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Yi-Hsin Elsa Hsu, Wender Lin, Joseph J. Tien, Larry Y. Tzeng, Measuring inequality in physician distributions using spatially adjusted Gini coefficients, International Journal for Quality in Health Care, Volume 28, Issue 6, December 2016, Pages 657–664, https://doi.org/10.1093/intqhc/mzw110
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Abstract
To measure inequality in physician distributions using Gini coefficient and spatially adjusted Gini coefficients.
Measurements were based on the distribution of physician data from the Taiwan National Health Insurance Research Database (NHIRD) and population data from the Ministry of the Interior in Taiwan.
The distribution of population and physicians in Taiwan from 2001 to 2010.
This study considered 35 000 physicians who are registered in Taiwan.
To calculate the Gini coefficient and spatially adjusted Gini coefficients in Taiwan from 2001 to 2010.
The Gini coefficient for each year, from 2001 to 2010, ranged from 0.5128 to 0.4692, while the spatially adjusted Gini coefficients based on travel time and travel distance ranged, respectively, from 0.4324 to 0.4066 and from 0.4408 to 0.4178. We found that, in each year, irrespective of the type of spatial adjustment, the spatially adjusted Gini coefficient was smaller than the Gini coefficient itself. Our empirical findings support that the Gini coefficient may overestimate the maldistribution of physicians.
Our simulations demonstrate that increasing the number of physicians in medium-sized cities (such as capitals of counties or provinces), and/or improving the transportation time between medium-sized cities and rural areas, could be feasible solutions to mitigate the problem of geographical maldistribution of physicians.
Introduction
Health inequality is a worldwide phenomenon especially in developing countries [1]. Some literature has indicated that factors relating to race or ethnicity could cause health inequality [2–4], while other literature has found that socioeconomic status leads to health inequality [5–7].
The medical services provided by physicians are considered the most significant factor affecting health care [8]. Thus, physician maldistribution is an important topic for governments in many countries. Physician maldistribution is generally characterized by a concentration of physicians in urban areas, and a relative shortage in rural areas [9–14]. Further, the literature on health economics indicates that an inequality in the supply of physicians is a critical problem for health improvement, which has thus received much attention from regulators [14, 15].
Although previous studies measuring inequality in physician distributions have provided many insightful findings, they share a common drawback that their data ignore geographical relationships. Specifically, as pointed out by Kleinman and Makuc [16], and Newhouse [17], the shortage of medical services in rural areas could be overestimated. For example, people in rural areas could drive a couple of hours to a nearby city for medical services. Thus, despite the lack of physicians providing medical services in such rural areas, people in these rural areas still have access to medical services [18, 19].
In this paper, we discuss the utility of spatially adjusted Gini coefficients to assess physician maldistribution. (The traditional Gini coefficient is an effective way to measure inequality in physician distribution. Without checking the need index, we reconsider utilizing different kinds of spatially adjusted Gini coefficients to investigate this issue. The purpose of this study was to evaluate the problem of physician maldistribution based on spatial statistic adjustments.) Although previous studies used Gini coefficients to evaluate the inequality in physician distributions, the traditional Gini coefficient ignores the fact that people living in adjacent regions may share medical services. Thus, to measure inequality in physician distributions more accurately, we computed spatially adjusted Gini coefficients based on neighborhood, travel distance and travel time. Additionally, we used data from the Taiwan National Health Insurance Research Database (NHIRD) from 2001 to 2010, to examine inequality in physician distributions by calculating spatially adjusted Gini coefficients.
Taiwan's National Health Insurance (NHI) program is a public social health insurance program, which provides every citizen with equal access to health services everywhere in Taiwan. No special restrictions are placed on patients’ access to any kind of physician services in any level of medical care facility apart from a higher copayment for ambulatory care provided by hospitals without referrals. Therefore, without any restrictions for physician services, it is more appropriate to measure inequality in physician distribution.
An analysis of Taiwan revealed that the Gini coefficient for each year from 2001 to 2010 ranged from 0.5128 to 0.4692. Furthermore, the spatially adjusted Gini coefficients based on travel time and travel distance ranged, respectively, from 0.4324 to 0.4066 and from 0.4408 to 0.4178. Additionally, the present paper raises two policies that may improve the inequality in physician distribution, based on practical simulations that we conducted. Our simulations revealed that increasing the number of physicians in medium-sized cities (such as capitals of counties or provinces) might mitigate the problem of maldistribution of physicians. We showed that by adding 50 physicians to each county capital, the spatially adjusted Gini coefficients based on neighborhood, travel distance and travel time decrease from 0.3785, 0.4178 and 0.4066 to 0.3765, 0.4152 and 0.4035, respectively.
