US 9,811,504 B1  
Lifespan in multivariable binary regression analyses of mortality and survivorship  
Michael Epelbaum, Nashville, TN (US)  
Filed by Michael Epelbaum, Nashville, TN (US)  
Filed on May 29, 2017, as Appl. No. 15/607,598.  
Application 15/607,598 is a continuation in part of application No. 14/536,238, filed on Nov. 7, 2014, abandoned.  
Claims priority of provisional application 61/962,502, filed on Nov. 8, 2013.  
Int. Cl. G06F 17/18 (2006.01) 
CPC G06F 17/18 (2013.01)  16 Claims 
1. A method for including and distinguishing lifespan in multivariable binary regression analysis of one of mortality and
survivorship, said method comprising:
at least one of obtaining and creating data about N individuals i at respective J situations j, said data including variable
Y_{ij }and at least two variables X_{vij};
conducting a multivariable binary regression analysis of said data, analyzing the relationship between a dependent variable
Y_{ij }and independent variables X_{vij }for one of Y_{ij}=M_{ij }and Y_{ij}=S_{ij}, said analyzing utilizing model n_{ij}=β_{0}+β_{v}X_{vij}+ . . . +β_{W}X_{Wij }and binary link function B(n_{ij});
effectuating said multivariable binary regression analysis into yielding at least one result of said analysis;
wherein at least one of the steps is carried out by a computer; and
wherein:
i=1:N, indicating that i are sequential positive integers 1 through N;
i denotes an individual;
N denotes the total number of individuals i in said data;
j=1:J, indicating that j are sequential positive integers 1 through J;
j denotes a situation of individual i in reference to said variables X_{vij }and Y_{ij};
J denotes the total number of situations of an individual i in said data, allowing distinct J for distinct individuals i;
M_{ij }denotes the mortality status of individual i at situation j;
S_{ij }denotes the survivorship status of individual i at situation j;
Y_{ij}ε{0,1}, indicating that Y_{ij }is a binary variable that adopts one of values 0 and 1 for one of Y_{ij}=M_{ij }and Y_{ij}=S_{ij }of individual i at situation j;
v=1:W, indicating that v are sequential positive integers 1 through W;
W≧2;
v denotes an index of each of the following: variables X_{v}, variables X_{vij }of individual i at situation j, and coefficients β_{v};
W denotes the following: total number of variables X_{v}, total number of variables X_{vij }of individual i at situation j, and total number of coefficients β_{v};
X_{vij }denotes a variable X_{v }of individual i at situation j;
r=1:R, indicating that r are sequential positive integers 1 through R;
R≧2;
W≧R;
r denotes an index of each of the following: variables K_{r }and variables K_{rij};
K_{r }denotes a variable that directly denotes a distinct phenomenon, and R respective variables K_{r }respectively directly denote R distinct phenomena;
K_{rij }denotes a variable K_{r }of individual i at situation j;
T denotes a transformation function, allowing identity transformation;
q=1:Q, indicating that q are sequential positive integers 1 through Q;
X_{v}=T_{q}(K_{r}), indicating that X_{v }is a transformation T_{q }of variable K_{r }that directly denotes a specific phenomenon, further indicating that X_{v }indirectly denotes said specific phenomenon;
X_{vij}=T_{q}(K_{rij}), indicating that X_{vij }is a transformation T_{q }of K_{rij }that directly denotes a specific phenomenon, further indicating that X_{vij }indirectly denotes said specific phenomenon;
Q denotes the total number of transformations T_{q}(K_{r}) for a specific K_{r}, and Q also denotes the the total number of transformations T_{q}(K_{rij}) for a specific K_{rij }of individual i at situation j, allowing distinct Q for distinct variables K_{r}, and allowing distinct Q for distinct variables K_{rij }of individual i at situation j;
R denotes the following: the total number of variables K_{r}, the total number of variables K_{rij }of individual i at situation j, the total number of phenomena denoted by variables K_{r}, and the total number of phenomena denoted by variables K_{rij }of individual i at situation j;
A directly denotes age;
L directly denotes lifespan;
K_{1}=A and K_{2}=L, indicating that one of at least two variables K_{r }directly denotes age, and indicating that another of said at least two variables K_{r }directly denotes lifespan;
K_{1ij}=A_{ij }and K_{2ij}=L_{ij}, indicating that one of at least two variables K_{rij }directly denotes the age of individual i at situation j, and indicating that another of said at least two variables K_{rij }directly denotes the lifespan of individual i at situation j;
β denotes a regression coefficient; and
β_{0 }denotes the regression coefficient for the intercept, allowing β_{0 }to be one of the following: estimated, suppressed, and userprovided.
