Quantitative PCR: Procedures and precisions

We develop a multitype branching-process model for the Polymerase Chain Reaction (PCR). We apply the model to a comparison of three methods for estimating the initial number of molecules of target present in a PCR. These three methods are: one which uses a coamplified, internal control; one which uses an external control series; and one which uses simple extrapolation of log outputvs time (no control). We identify assumptions for each method which permit mathematical analysis of bias and precision. All three methods perform well if: (1) replication efficiencies are stable among reactions; (2) other method-specific conditions on efficiencies are met; and (3) product accumulates exponentially throughout the range where it is observed. When replication efficiencies vary among reactions but other optimal conditions for each method hold, the no-control and external-control methods lose precision relative to the internal control method, but they may still perform satisfactorily for many applications. The internal control method continues to perform well even if accumulation of product plateaus. This method depends, however, on a condition we call equivalence of replication efficiencies, the attainability of which in practice remains to be proven.