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18. Presentation of results

The primary output of the directly attributable health loss approach described above (based on Equations (1)-(4)) is the potential annual change in health effect for the assessed population (expressed in QALYs or DALYs) that results from implementing the alternative scenario instead of the reference scenario. However, it is also very informative to show also intermediate results such as the contributions of different health effects to the total, and the severity, incidence and years of life lost for each effect.

The format used by the Qalibra software for displaying these primary numerical outputs is illustrated in Table 3. This shows results for 2 health effects from an assessment on consumption of oily fish done as a case study in the Qalibra project (the full assessment includes additional adverse and beneficial effects). The dietary change (increasing fish consumption to 200g/week for those individuals whose current consumption is lower) has a beneficial impact on both health effects so the individual and total changes in DALYs are negative. The assessment relates to 999 individuals (the number specified by the user who created the assessment), and the results are estimates of the annual average health impact for that population.

Table 3 is divided into several sections, in descending order:

·          The change in DALYs between scenarios, for each effect and overall

·          The DALYs for each scenario (reference and alternative)

·          The incidence of the effects in each scenario

·          The average magnitude of effects in each scenario (this applies only to continuous effects, and shown as zero for quantal effects)

·          Results for those individuals who recover from each effect (the number of individuals in this group, the average duration of disease YLD, and the total DALYs)

·          Results for individuals who continue with the effect to their normal life expectancy (as above)

·          Results for individuals who die from each effect (as above plus the average years of life lost YLL).

The Qalibra software generates 95% uncertainty intervals for every output, although due to limitations of space these are shown only in the top row in Table 3. These intervals represent the combined effect of the uncertainties the user has quantified for the various inputs (uncertainty in the dose-response relationships for probability of effects).

Numerical results are shown to 6 decimal places, to enable the user to check the stability of the estimates by comparing different model runs. Given the many uncertainties affecting such assessments, it is recommended to truncate the results to fewer significant figures for general presentation.

The numerical results shown in Table 3 are aggregated over the population of individuals specified by the user (this can be any positive number). The Qalibra software also generates 4 types of graphical output that show how contributions to the overall health impacts vary across the population. This may be useful both in helping the user to understand the way the totals are built up, and for identifying situations where part of the population experiences a net health gain while another part experiences a net loss.

Three of the graphical outputs generated by Qalibra are illustrated in Figures 3-5, and the fourth is a variant of Figure 3 that uses a pie chart to show the proportions of individuals with zero and non-zero DALY changes. Figures 3-5 all relate to the same example assessment as Table 3.

Figure 3 is a histogram showing the distribution of individual contributions to the total annual DALY change for the population, i.e. how the total shown in the top right hand corner of Table 3 is distributed between the 999 individuals modelled in that assessment. It can be seen there is a large peak of individuals with close to zero DALY change, and a proportion of individuals with varying degrees of expected benefit (negative DALY change, to the left of the figure). Note that even though the actual impact of stroke or fatal CHD is not small (e.g. a total of around 15 years of life lost for fatal CHD) the expected impact per person per year is very small because (a) the probability of a particular individual getting CHD in a given year is small, and (b) the change in that probability between the reference and alternative scenarios is still smaller.

Figure 4 shows the same distribution as Figure 3, but plotted as a complementary cumulative distribution function. This provides more detail on the shape of the modelled distribution than the histogram, and also allows the uncertainty intervals to be plotted. The curve shows the percentage of the population (on the vertical axis) with DALY changes more positive than each point on the horizontal axis; for example, it can be seen that about 35% of the population have no change in health: this is because these individuals already consume over 200g fish per week in the reference scenario, and it is assumed their consumption is unchanged in the alternative scenario.

Figure 5 shows the same DALY changes as Figures 3 and 4, plotted against the two covariates used in this assessment: age (a mandatory covariate in every assessment) and gender. Close examination of the left hand graph suggests that although most changes are very close to zero, larger changes are more likely at lower ages: this reflects the fact that individuals who experience onset of a disease at young ages have more years of life remaining to be lost or affected by disease than do older individuals. The right hand graph suggests that the larger changes are more likely for males than females: this is a consequence of different dose-response relationships for males and females in this assessment.  