Our simulations also demonstrated that improving the transportation network between county capitals and rural areas could be another feasible policy to reduce the problems arising from the maldistribution of physicians. We found that, in cases where the travel time between two subdivisions was more than 120 min, a 30-min reduction in travel time led to a decrease in the spatially adjusted Gini coefficient from 0.4066 to 0.4062. The spatially adjusted Gini coefficient may provide another perspective related to measuring inequality in physician distributions.
The remainder of this paper is organized as follows. Section 2 presents our methods, including details about the data and an explanation of how we measured the inequality in the distribution of physicians. Section 3 describes our results, Section 4 provides a discussion based on our findings and limitations, and Section 5 presents the conclusions derived from this study.
Methods
Data
Our data derived from two databases in Taiwan: the NHIRD [20] and another population database created by the Ministry of the Interior [21]. Taiwan's NHI program, launched on 1 March 1995, is its social health insurance program. The goal of the NHI program is to provide every citizen with equal access to health and medical services regardless of their socio-economic background. Since participation in the NHI was made compulsory, the coverage rate increased to 99.5% in 2012, compared with the initial 92.34% in 1995. The NHI database contains registration files (registry for contracted medical facility, medical services, board-certified specialists, drug prescriptions and beneficiaries) and original claim data for reimbursement. Thus, the NHI database provides us with detailed physician distribution information, while the database from the Ministry of the Interior contains detailed population information.
Taiwan has five special municipalities (Taipei, New Taipei, Taichung, Tainan and Kaohsiung) and twelve counties (Keelung, Taoyuan, Hsinchu, Miaoli, Changhua, Nantou, Yunlin, Chiayi, Pingtung, Taitung, Yilan and Hualien). These five special municipalities can be further classified into 170 districts, and the twelve counties can be further classified into 12 county capitals, 30 urban townships and 137 rural townships. Thus, Taiwan consists of 349 basic geographical and administrative regions. Based on the physician and population distribution information in these 349 basic geographical and administrative units, we first calculated the Gini coefficients using physician-to-population ratios in each subdivision. We further calculated the spatially adjusted Gini coefficients by utilizing travel time and travel distance obtained from Google Maps.
Table 1 shows the number of physicians and population distribution in each city and county of Taiwan from 2001 to 2010. It is evident that the total number of physicians increased from 31 599 in 2001 to 36 640 in 2010. The total population in Taiwan increased from 22 million in 2001 to nearly 23 million in 2010. Furthermore, the aggregate physician-to-population ratio improved from 0.0014 in 2001 to 0.0016 in 2010. We found that the capital of Taiwan, Taipei City, has the highest physician-to-population ratio. However, some counties have a very low physician-to-population ratio (such as Yunlin, Nantou, Taitung), indicating that the disparity of physicians distribution still exists in Taiwan. According to health statistics from the Organization for Economic Co-operation and Development (OECD), the number of physicians per unit population has risen in most developed countries. Similarly, the number of physicians per unit population in Taiwan also has increased over the last decade.
