S-TIME-DISTANCE – DUAL PARALLEL SYSTEM FOR ANALYSING INDICATORS EXAMPLE OF GENDER DIFFERENCES IN LIFE EXPECTANCY IN THE WORLD

P. Sicherl. Prof. Dr., Sicenter and University of Ljubljana, Slovenia. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 01 October 2018 Final Accepted: 03 November 2018 Published: December 2018

The S-time-distance method enables two-dimensional analysis of disparities in time series indicators: distance in time for a given level of the variable is complementing prevailing static distance at a given point of time. Expressed in time units it is intuitively understandable to everybody and comparable across variables, fields of concern and units of comparison. We need new data and indicators, but we also need innovative concepts of looking at data and new generic statistical measures to better perceive and exploit the information available in existing data. It is recommended that for time series analysis in many fields S-time-distance may be tested to provide new insight from existing data. Two generic statistical measures, S-time-distance and Stime-step, S-time-matrix and novel application for monitoring implementation of targets are discussed and demonstrated on the example of gender differences in life expectancy at birth in the world. The degree of disparity may be very different in static terms and in Stime-distance; for gender disparity in life expectancy in EU static index is less than 7 percent while S-time-distance amounts to 26 yearsa very different perception of the divide. Comparing four indicators for 200 countries, for life expectancy and obesity prevalence women consistently show higher values, men lag them in about 100 countries for more than 20 years. For mean BMI gender differences are more balanced, while for diabetes prevalence the situation is different, incidence for men is ahead of women, in 34 countries men are ahead of women for more than 20 years.

…………………………………………………………………………………………………….... Introduction:-
At the theoretical level the S-time-distance methodology adds innovative dual parallel generic system for analyzing indicators in the parallel universe of time beyond the static differences, adding new vocabulary and not replacing the current methods. In analysis of time series indicators differences between two (or more) time series can and should be compared in both dimensions of the scatter diagram with axis of the selected variable Y and time X, vertically and horizontally. This idea led to the introduction of the S-time-distance concept as a measure of disparities in economic and social development (Sicherl, 1973) but has over the years evolved towards a much more general approach. The approach is universal, results expressed in time units are easily understandable by everyone, and applicable to a wide variety of fields at both the macro and micro levels. Since S-time-distance view provides an Resources for the study of gender differences over long period of time were possible for life expectancy with UN data for quite some time but the extension to body mass index and diabetes was made available by two studies in Lancet: the study of trends in adult body-mass index (NCD Risk Factor Collaboration; NCD-RisC, 2016a) and the study on diabetes (NCD-RisC, 2016b) (and with more details on www.ncdrisc.org). These and some other data provided by the Institute of Health Metrics and Evaluation (IHME) were the resource over the long-time horizon at disaggregated gender level that made it possible that S-time-distance framework could examine the astonishing magnitudes of time gaps for gender difference in either directions. IHME also used the time distance concept to analyse the lag of the US counties for life expectancy behind an international context (Kulkarni et al., 2011).
Procedure for calculating S-time-distances may be as follows. For each country three time series of data are ordered: time, female and male life expectancy. For each year one takes the value of male life expectancy for a given year, searches the series of female life expectancy and determines in which year the value of the comparing male life expectancy was attained, and subtracts the respective two times. If time series are ordered vertically, this means vertical look-up procedure; if horizontally, then horizontal look-up procedure. For large time series it is useful to prepare software tool for such procedure.
Another resource for long-term S-time-distance analysis was the database from International Telecommunication Union (ITU). In the Measuring the Information Society 2010 report in the section on time distance analysis ITU and SICENTER established the time lead or time lag behind Sweden for about 200 individual economies for mobile cellular penetration. It was also established that for the average of developing countries the lag for mobile cellular penetration rate behind Sweden was because the very high dynamics less than 10 years while for life expectancy it was more than 60 years (ITU, 2010). Furthermore, the resource for a shorter time span was the database for Millennium Development Goals (MDGs) implementation (UN 2014, 2015a, 2015b, 2015c).

