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Spatial data visualisation is the accurate description of data taking into account the component of space⁽¹⁾. One of the most important parts of spatial data analysis is data visualisation⁽²⁾. Although plots of data such as box plot are among the fundamental tools for data visualisation in general, for the spatial data visualising maps are the most important tools⁽¹⁾.

Nowadays, the use of mapping in the medical context has developed so rapidly⁽³⁾ that the presentation of maps is established as a basic tool in the analysis of public health data^(4&5).

However, it should be noted that there are two main classes of disease maps. They are maps of standardised rates, and maps of statistical significance of the difference between disease risk in each area and the overall risk averaged over the entire map⁽⁶⁾.

It has been emphasised that mapping standardised rates in small areas might create a misleading picture. Furthermore, employing statistical significance instead of standardised rates, especially in areas with large populations, might produce small values of 'P', which are statistically significant but not scientifically interesting⁽⁷⁾.

Given the above facts, it is now generally acceptable, to map standardised rates rather than 'P values'⁽⁸⁾. However, there is one more important question remaining to be answered. What kind of standardisation is the best choice in the area of disease mapping? The aim of the present article is to discuss the pros and cons of two most important ways of standardisation i.e. direct and indirect standardisation methods using a hypothetical example.

Age and sex influence the risk of most diseases and therefore, comparisons of risk in the form of maps must take this important issue into account. Otherwise, observed differences could be confounded by these variables. As a result the process of age and sex adjustment has an important role to play in producing disease mortality and morbidity maps. The aim of an adjustment process is to produce a single summary value, which is unaffected by differences in age and sex distributions⁽⁹⁾.
The two most common approaches of age adjustment are by direct and indirect weighting of stratum-specific rates⁽¹⁰⁾. In the direct approach a weighted average of the age-specific rates from a study population is created based on the age distribution of a reference population⁽¹¹⁾. The corresponding formula is

Direct age adjustment =

in which capital letters represent values that come from the reference population and small letters represent values from the study population. For instance, Ni denotes the number of people in stratum of the reference population. Similarly, n_i and d_i, respectively represent the number of people and the number of cases in stratum in the study population. Finally, represents the summation sign⁽¹¹⁾.
It is also possible to obtain an easily interpreted ratio from the directly standardised rate. This is achieved by dividing the expected number of deaths in the reference population by the observed number of deaths in the reference population over the same period of time⁽¹²⁾. This ratio is termed either the comparative mortality figure (CMF), or equivalently the standardised incidence rate ratio (SRR)⁽¹³⁾.

in which D_i represents the number of cases in stratum i of the reference population. Other symbols in this formula are the same as in the previous one. Furthermore, the approximate standard error (SE) of the SRR can be achieved by using the following formula

The skewed distribution of the SRR may make logarithmic transformation of it more preferable. Therefore, the approximate standard error for the transformed SRR can be obtained by using the following formula

and the 95 per cent confidence interval can be taken from⁽¹²⁾

95% CI = exp (ln(SRR)+1.96*SE (ln(SRR)

In order to adjust the rate using the indirect method, the crude rate in the study population is multiplied by a ratio known as the standardised mortality ratio (SMR)⁽¹¹⁾. The SMR is given by dividing the observed number (O) by the expected number (E) of cases:

and the expected number of cases is given by:

using the symbols as previously described⁽¹¹⁾. The approximate standard error (SE) of the SMR is given by

As with SRR it may be better to use the log transformed SMR to take into account its skewed distribution. Therefore, the approximate standard error for the transformed SMR can be obtained by

and the 95 per cent confidence interval can be taken from⁽¹²⁾

95% CI = exp (ln(SMR)+1.96*SE (ln(SMR)

Direct and indirect adjustment techniques could apply equally to adjustment by factors other than age or in combination with age. For instance, one might adjust rates by sex and age to derive sex and age-specific rates. Therefore, the comparison can be made without concern for confounding by these factors.

The pros and cons of direct and indirect methods of standardisation

It has been argued that if the age distributions of two regions differ, the comparison of their SMRs suffers from the possible bias comparable to statistical confounding. Take, for example, the following hypothetical regions (Table 1).

It should be noted that the stratum-specific incidence rate ratios are all equal to 1. Therefore, the SMR of region one versus region two is also equal to 1, as are all other weighted incidence rate ratios. However, when one compares these two regions with a large reference population, one certainly will find two different SMRs. For instance, take the following hypothetical reference population (Table 2).

Based on this reference population SMR for region one equals 70, while for region two it equals 177.14. However, the directly standardised rate ratios for two regions are identical and equal 42.66. Therefore, when comparing to an external reference population, the SMR yields different rate ratios for regions with a different demographic structure even though the incidence rates within strata are identical⁽¹⁴⁾.

It should be also noted that applying directly adjusted rates also has its own problems. For instance, in this approach the standard error depends on variations in the age specific number of cases rather than the total number of cases, which may provide less stable estimates. As a result the standard error is generally larger than that of indirectly adjusted rates⁽¹²⁾. Nevertheless, this advantage of the SMR is easily outweighed by its disadvantage in terms of validity⁽¹³⁾. Finally, it is usual to use the national population as the standard population in summarising age- and sex- specific rates for geographical regions within a country⁽¹⁵⁾.

Based on the above discussion it has been concluded that morbidity and mortality maps can be misleading when based on indirectly adjusted rates or a function of them. Therefore, the use of the direct method of age adjustment for mapping purposes, accompanied by an examination of age-specific rate patterns is recommended⁽¹⁶⁾.

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