Solve the following question. Explain your answers appropriately.

A medical study was carried out between 1 January 2001 and 1 January 2006, to assess the survival rates of cancer patients. The patients all underwent surgery during 2001 and then attended 3-monthly check-ups throughout the study. The following data were collected: For those patients who died during the study exact dates of death were recorded as follows: Patient Date of surgery Date of death 1 April 2001 1 August 2005 1 April 2001 1 October 2001 1 May 2001 1 March 2002 1 September 2001 1 August 2003 1 October 2001 1 August 2002 For those patients who survived to the end of the study: Patient Date of surgery 1 February 2001 1 March 2001 1 April 2001 1 June 2001 1 September 2001 1 September 2001 1 November 2001 For those patients with whom the hospital lost contact before the end of the investigation: Patient Date of surgery Date of last check-up M 1 February 2001 1 August 2003 N 1 June 2001 1 March 2002 1 September 2001 1 September 2005(i) Explain whether and where each of the following types of censoring is present in this investigation: (a) type I censoring (b) interval censoring; and (c) informative censoring. [3] (ii) Calculate the Kaplan-Meier estimate of the survival function for these patients. State any assumptions that you make. [7] (iii) Hence estimate the probability that a patient will die within 4 years of surgery. [1] [Total 11]