Assignment Task
Question 1
The table below lists India’s male and female life expectancy at birth for the period 2010-2021.
Year Male Female
2010 65.72 67.73
2011 66.12 68.22
2012 66.49 68.68
2013 66.84 69.11
2014 67.17 69.49
2015 67.47 69.84
2016 67.75 70.14
2017 68.00 70.43
2018 68.24 70.69
2019 68.46 70.95
2020 68.68 71.20
2021 68.22 66.20
(a) Draw the time series and plot of the two sets of exponentially smoothing values (w=0.3) and (w=0.8) for both sexes and determine which exponentially smoothed values are better
(b) Give 3 reasons why females have a greater life expectancy than males in India, and compared with 2019, why did life expectancy for both sexes drop in 2021?
Question 2
A large hospital in Nepal followed-up men with prostate cancer for 11 years. The data is summarised in two tables below, differentiating patients according to treatment status (With and without chemotherapy) and providing the necessary information to calculate survival probabilities.
Table 1: Patents with chemotherapy
| Years | Number at risk | Death | Censored | Survival | Survival probability |
| 1 | 197 | 1 | 15 | ||
| 2 | 3 | 21 | |||
| 3 | 6 | 23 | |||
| 4 | 1 | 21 | |||
| 5 | 3 | 29 | |||
| 6 | 0 | 11 | |||
| 7 | 3 | 5 | |||
| 8 | 1 | 16 | |||
| 9 | 0 | 9 | |||
| 10 | 0 | 11 | |||
| 11 | 1 | 17 |
Table 2: Patents without chemotherapy
| Years | Number at risk | Death | Censored | Survival | Survival probability |
| 1 | 103 | 0 | 5 | ||
| 2 | 8 | 7 | |||
| 3 | 7 | 6 | |||
| 4 | 2 | 5 | |||
| 5 | 4 | 17 | |||
| 6 | 3 | 5 | |||
| 7 | 0 | 6 | |||
| 8 | 0 | 7 | |||
| 9 | 1 | 7 | |||
| 10 | 0 | 5 | |||
| 11 | 0 | 8 |
Calculate the survival probabilities for the two treatment groups
- Draw a graph showing both survival probabilities?
- Investigate the two survival probabilities curves carefully. For survival benefits, suggest whether it would be beneficial for a patient to accept chemotherapy or not? and why?
- Compare the two groups of patients by means of a log-rank test (α=0.05; two-sided)