Method:-S-time-distance methodology
Events are dated in time, therefore in time series comparisons the notion of time distance was always there as a "hidden" dimension. What was needed was to systematise and formalise the approach and define an appropriate statistical measure for operational use.
A broader theoretical framework is needed. The conventional approach does not realise that in addition to the disparity (difference, distance) in the indicator space at a given point in time, in principle there exist a theoretically equally universal disparity (difference, distance) in time when a certain level of the indicator is attained by the two compared units. It follows that S-time-distance has an important role to play in complementing the conventional static perception and measures of disparity. The perception of and the conclusions about the degree of disparity based on two-dimensional analysis of proximity provide a better understanding of the situation; a new dimension is added while no earlier results are lost or replaced.
Time distance in general means the difference in time when two events occurred, and the concept is applied in many fields. In our case, for analysis of time series indicators, a special category of time distance S-time-distance is defined, 179 which measures the distance (proximity) in time between the points in time when the two series compared reach a specified level of the indicator X. The observed distance in time (the number of years, quarters, months, etc.) is used as a dynamic (temporal) measure of disparity between the two series in the same way that the observed difference (absolute or relative) at a given point in time is used as a static measure of disparity (Sicherl 2011a(Sicherl , 2011b(Sicherl , 2004. In other words, while most of the analysis of disparities are based on static analysis, it is obvious that for time series indicators differences between two (or more) time series can and should be compared in both dimensions of the scatter diagram with axis of the selected variable Y and time X, vertically and horizontally. The only question is: why not? Why not experimenting out of the box? Is there a limiting belief that static analysis in disparity and inequality field is good enough and that it fully exploits the information available in database? Technically, why gaps between two or more time series are not studied in both directions (dimensions)? An additional view of existing databases can provide better utilisation of information content and derive new insights from existing data.
Time has until now been used in comparisons mainly as location information, i.e.as a coordinate in a parameter frame forming a coordinate system that is used to organise (or index) a set of variables. In other words, it has played the role of a descriptor, subscript or identifier. The new S-time-distance approach offers new avenues for detecting additional information content, without replacing the existing views. If we choose to interchange in the time series database the roles of the level of the variable and of time, the given level of the variable becomes a descriptor or identifier and time becomes a numeraire in which certain distances between the compared units and time series can be expressed and measured. For a given level of X L , X L = X i (t i ) = X j (t j ), the time span separating unit (i) and unit (j) for the level of variable X L will be written as S ij (X L ) = t (X L ) = t i (X L )t j (X L ) Three subscripts are used to indicate the specific value of S-distance: (1 and 2) between which two units is the time distance measured and (3) for which level of the indicator (in the same way as the time subscript is used to identify the static measures). In some cases also the fourth subscript may be necessary to indicate to which point in time it is related.

Sicherl-time-step (in short S-time-step, SLTS, level time step)
The S-time-step measures the time elapsed between two levels of a single time series, providing an alternative description of its growth rate, measuring the growth of a series by using the inverse relation to the conventional X/t growth rate metrics. For instance, as shown in Table 1 for the EU that the average female life expectancy needed in the past about 6 years, and male life expectancy 5 years, to increase the life expectancy for one year from 79 to 80 years for females, and from 77 to 78 years for males. This is a complementary description of the dynamics of life expectancy to the conventional growth rate value of about 0.2 percentage per year. Both measures are valid description of the dynamics of change, while for general public S-time-step might be even easier to understand and perceive. S-time-step is expressed in units of time and is defined as: The simple example of visualisation of time series indicators and measures is illustrated in Fig. 1. The difference between female and male life expectancy for EU28 in 2015 is estimated at 5.4 years. This absolute measure of gender 180 differences for the value of life expectancy of 77.9 years for male average in 2015 is the first and easy understandable perception of the disparity between sexes in this indicator. This may also be expressed in index or percentage.  Table 4 and for obesity prevalence, mean BMI and diabetes prevalence in Table 5.

Sicherl-time-matrix (STM) is a tool that provides a table-graph format which is defined by levels of the variable
and derives times when such variables were attained. One problem with the conventional tabular presentation of time series data is that the full matrix cannot be easily presented when these data span very long periods. Hence, STM presents a more parsimonious way to available evidence. The conventional  (Sicherl, 2005) or days or seconds in some experiments. Study EU at a Glance (Sicherl, 2014c) presents S-time-matrix overview of 30 selected indicators over 28 EU countries over time, which is probably the most condensed summary picture of disparities and dynamics of EU countries over many domains over time.

