For inclusion in the study patients must fulfil the following criteria:

          1. Male or female, aged at least 18 years.

          2. Histological or cytological confirmation diagnosis of NSCLC.

          3. Radiological documentation of disease progression while on a previous continuous
             treatment with an EGFR TKI, eg, gefitinib, erlotinib or afatinib. In addition, other
             lines of therapy may have been given. All patients must have documented radiological
             progression on the last treatment administered prior to enrolling in the study.

          4. Confirmation that the tumour harbours an EGFR mutation known to be associated with
             EGFR TKI sensitivity (including G719X, exon 19 deletion, L858R, L861Q).

          5. Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1 with no
             deterioration over the previous 2 weeks (Appendix G).

          6. Patients must have a life expectancy of ≥12 weeks as estimated at the time of
             screening.

          7. Females should be using adequate contraceptive measures and must have a negative
             pregnancy test prior to start of dosing if of child-bearing potential, or must have
             evidence of non-child-bearing potential by fulfilling one of the following criteria at
             screening: Post-menopausal defined as aged more than 50 years and amenorrhoeic for at
             least 12 months following cessation of all exogenous hormonal treatments; Women under
             50 years old would be considered post-menopausal if they have been amenorrhoeic for 12
             months or more following cessation of exogenous hormonal treatments and with
             luteinising hormone (LH) and follicle stimulating hormone (FSH) levels in the
             post-menopausal range for the institution; Documentation of irreversible surgical
             sterilisation by hysterectomy, bilateral oophorectomy, or bilateral salpingectomy, but
             not tubal ligation.

          8. Patients are willing and able to comply with the protocol for the duration of the
             study including undergoing treatment and scheduled visits and examinations.

          9. Male patients should be willing to use barrier contraception, ie, condoms.

        Exlusion Criteria:

          1. Participation in another clinical study with an IP in last 14 days (or longer
             depending on the defined characteristics of the agents used).

          2. Any patient of Asian ethnicity or has a parent who is of Asian ethnicity (eg, Chinese,
             Filipino, Japanese, Korean and Vietnamese). If only a grandparent is Asian, this is
             acceptable. Asian Indians are acceptable.

          3. Treatment w/ any of the following: an EGFR TKI (eg, erlotinib, gefitinib or afatinib)
             within 8 days or approx. 5 x half-life, whichever is the longer, of the first dose of
             study treatment; Any cytotoxic chemotherapy, investigational agents or other
             anticancer drugs from a previous treatment regimen or clinical study within 14 days of
             the first dose of study treatment; Major surgery (excluding placement of vascular
             access) w/in 4 weeks of the 1st dose of study treatment; Radiotherapy with a limited
             field of radiation for palliation w/in 1 week of the first dose of study treatment,
             with the exception of patients receiving radiation to more than 30% of bone marrow or
             with a wide field of radiation which must be completed w/in 4 weeks of the 1st dose of
             study treatment; Patients currently receiving (or unable to stop use prior to
             receiving the first dose of study treatment) medications or herbal supplements known
             to be potent inhibitors of CYP3A4 (at least 1 week prior) and potent inducers of
             CYP3A4 (at least 3 week prior). All patients must avoid concomitant use of any
             medications, herbal supplements and/or ingestion of foods with known
             inducer/inhibitory effects on CYP3A4.

          4. Unresolved toxicities from prior therapy > CTCAE Grade 1 at the study start besides
             alopecia and Grade 2, prior platinum-therapy related neuropathy.

          5. Any intake of grapefruit, grapefruit juice, Seville oranges, Seville orange marmalade,
             or other products containing grapefruit or Seville oranges within 7 days of the first
             administration of the IP until the final PK sample collection on Day 35 of Part A.

          6. Spinal cord compression or brain metastases unless asymptomatic, stable and not
             requiring steroids for at least 4 weeks prior to start of study treatment.

          7. Any evidence of severe or uncontrolled systemic diseases, including uncontrolled
             hypertension and active bleeding diatheses, which in the PI's opinion makes it
             undesirable for the patient to participate in the study or which would jeopardise
             compliance with the protocol, or active infection including hep B, hep C and HIV.
             Screening for chronic conditions is not required.

          8. Inadequate bone marrow reserve or organ function as demonstrated by any of the
             following laboratory values: ANC<1.5 x 10^9/L; Platelet count <100 x 10^9/L;
             Haemoglobin <90 g/L; ALT >2.5 times ULN if no demonstrable liver metastases or >5
             times ULN in the presence of liver metastases; AST >2.5 times ULN if no demonstrable
             liver metastases or >5 times ULN in the presence of liver metastases; Total bilirubin
             >1.5 times ULN if no liver metastases or >3 times ULN in the presence of documented
             Gilbert's Syndrome (unconjugated hyperbilirubinaemia) or liver metastases; Creatinine
             >1.5 times ULN concurrent with creatinine clearance <50 mL/min (measured or calculated
             by Cockcroft and Gault equation); confirmation of creatinine clearance is only
             required when creatinine is >1.5 times ULN.

          9. Any of the following cardiac criteria: Mean resting corrected QT interval corrected
             for heart rate using Fridericia's correction factor (QTcF) >470 msec obtained from 3
             ECGs; Any clinically important abnormalities in rhythm, conduction or morphology of
             resting ECG eg, complete left bundle branch block, third degree heart block, second
             degree heart block, PR interval >250 msec; Any factors that increase the risk of QTc
             prolongation or risk of arrhythmic events such as heart failure, hypokalaemia,
             congenital long QT syndrome, family history of long QT syndrome or unexplained sudden
             death under 40 years of age or any concomitant medication known to prolong the QT
             interval

         10. Patients unable to swallow orally administered medication or patients with
             gastrointestinal disorders or significant gastrointestinal resection likely to
             interfere with the absorption of AZD9291.

         11. Past medical history of ILD, drug-induced ILD, radiation pneumonitis which required
             steroid treatment, or any evidence of clinically active ILD.

         12. Women who are breastfeeding.

         13. Patients with a known hypersensitivity to AZD9291 or rosuvastatin or any of the
             excipients of the products.

         14. Concomitant medication contraindicated for use with rosuvastatin due to drug
             interaction and/or associated with increased risk of rhabdomyolysis (including, but
             not limited to): fibrates (eg, gemfibrozil, fenofibrate), niacin, cyclosporine,
             lopinavir/ritonavir or atazanavir/ritonavir and colchinine.

         15. Past medical history of drug-related rhabdomyolysis and/or myalgia.

         16. Use of 3-hydroxy-3-methyl-glutaryl coenzyme A-reductase inhibitors, such as lovastatin
             and simvastatin (Part A only).