The Qalibra software also allows the user to download the DALY estimates for the individual persons for each cell in the top three rows of Table 3. This enables the user to examine, outside the Qalibra software, the variation between individuals within the population and to generate statistics and graphs in the format of their choosing.

It is emphasised that results should always be accompanied by a clear explanation of how they should be interpreted, including that they represent an indication of the potential annual change in health impact for the population (see next section). In addition, the quantitative results should always be accompanied by evaluation of the many uncertainties that inevitably affect risk-benefit assessment, some of which were indicated in the preceding sections and Table 1. It is recommended to use the format illustrated in Table 2 to summarise the uncertainties together with an evaluation of their potential impact on the assessment outcome. It is also recommended that each assessment should be concluded with an overall narrative characterisation of the net health impact, which takes account of both the quantitative and qualitative evaluations and also any other relevant evidence regarding the health impact of the scenarios under assessment, e.g. comparisons with epidemiological data that have not been used as model inputs.

Table 3. Example of tabular risk-benefit assessment results generated by Qalibra software for effects of oily fish consumption on incidence of stroke and fatal coronary heart disease (CHD). Reference scenario = current Dutch diet, alternative = oily fish consumption increased to 200g/week for those individuals whose current consumption is lower. Results are estimates of annual directly attributable health effects for a sample population of 999 individuals, expressed in DALYs. 95% uncertainty intervals are shown in brackets (produced for all results but shown only in top row here). See text for more explanation.  

 

Incidence of stroke  

Incidence of fatal CHD  

Total:

Change in TOTAL DALY from Reference scenario to Alternative scenario

-2.575496 (-5.334609, 0.017958)

-1.760700 (-3.211928, -0.270590)

-4.323598 (-7.520069, -1.367580)

TOTAL DALY, Reference scenario

34.782921

16.229677

51.015229

TOTAL DALY, Alternative scenario

32.208514

14.468424

46.686763

Incidence (per year) in 999 individuals, Ref scenario

3.296041

1.040699

 

Incidence (per year) in 999 individuals, Alt scenario

3.062299

0.932302

 

Average magnitude of effect, Reference scenario

0.000000

0.000000

 

Average magnitude of effect, Alternative scenario

0.000000

0.000000

 

Recover, Reference scenario

0.000000

0.000000

 

Recover, Alternative scenario

0.000000  

0.000000

 

Total YLD if recover, Reference scenario

0.000000

0.000000

 

Total YLD if recover, Alternative scenario

0.000000

0.000000

 

TOTAL DALY if recover, Reference scenario

0.000000

0.000000

 

TOTAL DALY if recover, Alternative scenario

0.000000

0.000000  

 

Survive (with effect), Reference scenario

3.296041

0.000000

 

Survive (with effect), Alternative scenario

3.062299

0.000000

 

Total YLD if survive (with effect), Ref scenario

57.021182

0.000000  

 

Total YLD if survive (with effect), Alt scenario

52.800843

0.000000

 

TOTAL DALY if survive (with effect), Ref scenario

34.782921

0.000000

 

TOTAL DALY if survive (with effect), Alt scenario

32.208514

0.000000

 

Die (from effect), Reference scenario

0.000000

1.040699

 

Die (from effect), Alternative scenario

0.000000

0.932302

 

Total YLD if die (from effect), Reference scenario

0.000000

0.000000

 

Total YLD if die (from effect), Alternative scenario

0.000000

0.000000

 

Total YLL if die (from effect), Reference scenario

0.000000

16.229677

 

Total YLL if die (from effect), Alternative scenario

0.000000

14.468424

 

TOTAL DALY if die (from effect), Reference scenario

0.000000

16.229677

 

TOTAL DALY if die (from effect), Alternative scenario

0.000000

14.468424

 


 

Figure 3. Histogram of individual contributions to the change in annual population DALYs between reference and alternative scenarios, for the assessment shown in Table 3. See text for details.

Figure 4. Complementary cumulative distribution of individual contribution to annual change in population DALYs between reference and alternative scenarios, for the assessment shown in Table 3. See text for details. The curve shows the percentage of the population (on the vertical axis) with annual DALY changes more positive than each point on the horizontal axis.

Figure 5. Individual contributions to annual change in population DALYs between reference and alternative scenarios shown in relation to age (left hand graph) and gender (right hand graph) for the assessment shown in Table 3. See text for details.