The planning model should include the relationship between materiality, audit risk and sampling. The impact of test of controls on the sample size is also an expectation.
I have done some work on changes in audit methodologies … If I understand your question this may help
In fact, audit practice has gone through a constant process of change to respond to changes in the economy, the business community, the developments on other fields, and the utilisation of the technology advancement. Even though there is an overlap between audits approaches, researchers frequently view them in terms of four “generations”: the detailed testing audit, the system-based audit, the risk-based audit, and the BRA.
During the mid-1960s and, notably, through the 1970s, the system-based audit approach guided the audit process, particularly for large engagements. Under this approach, auditors used to evaluate the internal control of the client, with particular attention to the usefulness of the client’s accounting system and the flow of information existence and operation) for planning the substantive testing.
In the 1980’s, risk concepts formulated in the audit risk model were incorporated into audit approaches and professional standards, which resulted in what is called ‘the risk-based audit approach’. According to this approach, the audit risk model provides a framework to link audit procedures to audit objectives and guide the substantive tests. By the mid-1990s, a new movement in audit approaches of large international audit firms, exemplified in the ‘Business Measurement Process’
In fact audit practices and technologies serve different social and technical functions. For instance, Humphrey and Moizer (1990) studied the audit planning processes and found that, in addition to the technical functions emphasised in most research, the audit risk model serves ideological and marketing functions. Power (1995) later asserted that the audit risk model functions in a variety of related ways: a scientifically rational image of the audit process, a rational reorganisation of audit work, a reduction of detailed testing, and a justification for operational decisions to internal and external parties. Power (1992) also showed that sampling serves functions other than the technical ones, such as providing legitimate ground for less
audit work. Curtie & Turley (forthcoming) illustrated that the literature investigating audit methodology in its social and institutional context revealed four roles for audit methodology: the production of legitimacy for the profession, for set of work papers on individual audit, a system for controlling and directing the work of the practitioners and encoding knowledge into the organizational structure to assist in the achievement of the organizational profitability. Power (2003) provided a review of research studies adopting a sociological view of audit practices and asserted that the reviewed studies have contributed significantly to our understanding of the production of legitimacy in auditing.