. | 2001 . | 2002 . | 2003 . | 2004 . | 2005 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 7810 | 2 633 802 | 0.0030 | 7976 | 2 641 856 | 0.0030 | 7840 | 2 627 138 | 0.0030 | 6183 | 2 622 472 | 0.0024 | 6342 | 2 616 375 | 0.0024 |
NewTaipei | 2636 | 3 610 252 | 0.0007 | 2779 | 3 641 446 | 0.0008 | 2856 | 3 676 532 | 0.0008 | 2934 | 3 708 099 | 0.0008 | 2996 | 3 736 677 | 0.0008 |
Keelung | 518 | 390 966 | 0.0013 | 541 | 391 450 | 0.0014 | 565 | 392 242 | 0.0014 | 510 | 392 337 | 0.0013 | 475 | 391 727 | 0.0012 |
Taoyuan | 2654 | 1 762 963 | 0.0015 | 2592 | 1 792 603 | 0.0014 | 2847 | 1 822 075 | 0.0016 | 2783 | 1 853 029 | 0.0015 | 2561 | 1 880 316 | 0.0014 |
Hsinchu | 762 | 819 596 | 0.0009 | 792 | 831 476 | 0.0010 | 846 | 842 174 | 0.0010 | 868 | 854 196 | 0.0010 | 785 | 868 369 | 0.0009 |
Miaoli | 465 | 560 640 | 0.0008 | 471 | 560 766 | 0.0008 | 471 | 560 903 | 0.0008 | 469 | 560 643 | 0.0008 | 451 | 559 944 | 0.0008 |
Taichung | 3858 | 2 485 968 | 0.0016 | 4058 | 2 508 495 | 0.0016 | 4205 | 2 499 763 | 0.0017 | 3908 | 2 547 332 | 0.0015 | 3783 | 2 566 220 | 0.0015 |
Changhua | 1286 | 1 313 994 | 0.0010 | 1350 | 1 316 179 | 0.0010 | 1464 | 1 316 443 | 0.0011 | 1476 | 1 316 762 | 0.0011 | 1377 | 1 315 826 | 0.0010 |
Nantou | 432 | 541 818 | 0.0008 | 436 | 541 292 | 0.0008 | 455 | 540 397 | 0.0008 | 500 | 538 953 | 0.0009 | 480 | 537 168 | 0.0009 |
Yunlin | 480 | 774 520 | 0.0006 | 499 | 742 797 | 0.0007 | 553 | 710 501 | 0.0008 | 600 | 736 772 | 0.0008 | 572 | 733 330 | 0.0008 |
Chiayi | 960 | 831 331 | 0.0012 | 1015 | 830 301 | 0.0012 | 1089 | 830 004 | 0.0013 | 1097 | 828 244 | 0.0013 | 1076 | 828 802 | 0.0013 |
Tainan | 3557 | 1 848 243 | 0.0019 | 2281 | 1 852 664 | 0.0012 | 2379 | 1 856 562 | 0.0013 | 2377 | 1 860 591 | 0.0013 | 2248 | 1 862 918 | 0.0012 |
Kaohsiung | 4184 | 2 731 415 | 0.0015 | 4315 | 2 742 905 | 0.0016 | 4371 | 2 746 819 | 0.0016 | 3873 | 2 751 602 | 0.0014 | 4024 | 2 753 486 | 0.0015 |
Pingtung | 810 | 894 879 | 0.0009 | 846 | 892 862 | 0.0009 | 847 | 890 557 | 0.0010 | 931 | 887 060 | 0.0010 | 847 | 885 011 | 0.0010 |
Taitung | 184 | 238 131 | 0.0008 | 191 | 237 231 | 0.0008 | 207 | 236 085 | 0.0009 | 245 | 233 584 | 0.0010 | 204 | 232 037 | 0.0009 |
Yilan | 455 | 465 799 | 0.0010 | 472 | 464 107 | 0.0010 | 490 | 463 285 | 0.0011 | 499 | 462 286 | 0.0011 | 487 | 461 586 | 0.0011 |
Hualien | 548 | 353 139 | 0.0016 | 567 | 352 154 | 0.0016 | 630 | 351 146 | 0.0018 | 693 | 349 149 | 0.0020 | 644 | 347 298 | 0.0019 |
Total | 31 599 | 22 257 456 | 0.0014 | 31 181 | 22 340 584 | 0.0014 | 32 115 | 22 362 626 | 0.0014 | 29 946 | 22 503 111 | 0.0013 | 29 352 | 22 577 090 | 0.0013 |
. | 2001 . | 2002 . | 2003 . | 2004 . | 2005 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 7810 | 2 633 802 | 0.0030 | 7976 | 2 641 856 | 0.0030 | 7840 | 2 627 138 | 0.0030 | 6183 | 2 622 472 | 0.0024 | 6342 | 2 616 375 | 0.0024 |