S-time-distance monitoring of implementation of targets
There are many possible applications of S-time-distance methodology, some of them are available on www.gaptimer.eu. In this section the attention is brought to a line of applications that is very practical in very broad set of situations where targets, benchmarks, projections and hypotheses are compared with actual values and are formed as differences between two time series. Again, the two relevant time series of expected and actual values over time are compared vertically and horizontally in Figure 2. Figure 2 deals with a specific application of the time distance methodology to monitoring implementation of MDG targets (Sicherl 2015), and more generally to comparing actual values with target values, forecasts, budgets, scenarios and plans. For the study for monitoring implementation of MDG targets the continuously increasing or decreasing lines to targets were appropriate. Therefore, the procedure was easy to apply to monitoring implementation of the 10 selected MDG indicators for world regions and in details for five MDG indicators for 125-154 countries (Sicherl, 2015). This application can be used again for the implementation of ongoing UN Sustainable Development Goals (SDGs), for world regions as well for individual countries of the numerous sets of indicators. Also, The National Statistical Co-ordination Board in Philippines is an example of how one policymaker in one country used the timedistance measure of MGDs implementation together with other measures (Sicherl, 2013).
In a broader context the meaning of the line to target in Figure 2 could be interchanged to represent regression line or projection so that the two-dimensional dual parallel system for analysing indicators can be extended also to evaluating goodness-of-fit in regressions, models and forecasting (Sicherl, 2011a). For more complicated cases one should consult Granger and Yeon (2003a and 2003b) for application of forecasting inflation in the USA.
Monitoring implementation of targets is an integral part of decision making at many levels and in many domains. The innovation is that implementation of targets is described in two dimensions: static deviation from the line to target at a given point in time and S-time-deviation at a given level of the indicator. Describing the implementation of targets as leading or lagging in time against the line to specified targets or projections is very useful. The 183 characteristics that it is expressed in time units means that it is comparable across variables, fields of concern and units of comparison, which makes S-time-distance an excellent complementary analytical and presentation tool for policy, business and scientific debates. It can help us to form a new perception of the magnitude of the gap between the implementation and proclaimed targets for a given indicator as well as across more indicators.

Overview of gender disparities in life expectancy in the world
The UN estimates show nearly unanimous conclusion that female life expectancy at birth is higher than that for males, this holds for countries including 99.5% of the world population. Without major changes in health conditions the UN estimates expect that higher female than male life expectancy at birth would prevail over the whole period of 150 years (1950-2100) (UN, 2011). Table 2 shows the absolute value of the gender difference in life expectancy over the period of 55 years for selected regions. The gender difference is higher in more developed regions (MDR) than in the less developed regions LDR (as defined by UN DESA), of over 6 years and 3 years, respectively. This is confirmed also by comparing USA and EU28 to China and India. Whether this gender differences are large or small is a question of the subjective weights that people assign to the magnitude of such disparity.
The conclusion that the gender disparity in life expectancy is very persuasive and a long-standing phenomenon is further confirmed by introducing the S-time-distance statistical measure as another complementary perception of the degree of the female-male disparity in life expectancy. Table 3 shows this additional perspective, comparing timeseries in the horizontal dimension, i.e. for a given level of the variable.  S-time-distance measures provide another impression about the magnitude of the degree of the gender differences in life expectancy as compared to percentage differences. For the USA and the EU the S-time-distance lags of about 38 years and 26 years, respectively, give impressions of much larger disparity than the static difference below 10 percent. Looking over a longer period the low growth rate of life expectancy indicates that this gender disparity will be very difficult to change or even eliminate, while the disparity of less than 10 percent would give a very different impression. More detailed regional examination is made available in Table 4. After analysing gender differences by S-timedistances for each of 200 countries it is possible to systematise the results and conclude that within the very clear overall tendency there were very great differences between countries and regions. The S-time-distance results in years are ordered in two sections: male ahead of female, and male behind female. At a glance one can observe that in only two countries (in Sub-Saharan region) the life expectancy estimates at birth for males are higher than for females, for 198 countries out of 200 countries life expectancy for females is higher than for males. By counting the number of countries, this means 1 percent, in terms of population even less. Countries are then in each section ordered by the magnitude of S-time-distance disparity in classes of 10 years.  In percentage terms in 2015 the range of sex differences for 200 countries varied from -2.9 percent in Swaziland to about 15 percent for Belarus. The perception of the magnitude of sex differences is very different as S-timedistances varied from five year in favour of men in Swaziland to about 60 years! in Belarus in favour of women. We need both measures to understand the reality. Across regions for life expectancy S-time-distances of male behind female were higher than 20 years in Central and Eastern Europe, followed by Latin America and Caribbean, high income Western countries, and Central Asia, Middle East and North Africa. On the contrary, for countries in the South Asia region the S-time-distance lag did not exceed ten years. Though the S-time-distances for the past should not be taken as prediction for the future, these values indicate that the gender disparity in life expectancy is very persistent and will be in most countries very difficult to change. These measures of gender differences can be used also as dependent variable for further studies of the factors leading to these differences.

