Definition of Risk Sets and Matching Sample Clauses

Definition of Risk Sets and Matching.  Matching is performed by minimizing the squared distance between the values of the GPSIP or PP of treated and individuals in the corresponding risk set. The GPSIP is a scalar value for each individual, the squared distance between a treated individual i and a member of the risk set ij is computed in the same manner as in the case of GPSBL, Qm,IP = (GPSIP,i − GPSIP,ij ) . On the other hand, since the PP is a function of time for each individual, we define the metric for matching in equation (3.6), which is the integration of the squared difference of the two curves with respect to time. Qm,PP = TZ,i ∫ 0 (PPi(t) − PPij (t)) dt (3.6) The risk set of a treated individual i includes both individuals who never receive treatment during follow up and those who receive treatment later than the treatment time of individual i, i.e., TZ,ij > TZ,i. Referring once again to Figure 3.1, “Treated” represents an individual who is treated at TZ, its risk set for matching may include Eligible Controls 1 and 2 as TZ,EC1 > TZ and TZ,EC2 = to if they have not been matched to another treated individual but the individual labeled as “Control-Ineligible due to Death” is excluded from the risk set as TS,IC < TZ. Risk sets of individuals who are available for matching are built chronolog- ically by time using sequential matching algorithms. Individuals in the risk set with the smallest distance Qm are matched to the individual with the earliest time of treatment, TZ(1). After matching, all members of matched pairs must be removed from risk sets of later time points, and the process is continued chronologically by TZ,i until all treated individuals are matched or until there are no suitable controls available for matching.
Sample 1
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