NewTaipei | 2636 | 3 610 252 | 0.0007 | 2779 | 3 641 446 | 0.0008 | 2856 | 3 676 532 | 0.0008 | 2934 | 3 708 099 | 0.0008 | 2996 | 3 736 677 | 0.0008 |
Keelung | 518 | 390 966 | 0.0013 | 541 | 391 450 | 0.0014 | 565 | 392 242 | 0.0014 | 510 | 392 337 | 0.0013 | 475 | 391 727 | 0.0012 |
Taoyuan | 2654 | 1 762 963 | 0.0015 | 2592 | 1 792 603 | 0.0014 | 2847 | 1 822 075 | 0.0016 | 2783 | 1 853 029 | 0.0015 | 2561 | 1 880 316 | 0.0014 |
Hsinchu | 762 | 819 596 | 0.0009 | 792 | 831 476 | 0.0010 | 846 | 842 174 | 0.0010 | 868 | 854 196 | 0.0010 | 785 | 868 369 | 0.0009 |
Miaoli | 465 | 560 640 | 0.0008 | 471 | 560 766 | 0.0008 | 471 | 560 903 | 0.0008 | 469 | 560 643 | 0.0008 | 451 | 559 944 | 0.0008 |
Taichung | 3858 | 2 485 968 | 0.0016 | 4058 | 2 508 495 | 0.0016 | 4205 | 2 499 763 | 0.0017 | 3908 | 2 547 332 | 0.0015 | 3783 | 2 566 220 | 0.0015 |
Changhua | 1286 | 1 313 994 | 0.0010 | 1350 | 1 316 179 | 0.0010 | 1464 | 1 316 443 | 0.0011 | 1476 | 1 316 762 | 0.0011 | 1377 | 1 315 826 | 0.0010 |
Nantou | 432 | 541 818 | 0.0008 | 436 | 541 292 | 0.0008 | 455 | 540 397 | 0.0008 | 500 | 538 953 | 0.0009 | 480 | 537 168 | 0.0009 |
Yunlin | 480 | 774 520 | 0.0006 | 499 | 742 797 | 0.0007 | 553 | 710 501 | 0.0008 | 600 | 736 772 | 0.0008 | 572 | 733 330 | 0.0008 |
Chiayi | 960 | 831 331 | 0.0012 | 1015 | 830 301 | 0.0012 | 1089 | 830 004 | 0.0013 | 1097 | 828 244 | 0.0013 | 1076 | 828 802 | 0.0013 |
Tainan | 3557 | 1 848 243 | 0.0019 | 2281 | 1 852 664 | 0.0012 | 2379 | 1 856 562 | 0.0013 | 2377 | 1 860 591 | 0.0013 | 2248 | 1 862 918 | 0.0012 |
Kaohsiung | 4184 | 2 731 415 | 0.0015 | 4315 | 2 742 905 | 0.0016 | 4371 | 2 746 819 | 0.0016 | 3873 | 2 751 602 | 0.0014 | 4024 | 2 753 486 | 0.0015 |
Pingtung | 810 | 894 879 | 0.0009 | 846 | 892 862 | 0.0009 | 847 | 890 557 | 0.0010 | 931 | 887 060 | 0.0010 | 847 | 885 011 | 0.0010 |
Taitung | 184 | 238 131 | 0.0008 | 191 | 237 231 | 0.0008 | 207 | 236 085 | 0.0009 | 245 | 233 584 | 0.0010 | 204 | 232 037 | 0.0009 |
Yilan | 455 | 465 799 | 0.0010 | 472 | 464 107 | 0.0010 | 490 | 463 285 | 0.0011 | 499 | 462 286 | 0.0011 | 487 | 461 586 | 0.0011 |
Hualien | 548 | 353 139 | 0.0016 | 567 | 352 154 | 0.0016 | 630 | 351 146 | 0.0018 | 693 | 349 149 | 0.0020 | 644 | 347 298 | 0.0019 |
Total | 31 599 | 22 257 456 | 0.0014 | 31 181 | 22 340 584 | 0.0014 | 32 115 | 22 362 626 | 0.0014 | 29 946 | 22 503 111 | 0.0013 | 29 352 | 22 577 090 | 0.0013 |
. | 2006 . | 2007 . | 2008 . | 2009 . | 2010 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 6496 | 2 632 242 | 0.0025 | 7110 | 2 629 269 | 0.0027 | 7089 | 2 622 923 | 0.0027 | 7513 | 2 607 428 | 0.0029 | 7747 | 2 618 772 | 0.0030 |
NewTaipei | 3144 | 3 767 095 | 0.0008 | 3342 | 3 798 015 | 0.0009 | 3757 | 3 834 276 | 0.0010 | 3972 | 3 873 653 | 0.0010 | 4067 | 3 897 367 | 0.0010 |