Results:
Expanding the method to obesity, mean BMI, and diabetes: are gender differences large or small? The availability of new data of longer time series for 200 countries makes possible productive application of S-timedistance methodology for describing and analyzing differences between females and males in the parallel dimension of time. As the focus in utilising the available datasets the gender difference in these indicators were selected, which can be attractive from both the medical and social standpoint and these results can be further elaborated in much more details with additional studies. They present a very remarkable broad effort for preparing the database and analysis on these topics. Source: Own calculations based on data from UN (2015d) and NCD-RisC (2016c).

186
Here the results of the S-time-distance measure for 200 countries are presented to analyse how the time lead or time lag vary among four indicators: life expectancy, obesity, mean BMI and diabetes. It was observed that the number of countries where the stability of male female relationship would prevail over many years in one or the other direction is very different for the four selected indicators.
The number of countries where females are ahead of males is falling from the left to the right: life expectancy 198, obesity prevalence 176, mean BMI 139, and diabetes prevalence 89 (where the balance is turned to values for males being ahead of females). The circles in Table 5 indicate cases when the S-time-distance results show gender disparity as larger in direction of either gender for over 20 years. First two, life expectancy and obesity are tilted strongly in the direction of dominance of females being ahead of males. For obesity prevalence even 103 countries are in the category males behind females for more than 20 years.
China and India show obesity prevalence below 10 percent, while for Egypt, Turkey and South Africa the female obesity percentages are at or above 36 percent. For USA the percentage is also high at 34 percent, for United Kingdom at 28 percent. However, there is an important distinction. For USA and for the United Kingdom the obesity prevalence is high also for men so that gender time distances are only few years. For Egypt, Turkey and South Africa the time distances show large time differences of 28, 24 and more than 40 years, respectively, for higher values for women.
Gender distribution of countries for mean BMI is more balanced, yet there are tremendous differences between countries; with 45 countries S-time-distance being in the range of 20 years to more than 40 years of lag of males (like Swaziland) confronting the other group of 20 countries with values in the range -20 years to less than -40 years, with time lead of males (like Switzerland). This is a very different perception of the gender disparities in the countries as those of percentage differences at given point in time. For the two countries mentioned the perception based on percentage differences is moderate, around 15 percent in either direction. This range of percentages does not give the impression that the gender difference would be very difficult to change over time; the time gap between genders of 40 years leads to a very different conclusion.
For diabetes the gender distribution is significantly different. The number of countries (111) with males outnumbered females for diabetes prevalence, showed a different situation than the situation for the earlier three indicators. The 34 countries showed time lead for males of more than 20 years indicating that diabetes is over a long time in these countries affecting more men than women. The diabetes data relate only to 35 years in the past.. The highest values for diabetes are happening in high income Western countries and high income Asia Pacific. For a group of these countries the S-time-distance showed that for diabetes prevalence women were experiencing lower values than men of more than 35 years.

