Grouping by season with weekly known fate survival data.

[Henry]

I would like to compare known fate survival by season (spring, summer, fall, winter) using annual survival data with 52 time intervals (each interval is 1 week) that is grouped by year (e.g. 2014 and 2015). For instance, is survival more dependent on a spring survvial model than a summer survival model. Getting more complicated I would also like to asses year and season interaction effects on survival.

My thought is to categorize weeks by season in the PIM such that spring would be 1 (weeks 1-13), summer 2 (weeks 14-26), fall 3 (weeks 27-39), and winter 4 (weeks 40-52) for survival by season for both years of data (no year effect). To include year * season survival I would just label the seasons 5-8 for the second year. I am not sure this is the correct method and this method will only indicate difference in survival by season and not allow me to understand if survival is, for example, more dependent on spring survival than summer survival. I would greatly appreaciate any advice on how to group or categorize this data such that I can run the following models:

B0: constant survival
B0 + B1 x time: weekly survival
B0 + B1 x year: survival by year
B0 + B1 x year + B2 x time: survival dependent on interaction of year and weekly time
B0 + B1 x spring: survival dependent on spring season
B0 + B1 x summer: survival dependent on summer season
B0 + B1 x fall: survival dependent on fall season
B0 + B1 x winter: survival dependent on winter season
B0 + B1 x Year + B2 x spring: survival dependent on interactive effect of year and spring season
B0 + B1 x year + B2 x summer: ...........
and so on for rest of combinations.......

Is this something that should be done in the design matrix or just coding in the input file? I do not have any covariates so I am guessing the Design Matrix may not be appropriate.
Thank you!