Publication: Modelización bayesiana de la prevalencia de la enfermedad en una población y de las medidas de validez en pruebas diagnósticas correladas, en ausencia de gold estándar
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2020-10
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Facultad de Estudios Estadísticos
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Abstract
Disponer de una prueba diagnóstica gold standard puede ser complicado debido a muchas razones: inexistencia, falta de disponibilidad, falta de ética al realizarla o un coste muy alto, entre ellas. Igualmente por estos motivos, no se suele disponer de los resultados de varias pruebas para poder compararlos, lo que hace imposible la estimación a través del enfoque frecuentista por saturación de parámetros en el modelo cuando hay poca información. A esto se le añaden todavía más dificultades cuando las pruebas diagnósticas son dependientes condicionadas al verdadero estado de la enfermedad, caso que suele ocurrir de forma muy frecuente en la realidad.
Por consiguiente, se ha planteado un problema en el que se tienen dos pruebas diagnósticas que no son gold standard y son dependientes condicionalmente con el objetivo de estimar la prevalencia de la enfermedad, así como las sensibilidades y especificidades de ambas pruebas diagnósticas, que haremos utilizando el enfoque bayesiano.
El modelo bayesiano construido se utilizó para comparar los resultados que se obtienen al considerar diferentes distribuciones a priori en las correlaciones entre pruebas diagnósticas en una base de datos real de refugiados camboyanos en Cánada y en tres muestras simuladas donde las pruebas diagnósticas tenían una correlación nula, moderada y alta. Para todos estos modelos, se consideró que las pruebas estaban correladas positivamente, ya que por bibliografía esto es así en la mayor parte de los casos.
Los resultados obtenidos en los datos reales confirmaron una mejoría del ajuste del modelo a los datos cuando se consideraron distribuciones a priori uniformes en (0,1) para las correlaciones frente al modelo que consideraba que existía independencia condicional entre las pruebas. En cuanto a las muestras simuladas, fueron mejores las estimaciones en aquellos modelos que consideraban una distribución a priori informativa en las correlaciones de las pruebas diagnósticas. Además, exceptuando los datos de las pruebas que no estaban correladas, la incorporación de las distribuciones uniformes en (0,1) para las correlaciones resulto ser mejor alternativa que considerar independencia condicional en el modelo, ya que, en el segundo caso, los intervalos de probabilidad 0.95 de las distribuciones a posteriori en la mayoría de los parámetros no tenían incluidos sus valores reales.
Having a gold standard diagnostic test can be complicated due to many reasons: non- existence, lack of availability, lack of ethics when performing it or a very high cost, among them. Also for these reasons, the results of several tests are not usually available for compa- rison, which saturates the model with more parameters than degrees of freedom when there is little information and makes it impossible to make the estimations through the frequentist approach. On top of this, even more difficulties are added when the diagnostic tests are condi- tionally dependent on the true status of the disease, a case that tends to occur very frequently in reality. Therefore, a problem has been formulated in which we have two diagnostic tests that are not gold standard but are conditionally dependent with the aim of estimating the prevalence of the disease, as well as the sensitivities and specificities of both diagnostic tests, which we will do using the Bayesian approach. The bayesian model built was used to compare the results obtained when considering different a priori distributions in the correlations between diagnostic tests in a real database of Cambodian refugees in Canada and in three simulated samples where the diagnostic tests had a null, moderate and high correlation. For all these models, the tests were considered to be positively correlated, since from literature this is the case in most of the real scenarios. The results obtained in the real data confirmed an improvement of the adjustment of the model to the data when uniform a priori distributions in (0,1) were considered for the correla-tions compared to the model that considered that there was conditional independence among the tests. As for the simulated samples, the estimates were better in those models that considered an informative a priori distribution in the correlations of the diagnostic tests. Furthermore, except for the data of the diagnostic tests that were not correlated, the incorporation of the uniform distributions in (0,1) for the correlations turned out to be a better alternative than considering conditional independence in the model, since, in the second case, the intervals of probability 0.95 of the a posteriori distributions in most of the parameters did not have their real values included. In view of the results, the importance of incorporating as parameters the correlations of the diagnostic tests in the model used to estimate the prevalence, sensitivities and specificities is confirmed, as well as the repercussion of considering conditional independence among the diagnostic tests in general, since this can lead to estimation errors, which become bigger the greater the real correlation among tests is.
Having a gold standard diagnostic test can be complicated due to many reasons: non- existence, lack of availability, lack of ethics when performing it or a very high cost, among them. Also for these reasons, the results of several tests are not usually available for compa- rison, which saturates the model with more parameters than degrees of freedom when there is little information and makes it impossible to make the estimations through the frequentist approach. On top of this, even more difficulties are added when the diagnostic tests are condi- tionally dependent on the true status of the disease, a case that tends to occur very frequently in reality. Therefore, a problem has been formulated in which we have two diagnostic tests that are not gold standard but are conditionally dependent with the aim of estimating the prevalence of the disease, as well as the sensitivities and specificities of both diagnostic tests, which we will do using the Bayesian approach. The bayesian model built was used to compare the results obtained when considering different a priori distributions in the correlations between diagnostic tests in a real database of Cambodian refugees in Canada and in three simulated samples where the diagnostic tests had a null, moderate and high correlation. For all these models, the tests were considered to be positively correlated, since from literature this is the case in most of the real scenarios. The results obtained in the real data confirmed an improvement of the adjustment of the model to the data when uniform a priori distributions in (0,1) were considered for the correla-tions compared to the model that considered that there was conditional independence among the tests. As for the simulated samples, the estimates were better in those models that considered an informative a priori distribution in the correlations of the diagnostic tests. Furthermore, except for the data of the diagnostic tests that were not correlated, the incorporation of the uniform distributions in (0,1) for the correlations turned out to be a better alternative than considering conditional independence in the model, since, in the second case, the intervals of probability 0.95 of the a posteriori distributions in most of the parameters did not have their real values included. In view of the results, the importance of incorporating as parameters the correlations of the diagnostic tests in the model used to estimate the prevalence, sensitivities and specificities is confirmed, as well as the repercussion of considering conditional independence among the diagnostic tests in general, since this can lead to estimation errors, which become bigger the greater the real correlation among tests is.