Discussion:-
Time is besides money one of the most important reference frameworks in a modern society. Yet the existing methods in social science and statistics do not fully utilise the information content with regard to certain aspects of the time dimension that are embodied in the analysed data and could contribute to a better understanding of the disparities. This is regrettable as time is tremendously important non-material resource for individuals, communities and nations. Being available for 24 hours per day for everybody it is the most equally distributed resource in the world. Time use is important characteristics of people as consumers, producers, citizen and human beings. People understand time and feel time as being one element of their perception regarding their position to other individuals, communities, and nations in the world. Sicherl (2011a) discussed the concept of "overall degree of disparity", arguing that disparities in society depend not only on static measures of inequality but also on time distances. Further discussion on intertemporal aspect of wellbeing was in Sicherl (2007) and in Sicherl (2014a) in the Springer Encyclopedia of Quality of Life and Well-Being Research. Such a broader concept of the overall degree of disparity can lead to a different perception of the extent of disparity than the conventional static measures alone.
These notions of S-time-distance and lead or lag in time are not unknown in sports and business practice. For instance, in some sport disciplines the relations between space and time are ordered in the way that distance in space is kept constant and the results are expressed as time distances for given distance in space. In skiing the length of track is the same for all competitors; this is true also for track competition in athletics or swimming.

187
Being expressed in units of time make the S-time-distance and S-time-step easy understand by everybody, which is important for creating perceptions and communication. American philosopher Ken Wilber underlines that time (calendars and clocks, hours, minutes months, years) represent mental software that people can use each and every day without giving them a second thought (Wilber, 2014).
In the broader context of measuring disparities over many indicators, units of comparison and various fields of concern (for which gender differences in life expectancy is used here as an example) comparing absolute values of differences for compared units is rather difficult due to different units of indicators (life expectancy in years, weight in kg, Hertz for vibration, etc.). This is most probably one of the reasons that researchers when comparing between various indicators use percentages as the dominant statistical measure for static comparisons.
This simple example of gender differences in life expectancy demonstrates that, beside percentages, an additional generic statistical measure S-time-distance is available that can be used for comparing disparities across indicators and between fields of concern. The S-time-distance approach brings about two persuasive advantages for extensive practical use. Expressed in time units (years, minutes, seconds, etc.) it is intuitively understood by policymakers, professionals, scientists, managers, media, and the general public thus facilitating their subjective perception about the situation in the time dimension. Another technical and presentation advantage is that time and time distance is comparable across variables, fields of concern, and units of comparison. This makes it an excellent analytical, presentation, and communication tool.

Conclusions and Recommendations:-
1. S-time-distance and the dual parallel system for analyzing time series indicators simultaneously in vertical and horizontal dimensions established important improvement over the conventional prevailing static analysis alone.
The present state-of-the art does not realise that, in addition to static comparison, there exists in principle a theoretically equally universal measure of difference (distance) in time when a given level of the variable is attained by the two compared time series. The broader framework shows that perceptions of the gender gap can be very different depending on the two statistical measures used, we need both to better understand the reality. 2. In the application to gender differences for four health indicators for 200 countries S-time-distance measure led to perception of greater gender disparities than the static measures. For selection of countries in the group with long persistent domination in time of either gender, those with S-time-distances as time lead or time lag of gender difference beyond duration of 20 years were selected. For life expectancy at birth and for obesity about 100 countries out of 200 analysed fall into this category. In both fields the prevailing dominance of women with values being higher than for men persevered for more than for two decades. For mean MBI the gender concentration is more balanced. Distinctly different, diabetes showed higher values for men than women, the countries being more than 20 years ahead of those for women were concentrated in high income countries. 3. What was astonishing were large differences between the four health indicators and large differences between countries in each group as measured with S-time-distances. The gender difference in these four indicators can be important from both the medical and social standpoint, and these results can be further elaborated in much more details with additional studies. On the one hand, the same data sources from the Institute of Health Metrics and Evaluation (IHME) at the University of Washington on many health conditions around the world can be additionally studied with S-time-distance methodology. On the other hand, for more elaborated studies of the multiple factors behind the astonishing magnitude of country differences in the gender gap across medical, social, and economic factors could benefit from these results and S-time-distance methodology. 4. With these three additional tools, two generic statistical measures and time matrix tabulation, it is possible to get from existing time series databases a new perspective related to time, i.e. new insights from existing data in units of time which is understood by everybody. An added complementary possibility to look at differences in the parallel universe of time, adding new vocabulary in the semantics of discussing and analysing differences in the real world, can be extended to very diverse fields of interest beyond the example of gender life expectancy here. The recommendation is that experts in numerous fields would examine how their substantive knowledge of the field can be combined with this dual parallel system suggested to help the discovery by, as Marcel Proust would say, "seeing with new eyes".