysis showed that R2 = 0.066; 95% CL = 1.234-2.765, p - value = 0.780 indicating an insignificant relationship between the outcome variable and the categorical predictor variables, signaling the end of analysis. For illustration purposes only, we estimated probabilities and used it to estimate any desired odds and odds ratios like the odds that the randomly selected mother has a male and female births with gestation length of more than 39.5 weeks gave 0.636 and 0.639 as odds for male and female respectively while odds ratio was 0.995 implying that for every 1000 female births with a gestation length of more than 39.5 weeks, there are 995 males’ births with the same gestation length of 39.5 weeks. We concluded that dummy variable regression enables one to estimate probabilities and odds ratios of continuous outcome variable and so compares favorably with logistic regression.
VL  - 11
IS  - 6
ER  -

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Author Information

Uchechukwu Marius Okeh

Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Nigeria;International Institute for Nuclear Medicine and Allied Health Research, David Umahi Federal University of Health Sciences, Uburu, Nigeria

Contact Email

http://orcid.org/0000-0001-5348-7914
Theophilus Sunday Igwe

Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Nigeria
Patrick Agwu Okpara

Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Nigeria

http://orcid.org/0009-0003-8475-2874

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Plain Text BibTeX RIS

APA Style

Okeh, U. M., Igwe, T. S., Okpara, P. A. (2025). Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration. International Journal of Theoretical and Applied Mathematics, 11(6), 86-100. https://doi.org/10.11648/j.ijtam.20251106.11

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ACS Style

Okeh, U. M.; Igwe, T. S.; Okpara, P. A. Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration. Int. J. Theor. Appl. Math. 2025, 11(6), 86-100. doi: 10.11648/j.ijtam.20251106.11

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AMA Style

Okeh UM, Igwe TS, Okpara PA. Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration. Int J Theor Appl Math. 2025;11(6):86-100. doi: 10.11648/j.ijtam.20251106.11

Copy | Download

@article{10.11648/j.ijtam.20251106.11,
  author = {Uchechukwu Marius Okeh and Theophilus Sunday Igwe and Patrick Agwu Okpara},
  title = {Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {11},
  number = {6},
  pages = {86-100},
  doi = {10.11648/j.ijtam.20251106.11},
  url = {https://doi.org/10.11648/j.ijtam.20251106.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20251106.11},
  abstract = {Dummy variable regression model assumes a linear relationship between the categorical variables and outcome variable. Also its coefficients of regression might not be directly interpretable in terms of probability changes or odds ratios, which may potentially limit the usefulness of the model. This might not hold true if the gestation length is dichotomous. This study explores an alternative method of using dummy variable regression in estimating probabilities, odds and odds ratios in gestational outcomes if the outcome variable is continuous rather than the use of logistic regression. This involves first partitioning each of the parent independent variables into a set of mutually exclusive categories or subgroups and then use dummy variables to represent these categories in a regression model. In such a regression model, each parent independent variable is represented by one dummy variable of 1’s and 0’s less than the number of its categories. Any level of a parent independent variable that is not specifically represented by a dummy variable is referred to as the excluded level of that parent variable while the others are termed the included levels in the regression model. This study is limited as follows: there is need to ensure that the model assumptions of linearity and independence of observations, continuity of the outcome variable as well as categorical nature of the predictor variables are met. A pilot cross sectional study design was carried out at Alex Ekwueme Federal University Teaching Hospital Abakaliki where data on age, parity and sex of last births were collected from 41 anti-natal women. The overall results of analysis showed that R2 = 0.066; 95% CL = 1.234-2.765, p - value = 0.780 indicating an insignificant relationship between the outcome variable and the categorical predictor variables, signaling the end of analysis. For illustration purposes only, we estimated probabilities and used it to estimate any desired odds and odds ratios like the odds that the randomly selected mother has a male and female births with gestation length of more than 39.5 weeks gave 0.636 and 0.639 as odds for male and female respectively while odds ratio was 0.995 implying that for every 1000 female births with a gestation length of more than 39.5 weeks, there are 995 males’ births with the same gestation length of 39.5 weeks. We concluded that dummy variable regression enables one to estimate probabilities and odds ratios of continuous outcome variable and so compares favorably with logistic regression.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Estimating Probabilities and Odds Ratios in Gestational Outcomes: A Dummy Variable Regression Illustration
AU  - Uchechukwu Marius Okeh
AU  - Theophilus Sunday Igwe
AU  - Patrick Agwu Okpara
Y1  - 2025/12/20
PY  - 2025
N1  - https://doi.org/10.11648/j.ijtam.20251106.11
DO  - 10.11648/j.ijtam.20251106.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 86
EP  - 100
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20251106.11
AB  - Dummy variable regression model assumes a linear relationship between the categorical variables and outcome variable. Also its coefficients of regression might not be directly interpretable in terms of probability changes or odds ratios, which may potentially limit the usefulness of the model. This might not hold true if the gestation length is dichotomous. This study explores an alternative method of using dummy variable regression in estimating probabilities, odds and odds ratios in gestational outcomes if the outcome variable is continuous rather than the use of logistic regression. This involves first partitioning each of the parent independent variables into a set of mutually exclusive categories or subgroups and then use dummy variables to represent these categories in a regression model. In such a regression model, each parent independent variable is represented by one dummy variable of 1’s and 0’s less than the number of its categories. Any level of a parent independent variable that is not specifically represented by a dummy variable is referred to as the excluded level of that parent variable while the others are termed the included levels in the regression model. This study is limited as follows: there is need to ensure that the model assumptions of linearity and independence of observations, continuity of the outcome variable as well as categorical nature of the predictor variables are met. A pilot cross sectional study design was carried out at Alex Ekwueme Federal University Teaching Hospital Abakaliki where data on age, parity and sex of last births were collected from 41 anti-natal women. The overall results of analysis showed that R2 = 0.066; 95% CL = 1.234-2.765, p - value = 0.780 indicating an insignificant relationship between the outcome variable and the categorical predictor variables, signaling the end of analysis. For illustration purposes only, we estimated probabilities and used it to estimate any desired odds and odds ratios like the odds that the randomly selected mother has a male and female births with gestation length of more than 39.5 weeks gave 0.636 and 0.639 as odds for male and female respectively while odds ratio was 0.995 implying that for every 1000 female births with a gestation length of more than 39.5 weeks, there are 995 males’ births with the same gestation length of 39.5 weeks. We concluded that dummy variable regression enables one to estimate probabilities and odds ratios of continuous outcome variable and so compares favorably with logistic regression.
VL  - 11
IS  - 6
ER  -

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