TABLE 1
Risk ratio is calculated by dividing the death or disease risk in a specific population group (Group weekend admission) by the risk of people from all other groups.
To calculate the risk in each group, we divide the number of people who died by the population totals in each group.
For this we calculated cumulative incidence in each group which is given by,
Cumulative incidence = Number of individuals experiencing a NEW event during a time period / Number of susceptible individuals at the BEGINNING of the time period
Cumulative incidence is also referred to as ‘incidence proportion’.
Cumulative incidence of weekend group (exposed population) is given by-
= 2,467 ÷ 23,297
= 0.1058
Cumulative incidence of weekday group (unexploded population) is given by-
= 5,929 ÷ 70,324
= 0.0843
Risk ratio is calculated as:
RR = Cumulative incidence in exposed population ÷ Cumulative incidence in unexposed population
RR = 0.1058 ÷ 0.0843
= 1.255
Attributable risk refers to the number of cases among the exposed group that can be attributed to the exposure. This is also referred to as ‘risk difference’ (RD). Absolute difference, in mortality rates by admission period is given by-
AR = Incidence in exposed – Incidence in unexposed
= 0.1058 – 0.0843
= 0.0215
This works for both cumulative incidence and incidence density.
Attributable fraction associated with a weekend admission is calculated as:
AF = ( Incidence in exposed – Incidence in unexposed) / Incidence in Exposed
= ( 0.1058 – 0.0843) / 0.1058
= 0.0215 / 0.1058
= 0.2032
It can alternatively be calculated as ( Risk ratio – 1) .
Attributable fraction for the population combines both the relative risk of an incident with respect to the factor, as well as the prevalence of the factor in the population. Values of AF close to 1 indicate that both the relative risk is high, and that the risk factor is prevalent.
Population attributable risk for weekend admission is given by-
PAR = Incidence in total population − Incidence in unexposed group
Incidence in total population is calculated as:
= 8,396 / 93,621
= 0.0896
Hence, Population attributable risk is-
= 0.0896 – 0.0843
= 0.0053
PAF = F * (RR-1) / 1 + F * (RR-1)
In a case-control study RR would be replaced with OR. F is the prevalence of the exposure in the population. You will either have a source for the prevalence of the exposure, or in a cohort study
F = Total number exposed / Total number in study
= 8,396 / 93, 621
= 0.0896
Therefore, PAF = 0.0896* ( 1.255 -1) / 1 + 0.0896 * ( 1.255-1)
= 0.0896 * 0.255 / 1 + 0.0896 * 0.255
= 0.022848 / 1.022848
= 0.02233
TABLE 2
1. For calculating stratum specific risk ratios, we need to calculate risk ratios for both the age groups, that is, for the age group below 65 years and for the age group of above 65 years.
Risk ratio for in hospital mortality, by admission period (weekday and weekend),among people admitted to a hospital for stroke, below the age of 65 years can be calculated as:
RR = Cumulative incidence in exposed population ÷ Cumulative incidence in unexposed population
RR = (390 ÷ 4927) / (647 ÷ 16,088)
= 0.0791 / 0.0402
= 1.9676
For the people with more than 65 years of age-
RR = ( 2077 ÷ 18,370) / (5,282 ÷ 54,236)
= 0.1130 / 0.0973
= 1.1613
2. Effect modification occurs when the magnitude of the effect of the primary exposure on an outcome (i.e., the association) differs depending on the level of a third variable. In our case, there is only a mild difference between the risk ratios of age 65 years above and below that. So, we cannot say that age group is an effect modifier.
References
Copeland, K. T., Checkoway, H., McMichael, A. J., & Holbrook, R. H. (1977). Bias due to misclassification in the estimation of relative risk. American journal of epidemiology, 105(5), 488-495.
Corsi, D. J., Mejía-Guevara, I., & Subramanian, S. V. (2016). Risk factors for chronic undernutrition among children in India: Estimating relative importance, population attributable risk and fractions. Social Science & Medicine, 157, 165-185.
McNutt, L. A., Wu, C., Xue, X., & Hafner, J. P. (2003). Estimating the relative risk in cohort studies and clinical trials of common outcomes. American journal of epidemiology, 157(10), 940-943.
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