Survival Analysis for School Admissions

[Deepanshu]

I am trying to calculate survival rate for all grades (Kindergarten to 12th Grade) of school. See the example below for Grade 1 students. Y0 refers to number of students enrolled in grade 1 in that particular year. Y1 : how many of them are still in the school 1 year later. These students would have moved to grade 2 in Y1. Similarly for the other years. I have similar data for other grades as well for years 2010 to 2019. As of now I am calculating survival rate based on (number of students in Yn divided by number of students in Y0). For example : In Y2 survival rate is column sum of Y2 divided by column sum of Y0 (excluding 2018 as data is not available in Y2 for 2018). It is 76%. I will do the same calculations for other Yn periods and for other grades and then average out all the annual rates.

I wanted to know is there any better way to calculate survival rate more statistically using Kaplan-Meier estimate
?

+------+-----+-----+-----+----+----+----+----+----+----+----+
|      | Y0  | Y1  | Y2  | Y3 | Y4 | Y5 | Y6 | Y7 | Y8 | Y9 |
+------+-----+-----+-----+----+----+----+----+----+----+----+
| 2010 |   3 |   3 |   3 |  2 |  2 |  2 |  2 |  2 |  2 |  2 |
| 2011 |  17 |  17 |  15 | 12 | 11 | 11 |  7 |  7 |  7 |    |
| 2012 |  47 |  39 |  35 | 30 | 26 | 24 | 22 | 22 |    |    |
| 2013 |  58 |  53 |  47 | 41 | 38 | 31 | 28 |    |    |    |
| 2014 |  72 |  61 |  49 | 45 | 45 | 39 |    |    |    |    |
| 2015 | 113 | 101 |  87 | 79 | 68 |    |    |    |    |    |
| 2016 | 128 | 113 |  95 | 85 |    |    |    |    |    |    |
| 2017 | 134 | 114 | 104 |    |    |    |    |    |    |    |
| 2018 | 114 |  98 |     |    |    |    |    |    |    |    |
+------+-----+-----+-----+----+----+----+----+----+----+----+

[SteveDenham]

Examine the examples for PROC LIFETEST in the documentation.  There should be at least one that fits what you want, although it will not give you an overall survival rate mean, as the probability of survival from one year to another is not constant.  You would also have to re-arrange your data to include certain other data.  See Example 70.3 Life-Table Estimates for Males with Angina Pectoris in the SAS/STAT (14.1) documentation.

SteveDenham