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Introduction:
The name Statistics was probably used in Egypt in 1549. The term Statistics, which was connected to the development of sovereign states, was coined in Germany in 1749 and used to designate the systematic collection of demographic and economic data by states.
Objective:
To present the most relevant and current statistical techniques in clinical medicine and epidemiology, as well as to show examples of the use of these techniques.
Material and Methods:
Review of the literature on the subject; presentation of some examples developed in class by professors of the subject Research Methodology and Statistics in Medical Sciences.
Development:
From the very beginnig, Statistics was used to characterize data based on their properties, as well as to develop information summary measures.
In the modern era, procedures and techniques were designated to facilitate valid inferences to the universe from the sampling theory, whose foundation is the probability theory.
Conclusions:
There is a need for the application of modern techniques and especially the multivariate ones used to explain biological phenomena, which cannot be explained by one or two variables. This makes possible that our universities, scientific research centers, and companies conduct studies using statistical techniques that involve many variables, which are supposed to be related to the variable under study.
Introducción:
El nombre de Estadística probablemente se usó en Egipto en 1549. El término Estadística se acuñó en Alemania en 1749, conectado con el desarrollo de estados soberanos y designando la recopilación sistemática de datos demográficos y económicos por estados.
Objetivo:
Presentar las técnicas estadísticas más relevantes en el campo de la clínica médica y la epidemiología actualmente y mostrar ejemplos del uso de dichas técnicas.
Material y métodos:
Revisión de la literatura sobre el tema, algunos ejemplos desarrollados en clases por profesores de la asignatura Metodología de la investigación y Estadística en carreras de Ciencias Médicas.
Desarrollo:
En sus inicios la Estadística caracterizaba los datos basados en sus propiedades, desarrollaron medidas de resumen de información.
En la era moderna se diseñaron procedimientos y técnicas para realizar inferencias válidas al universo a partir de la teoría del muestreo, cuyo fundamento es la teoría de probabilidades.
Conclusiones:
Necesidad de la aplicación de las técnicas modernas y especialmente las multivariadas para explicar los fenómenos biológicos, que no pueden ser explicados por una o dos variables, esto hace que nuestras universidades, centros de investigaciones científicas y empresas realicen sus estudios, utilizando técnicas estadísticas que envuelvan muchas variables que se suponen se relacionen con la variable objeto de estudio.
- Statistics;
- multivariate analysis;
- probabilities;
- sampling;
- correlation;
- regression.
- Estadística;
- análisis multivariante;
- probabilidades;
- muestreo;
- correlación;
- regresión.
Introduction
The name Statistics was probably used in Egypt in 1549. The term was coined in Germany in 1749 and connected to the development of Sovereign States.
It was also used to designate the systematic collection of demographic and economic data by states.
In the early 19th century,1,2) Statistics was the discipline concerned with the collection, summary, and analysis of data. Today, the data are collected and statistics are computed. It is widely distributed among the government, business, sports, and sciences.
The objective of this investigation is to present the most relevant statistical techniques used in the medical field.
Development
Inception
Descriptive Statistics: Tables of frequency; Measures of Central Tendency; Measures of Dispersion and Variation; Measures of Position to characterize data based on their properties.
Modern era
Inferential Statistics: t-tests; ANOVA; Regression (Factorial analysis); Multiple discriminant analysis and logistic regression; Cluster analysis; others to predict outcomes from known predictor variable(s).
Statistics in Sciences
The basis of Inferential Statistics relies on the Theory of Probability.
Inferential Statistics allows us to infer or generalize the results of the data taken from a sample of a “probabilistic type”.
Statistical techniques can show, whether and how, that strongly pairs of variables are related.
Simple: It uses an independent variable.
Multiple: It uses more than two independent variables.
Quantitative Variables: Pearson; Fisher; Kendall ; Gosset.
Qualitative Variables: Spearman.
The development of Information and Communication Technologies has allowed and facilitated education, research, and business management as well as biomedical research during the last decades of the 20th century and the first decades of the 21st century.
Biomedical phenomena cannot be explained only by counting and classifying data, but once the data have been classified and specific techniques have been used, techniques to make predictions, estimate parameters, and establish relationships between various characteristics are needed. In general, many variables are required so that the phenomenon under study can be explained. Therefore, the use of statistical techniques that help in this regard such as multivariate analyzes is a must.
Important contributors and founders of statistics
Sir Ronald Aylmer Fisher (17 february 1890 - 29 july 1962) was a Bristish statistician and geneticist. He was the most significant statistician of the 20thcentury.3) (Figure 1)
For his work in statistics, he has been described as a “genius” who almost single-handedly created the foundations for modern statistics.
