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Calculation of Hospital Mortality


  1. Calculating relative risk, also known as risk ratio, draws our attention to unfair differences in disease deaths and diagnosed cases due to weekend admission in spite of week day admission (McNutt et al., 2003).

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

  1. Absolute difference, is also known as risk difference or attributable risk.

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.

  1. Attributable fraction refers to the proportion of the outcomes among the exposed group that are due to the exposure.

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.

  1. Population attributable risk can be defined as the number of cases in the whole population that can be attributed to the exposure.

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

  1. Population attributable fraction can be defined as the proportion of the outcomes in the whole population that are due to the exposure. It is calculated as-

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

  1. A relative risk that is greater than 1.0 shows that there is an increased risk among the people in Group A, in our case it is the group of weekend admission. This means if the risk ratio was 1.255, people in Group A, that is, weekend admission patients would be 25% more likely than people in all other groups, in our case, weekday admission, to die from a cause. From the attributable risk and attributable fraction, we can say that the risk ratio is not that high. If the attributable fraction was close to 1, then there was the case when relative risk was high and the risk factor was prevalent. In our case, it is close to zero rather than 1 (Copeland, 1977). While attributable risk helps us estimate the excess risk among the exposed that can be attributed to the risk factor, from a public health perspective it is often more useful to re-define the attributable risk in terms of the whole population, and thus to know the proportion of cases in the total population that can be attributed to the risk factor. For this calculation, we use the population attributable risk (PAR). Population attributable risk depends not only on the excess risk imposed by the exposure, but also on the share of the total population that is exposed (Corsi, 2016).
  1. Other measures should also be calculated for the validity. Some measures like all cause mortality rate, disease specific mortality and case fatality rate should be calculated. For concluding that weekend admission are more prone to mortality than weekday admission, further analysis need to be done.


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.


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.

Remember, at the center of any academic work, lies clarity and evidence. Should you need further assistance, do look up to our Accounting and Finance Assignment Help

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