Comparación de algunas pruebas estadísticas asintóticas de no-inferioridad para contrastar dos proporciones independientes

Abstract

En este trabajo se comparan las pruebas asintóticas de no-inferioridad de Blackwelder, Farrington-Manning, Böhning-Viwatwongkasen, Hauck- Anderson, la prueba de razón de verosimilitudes generalizada y dos variantes de estas pruebas con base en sus niveles de significancia reales y en sus potencias. La prueba de Farrington-Manning es la que resultó tener la mejor aproximación del nivel de significancia real al nominal para tamaños de muestra 30 ≤ n ≤ 100 y para los tres límites de no-inferioridad más frecuentemente usados en el contexto de ensayos clínicos. La potencia de la prueba de Farrington-Manning resultó muy similar a las potencias de aquellas pruebas con buena aproximación del nivel de significancia real al nominal. Para pruebas exactas de no-inferioridad, Röhmel y Mansmann [25] probaron que si la región de rechazo cumple la condición de convexidad de Barnard, entonces el nivel de significancia en vez de calcularse como el supremo en todo el espacio nulo puede calcularse como el máximo en una parte de la frontera del espacio nulo. Esto tiene particular importan- cia debido al extenso tiempo de cómputo requerido para calcular niveles de significancia para pruebas de no-inferioridad, ver por ejemplo Röhmel [26]. En este trabajo se generaliza el teorema demostrado por Röhmel y Mansmann [25] en dos direcciones, en primer lugar se extiende el re- sultado para pruebas estadísticas en general (incluyendo pruebas exactas y asintóticas), en segundo lugar se relaja la condición de convexidad de Barnard a una condición menos restrictiva. El resultado incluye hipótesis de no-inferioridad para parámetros como la diferencia, la razón y la razón de momios. Este resultado permite calcular los niveles de significancia para pruebas como la de Blackwelder y la de Hauck-Anderson obteniendo el máximo en una parte de la frontera con una reducción sustancial del tiempo de cómputo.______In this work are compared the asymptotic tests for non-inferiority of Backwelder, Farrington-Manning, Böhning-Viwatwongkasen, Hauck- Anderson, generalized likelihood ratio test and two variants of these tests, comparison was made based in their real levels of significance and in their power. The test of Farrington-Manning has best aproximation of the real significance level to the nominal one for sample size 30 ≤ n ≤ 100 and for the three non-inferiority limits more often used in clinical trials. Power of the Farrington-Manning test is very similar to power of tests with good aproximation of the real level of significance to nominal. For exact tests of non-inferiority, Röhmel and Mansmann [25] proved that if the rejection region fulfills the Barnard convexity condition, then the level of significance can be computed as the maximum in a part of the boundary of the null space instead of the supremum in the whole null space. This is particularly important due to the great amount of time required to compute levels of significance in non-inferiority tests, e.g. see Röhmel [26]. In this work, the theorem demonstrated by Röhmel and Mansmann [25] is generalized in two directions, firstly the result for general statistical tests is extended (including exact and asymptotic tests), secondly the Barnard convexity condition is relaxed to a less restrictive condition. The result includes hypotheses of non-inferiority for parameters such as difference, ratio, and odds ratio. This result allows the computing of levels of significance for tests such as the Blackwelder and the Hauck- Anderson, obtaining the maximum in one part of the boundary with a substantial reduction in computing time.In this work are compared the asymptotic tests for non-inferiority of Backwelder, Farrington-Manning, Böhning-Viwatwongkasen, Hauck- Anderson, generalized likelihood ratio test and two variants of these tests, comparison was made based in their real levels of significance and in their power. The test of Farrington-Manning has best aproximation of the real significance level to the nominal one for sample size 30 ≤ n ≤ 100 and for the three non-inferiority limits more often used in clinical trials. Power of the Farrington-Manning test is very similar to power of tests with good aproximation of the real level of significance to nominal. For exact tests of non-inferiority, Röhmel and Mansmann [25] proved that if the rejection region fulfills the Barnard convexity condition, then the level of significance can be computed as the maximum in a part of the boundary of the null space instead of the supremum in the whole null space. This is particularly important due to the great amount of time required to compute levels of significance in non-inferiority tests, e.g. see Röhmel [26]. In this work, the theorem demonstrated by Röhmel and Mansmann [25] is generalized in two directions, firstly the result for general statistical tests is extended (including exact and asymptotic tests), secondly the Barnard convexity condition is relaxed to a less restrictive condition. The result includes hypotheses of non-inferiority for parameters such as difference, ratio, and odds ratio. This result allows the computing of levels of significance for tests such as the Blackwelder and the Hauck- Anderson, obtaining the maximum in one part of the boundary with a substantial reduction in computing time.