The PUVA study compared two treatments for psoriasis. The published results are https://pubmed.ncbi.nlm.nih.gov/10534635/. PUVA stands for Psoralen Ultraviolet A light, a longer wavelength than UV B light, and was viewed as an effective treatment, but with some side effects. It was thought that TL-01 treatment, a lamp focused on a narrower band of the UVB spectrum, may be safer, but its effectiveness compared to PUVA was unknown. The clinical trial randomized 100 patients with plaque-type psoriasis to twice-weekly treatment with either PUVA or TL-01. Of interest is the number of treatment visits required to clear the psoriasis. Additionally, we would like to understand whether the baseline severity of the psoriasis influences the time to clearance. The baseline severity is quantified very simply as a classification of whether the psoriasis plaques are "small" or "large." Define the time to event as the number of visits needed to clear the psoriasis. The data available on canvas. (a) Compute the Kaplan-Meier estimators of the time-to-clearance for each of the PUVA and TL-01 treatments (submit the estimated curves). Perform a logrank test of the null hypothesis that the time-to-clearance curves are the same for the two groups. What is your conclusion? (b) Fit the Cox proportional hazards model with treatment group assignment as predictor. What is your conclusion about the difference between the PUVA and TL-01 treatments? (c) Fit the Cox proportional hazards model with treatment group assignment as predictor, but now stratifying by baseline plaque type ("small" or "large"). Recall that this strat- ification permits the baseline hazard function to vary by baseline plaque type. With this more flexible model, is the effect of treatment on time-to-clearance statistically significant? Explain