Charles Edward Spearman (10 September 1863 - 17 September 1945), was an English psychologist who was known for his work in statistics as a pioneer of factor analysis, as well as for Spearman´s rank coefficient that is not parametric.4) (Figure 2)
William Lealy Gosset
He designed the famous Student´s t Test. He was called “student” as statistician.5
Inferential statistics techniques most frequently used today
Logistic Regression
It is a widely used statistical model.
Dependent Variable: binomial, multinomial.
Dichotomous; Dummy; In Range
Predictor variables may be either continuous or categorical.
In the Table 1, you can see the data for applying simple linear correlation.
Pearson Simple Linear correlation(correlation) r= 0,791. [-1; +1]
Simple Lineal Correlation
If r is close to 1, a hypothesis test must be performed.
You must prove that there is correlation. Without Correlation, Regression must not be stated
Equation of Linear Regression
Y* = a + bX
Substituted values
Y*=-0,2+1,18x
Particular value=8
Y*= 9,2
Y = a + bX
Normal equations
∑ summatory
∑y= na+b∑x
∑yx= a∑x+b∑x^2
In this case, it allows to find the values of “a” and “b”
Y = a + bX
69,5= 10a + (60,6) (1,18)
69,5= 10a + 71,5
-2= 10a
a= -0,2
Linear Regression Equation
Y* = a + bX
Substituted values
Y*=-0.2+1.18x
Particular value=8
Y*= 9.2
Equation of Linear Regression
It is used to estimate the values or the presence of the variable in the study in any type of correlation (multiple, linear or logistic). From there, an equation is derived.
In Table 2, you can see the presentation of data for multiple correlation.
Pearson´s Multiple correlation
The Multiple Regression Equation is derived from a system of Normal equations.
X₁*= a1,23 + b12,3X2+b13,2X3
X₁*= 62,113-0,464X2+0,017X3
r= 0,918
r²= 0,843
F= 18,827
p < 0,01
Pearson´s Multiple correlation6,7
X₁*= a1,23 + b12,3X2+b13,2X3
X₁*= 62,113-0,464X2+0,017X3
Estimation of X2=74 and X3 = 80
X₁*= 62,113-0,464 (74)+0,017(80)
X₁*= 62,113-34,336+1,36
X₁* = 29,137
Figures 3 and 4 show an example of the application of logistic regression.
There are variables that do not contribute, but their inclusion depends on the experience of the researcher.
Inference is a theory to aid decision making but it does not determine the final decision.
Conclusions
The need for the application of modern techniques and especially multivariate ones to explain biological phenomena, which cannot be explained by one or two variables, makes our universities, scientific research centers, and companies carry out their studies using statistical techniques that involve many variables that are supposed to be related to the variable under study.
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1. Instituto Superior de Ciencias médicas de La Habana. Bioestadística y Computación. La Habana: Editorial Pueblo y Educación; 1987.
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2. Instituto Superior de Ciencias médicas de La Habana. Cuaderno de ejercicios de Bioestadística. La Habana: Editorial Pueblo y Revolución; 1988.
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3. Efron B. Fisher in the 21st Century. Invited Paper Presented at the 1996 R.A. Fisher Lecture. Statistical Science [Internet]. 1998 [Citado 02/06/2021];13(2):95-122. Disponible en: https://www.mit.edu/~18.655/papers/efron1998.pdf
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4. Aruquipa J. Historia de la Estadística. The American statistician [Internet]. 2021 [Citado 02/06/2021]; 49(2):18. Disponible en: https://es.scribd.com/document/543874806/HISTORIA-DE-LA-ESTADISTICA
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5. David HA. Prueba t de Student. The American statistician [Internet]. 2020 [Citado 02/06/2021];44(4):322-6. Disponible en: https://www.studocu.com/ec/document/analisis-de-datos/prueba-t-de-student/19716076
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6. Joseph F. Análisis Multivariante [Internet]. Argentina: DocerArgentina; 2021 [Citado 02/06/2021]. Disponible en: https://docer.com.ar/doc/v1env
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7. Pearson ES. "Student'" as Statistician. Biometrika [Internet].1939;30(3/4):210-50. Disponible en: https://doi.org/10.2307/2332648
- » Received: 15/07/2021
- » Accepted: 17/09/2021
- » Publicado : 10/12/2021
La revista está: Certificada por el CITMA