Problem set 1: Disease frequency and association

The following questions related to Topics covered in the Disease Frequency and Association slides.

Background

A study on Human Immunodeficiency Virus (HIV) infection in two towns in Zambia began in January 2013. The two towns, termed town A and town B, were monitored for new cases of HIV and HIV-related deaths for a whole year. The entire adult population of each town was enrolled in the study. A public health information campaign on HIV took place in town A, whereas town B received financial support to strengthen its health centres. Assume that once a person gets infected with HIV, they are infected for the duration of the study.

The adult population of town A was 5,000 in January 2013. On 1st January, all inhabitants were screened by the research team and 800 were found to be infected with HIV. On 1st April, an additional 400 people were diagnosed with HIV. On 1st July, 500 cases that were diagnosed on 1st January, died. On 1st October, 1,100 adults arrived from a neighbouring city and settled in town A. They were all tested on the day of their arrival and, among them, 300 were HIV-positive. On 31st December, 400 of the original inhabitants of town A were newly diagnosed with HIV.

The adult population of town B was 8,000 in January 2013. On 1st January, they were all screened and 500 were found to be infected with HIV. On 1st April, 200 HIV-positive adults died. On 1st July, 400 additional people were diagnosed with HIV. On 1st October, 2,000 healthy inhabitants left town B and were lost to follow-up, while 1,300 of the remaining adults were diagnosed with HIV. On 31st December, 800 out of the 1,300 recently diagnosed cases died.

Questions

What was the prevalence of HIV infection in each town on 1st January?
What was the prevalence of HIV infection in each town on 31st December?
What were the odds of being HIV-positive in each town on 1st April?
What was the 6-month cumulative incidence (incidence proportion) of HIV infection in each town from 1st January to 1st July?
What was the incidence rate of HIV infection in each town during the entire year?
What was the incidence rate of HIV infection in each town during the first 6 months of the study?
What was the cumulative incidence ratio for the period 1st January to 1st July in town A compared to town B?
Interpret the cumulative incidence ratio that you calculated in (7). Give one associational and one causal interpretation.
What was the incidence rate ratio for the period 1st January to 1st July in town A compared to town B?
Interpret the incidence rate ratio that you calculated in (i). Give one associational and one causal interpretation.
What was the risk difference for the period 1st January to 1st July in town A compared to town B?
Interpret the risk difference that you calculated in (k). Give one associational and one causal interpretation.
How does the number that you calculated for the cumulative incidence ratio compare with the incidence rate ratio that you calculated for the same time period? Are they similar or different and why? Which measure is more useful?
Which intervention seems to be more effective in reducing the incidence of HIV infection? Apart from the effectiveness of the interventions, can you think of any other reasons that could explain the difference?