Assignment 1, Survival Analysis & Regression for Rates, POPH 90145 1 Survival Analysis & Regression for Rates POPH 90145: Assignment 1 This assignment is to be submitted for assessment by 11.59pm Monday 11th October 2021. The total number of marks available for this assign- ment is 25 (marks for individual questions are indicated below) which forms 30% of the total marks available for this subject. Do not include any Stata code or output in the main text of your submission - relegate any such ma- terial to one or more appendices. Please format any results you want to show in a way that would be suitable for inclusion in a report or research paper. You should be able to respond to the questions below in 4 - 6 pages. Ten pages is far too long! Marks may be deducted for poorly organised or excessively long submissions. Incidence Rates and Rate Ratios from Poisson Regression Safe Work Australia (SWA) is a statutory body established by the Australian federal government in 2008 to develop national policy relating to Work Health Safety (WHS) and workers’ compensation. They work in partnership with state and local governments, employers and employees to drive national pol- icy development on WHS and workers’ compensation matters that include collecting, analysing and reporting data. Their website... https://www.safeworkaustralia.gov.au/statistics-and-research ...offers access to a variety of data and published reports containing the re- sults of statistical analyses of these data. We’ll use a data set from SWA on work-related traumatic injury fatalities by industry between 2012 and 2016. The data have been arranged in a format ready for analysis and provided as a Stata dataset, swa.dta on Canvas. Note that the data are in grouped / aggregate format, so you do not need to use stset command. Use this dataset to to answering the following questions. The Stata data set swa2021.dta has four variables. They are (1) year: The calendar year between 2012 and 2016 inclusive, taking values 0, 1, 2, 3 and 4 indicating the number of years since 2012; (2) industry: The name of the industry group; (3) fatal: The number of work-related traumatic injury fatalities; and (4) pop: The number of workers. In other words, the data set contains counts of the number of fatalities and the number of workers for each industry in each year from 2012 to 2016 inclusive. Assignment 1, Survival Analysis & Regression for Rates, POPH 90145 2 1. Incidence rates ignoring year and industry 1(a). [2 marks] Calculate and state an estimate (and a 95% confidence interval (CI) for the corresponding population quantity) of the overall incidence rate (IR) of work-related fatalities (per 1,000,000 worker-years) during the period of 2012 to 2016 (so ignoring year and industry). 2. Annual incidence rates 2012 - 2016 ignoring industry 2(a). [2 marks] Use Poisson regression to estimate (with 95% CI) the population IR of work-related fatalities in each year, that is, gen- erate a separate estimate (and 95% CI) of the population IR for 2012, 2013, 2014, 2015 and 2016. Present the results in a table using per 1,000,000 worker-years as the units for the estimated incidence rates. In Stata the command bysort var: before the poisson command performs a separate analysis for each category of the var variable. 2(b). [2 marks] Assuming that there is a linear relationship between log(IR) and year, use Poisson regression to estimate (with 95% CI) the population incidence rate ratio comparing incidence rates one year apart (i.e. a one year increase in the value of year). 2(c). [2 marks] Is the assumption of constant IR over year implied by Question 1(a) reasonable? Justify your answer. 3. Incidence rates by industry aggregated over the five-year pe- riod 2012 - 2016 ignoring year 3(a). [2 marks] Use Poisson regression to generate and display an es- timate (with 95% CI) of the population work-related fatality IR for each of the 17 industries. 3(b). [2 marks] Which industries have a population work-related fatal- ity IR that is more than 40 per million worker-years? 3(c). [2 marks] Which industries have a population work-related fatal- ity IR that is less than 5 per million worker-years? Assignment 1, Survival Analysis & Regression for Rates, POPH 90145 3 4. Incidence rates by year and industry 4(a). [2 marks] Assuming that there is a linear relationship between log(IR) and year, use Poisson regression to estimate (with 95% CI) the incidence rate ratio comparing incidence rates one year apart (i.e. a one year increase in the value of year) adjusting for industry by including industry as a categorical variable (main effects only, no interaction between year and industry). 4(b). [2 marks] Is the assumption of constant IR over year implied by Question 1(a) still reasonable? Justify your answer. 5. Missing data: Five of the sixteen industries represented on the SWA data set have only four, not five, annual records. That is, they are missing data for one of the five years: Scientific & Technical and Retail for 2015 and Accommodation & Food, Education & Training, Real Estate and Wholesale for 2016. 5(a). [2 marks] Suggest a plausible reason for the missing data. 5(b). [5 marks] Suppose the six missing records are included in the data set and the analyses in Questions 1 - 4 are redone. Which of the estimates of IR’s and IRR’s are likely to change substantially, and which of the conclusions are likely to be affected? Why?