Statnote 39: The binomial distribution: comparing two proportions

Many populations consist of two classes only, e.g., alive or dead, present or absent, clean or dirty, infected or non-infected, and it is the proportion or percentage of observations that fall into one of these classes that is of interest to an investigator. An observation that falls into one of the two classes is considered a ‘success’ (S), and ‘p’ is defined as the proportion of observations falling into that class. If a random sample of size ‘n’ is obtained from a population, the probability of obtaining 0, 1, 2, 3, etc., successes is then given by the binomial distribution. The binomial distribution can be used as the basis of a number of statistical tests but is most useful when comparing two proportions. This statnote describes two such scenarios in which the binomial distribution is used to compare: (1) two proportions when the samples are independent and (2) two proportions when the samples are paired.

Lys9 for Glu9 substitution in glucagon-like peptide-1(7-36)amide confers dipeptidylpeptidase IV resistance with cellular and metabolic actions similar to those of established antagonists glucagon-like peptide-1(9-36)amide and exendin (9-39)

The incretin hormone glucagon-like peptide-1(7-36)amide (GLP-1) has been deemed of considerable importance in the regulation of blood glucose. Its effects, mediated through the regulation of insulin, glucagon, and somatostatin, are glucose-dependent and contribute to the tight control of glucose levels. Much enthusiasm has been assigned to a possible role of GLP-1 in the treatment of type 2 diabetes. GLIP-l's action unfortunately is limited through enzymatic inactivation caused by dipeptidylpeptidase IV (DPP IV). It is now well established that modifying GLP-1 at the N-terminal amino acids, His7 and Ala8, can greatly improve resistance to this enzyme. Little research has assessed what effect Glu9-substitution has on GLP-1 activity and its degradation by DPP IV. Here, we report that the replacement of Glu9 of GLP-1 with Lys dramatically increased resistance to DPP IV. This analogue (Lys9)GLP-1, exhibited a preserved GLP-1 receptor affinity, but the usual stimulatory effects of GLP-1 were completely eliminated, a trait duplicated by the other established GLP-1-antagonists, exendin (9-39) and GLP-1 (9-36)amide. We investigated the in vivo antagonistic actions of (Lys9)GLP-1 in comparison with GLP-1(9-36)amide and exendin (9-39) and revealed that this novel analogue may serve as a functional antagonist of the GLP-1 receptor.