Math/Physics/Economics/Statistics ProblemsA multi-center, randomized clinical trial conducted in six European hospitals. Between January 1, 1983 and January 1, 1987, 349 patients with liver disease were randomized to either treatment with an experimental drug UDC (176 patients) or placebo (173 patients).The purpose of the trial was to study the effect of treatment on the survival time. However, during the course of the trial an increased use of liver transplantation for patients with this disease made the investigators redefine the main response variable to be time to failure of medical treatment defined as either death or liver transplantation.Patients were followed from randomization until treatment failure, drop-out or end of follow-up January 1, 1989. During the follow-up period 61 patients died, another 29 were transplanted and 4 patients were lost to follow-up before January 1, 1989. At the time of entry of each patient a number of clinical, biochemical and histological variables, including serum bilirubin, serum albumin, sex, age were recorded.Data set: liver.sav:? ptno: patient identification number ? unit: hospital (1: DK1, 2: ENG1, 3: DEN2, 4: ESP1, 5: D1, 6: F1) ? tment: treatment (0: placebo, 1: UDC) ? sex: (1: male, 0: female) ? age: (years) ? stage: histological stage (1, 2, 3, 4) ? gibleed: previous gastrointestinal bleeding (1: yes, 0: no) ? crea: creatinine (umol/L) ? alb: albumin (g/L) ? bili: bilirubin (umol/L) ? alkph: alkaline phosphatase (IU/L) ? asptr: aspartate transaminase (IU/L) ? weight: body weight (kg) ? days: observation time (days) ? status: status at exit (0: censored, 1: liver transplantation, 2 : dead)Specific assignments1. Construct a Directed Acyclic Graph (DAG) based on the data. The time ordering is decided by you and needs no justification. The chosen ordering of the variables must be clear from your presentation. For associations between variables prior to time to failure, only the final models need to be reported. 2. Compare the time to failure distribution between the two treatment groups 3. Study how the treatment effect is affected by adjustment for sex, age, albumin and bilirubin. Interactions and non-linearities must be discussed. In particular, the non-linearity of bilirubin should be studied using different approaches which should be compared. Subsequently, the sex*bilirubin interaction should be described separately 4. Discuss the differences between the treatment effects estimated in the two previous questions in the light of the fact that the study was randomized. This includes discussing whether the randomization was successful. 5. The study was a multi-center study. Discuss how to account for a possible clustering effect of hospital.The end-point failure of medical treatment is composed of dead without liver transplantation and liver transplantation.6. Analyze how treatment affects the risk of death in the presence of the competing risk liver transplantation.:
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