Keelung | 507 | 391 633 | 0.0013 | 569 | 390 397 | 0.0015 | 583 | 388 979 | 0.0015 | 601 | 388 321 | 0.0015 | 633 | 384 134 | 0.0016 |
Taoyuan | 2678 | 1 911 161 | 0.0014 | 2889 | 1 934 968 | 0.0015 | 2979 | 1 958 686 | 0.0015 | 3034 | 1 978 782 | 0.0015 | 3091 | 2 002 060 | 0.0015 |
Hsinchu | 832 | 882 449 | 0.0009 | 900 | 894 846 | 0.0010 | 967 | 908 644 | 0.0011 | 989 | 922 469 | 0.0011 | 1020 | 928 359 | 0.0011 |
Miaoli | 466 | 559 986 | 0.0008 | 491 | 560 163 | 0.0009 | 498 | 560 397 | 0.0009 | 497 | 561 744 | 0.0009 | 500 | 560 968 | 0.0009 |
Taichung | 3693 | 2 587 558 | 0.0014 | 4112 | 2 606 794 | 0.0016 | 4419 | 2 624 072 | 0.0017 | 4623 | 2 635 761 | 0.0018 | 4806 | 2 648 419 | 0.0018 |
Changhua | 1472 | 1 315 034 | 0.0011 | 1587 | 1 314 354 | 0.0012 | 1503 | 1 312 935 | 0.0011 | 1726 | 1 312 467 | 0.0013 | 1743 | 1 307 286 | 0.0013 |
Nantou | 500 | 535 205 | 0.0009 | 531 | 533 717 | 0.0010 | 535 | 531 753 | 0.0010 | 558 | 530 824 | 0.0011 | 568 | 526 491 | 0.0011 |
Yunlin | 603 | 728 490 | 0.0008 | 696 | 725 672 | 0.0010 | 734 | 723 674 | 0.0010 | 774 | 722 795 | 0.0011 | 819 | 717 653 | 0.0011 |
Chiayi | 1130 | 826 205 | 0.0014 | 1181 | 824 420 | 0.0014 | 1284 | 822 524 | 0.0016 | 1313 | 821 577 | 0.0016 | 1346 | 815 638 | 0.0017 |
Tainan | 2409 | 1 866 727 | 0.0013 | 2534 | 1 870 061 | 0.0014 | 2648 | 1 875 757 | 0.0014 | 2748 | 1 875 406 | 0.0015 | 2823 | 1 873 794 | 0.0015 |
Kaohsiung | 4172 | 2 760 180 | 0.0015 | 4504 | 2 764 868 | 0.0016 | 4650 | 2 769 054 | 0.0017 | 4751 | 2 770 887 | 0.0017 | 4950 | 2 773 483 | 0.0018 |
Pingtung | 892 | 880 731 | 0.0010 | 929 | 876 911 | 0.0011 | 961 | 872 288 | 0.0011 | 978 | 870 020 | 0.0011 | 986 | 861 209 | 0.0011 |
Taitung | 214 | 229 062 | 0.0009 | 218 | 226 607 | 0.0010 | 236 | 224 668 | 0.0011 | 238 | 224 859 | 0.0011 | 228 | 222 816 | 0.0010 |
Yilan | 497 | 460 426 | 0.0011 | 471 | 460 398 | 0.0010 | 570 | 460 902 | 0.0012 | 576 | 461 625 | 0.0012 | 594 | 460 486 | 0.0013 |
Hualien | 646 | 345 303 | 0.0019 | 694 | 343 311 | 0.0020 | 694 | 341 433 | 0.0020 | 715 | 340 964 | 0.0021 | 719 | 338 805 | 0.0021 |
Total | 30 351 | 22 679 487 | 0.0013 | 32 758 | 22 754 771 | 0.0014 | 34 107 | 22 832 965 | 0.0015 | 35 606 | 22 899 582 | 0.0016 | 36 640 | 22 937 740 | 0.0016 |
. | 2006 . | 2007 . | 2008 . | 2009 . | 2010 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 6496 | 2 632 242 | 0.0025 | 7110 | 2 629 269 | 0.0027 | 7089 | 2 622 923 | 0.0027 | 7513 | 2 607 428 | 0.0029 | 7747 | 2 618 772 | 0.0030 |
NewTaipei | 3144 | 3 767 095 | 0.0008 | 3342 | 3 798 015 | 0.0009 | 3757 | 3 834 276 | 0.0010 | 3972 | 3 873 653 | 0.0010 | 4067 | 3 897 367 | 0.0010 |
Keelung | 507 | 391 633 | 0.0013 | 569 | 390 397 | 0.0015 | 583 | 388 979 | 0.0015 | 601 | 388 321 | 0.0015 | 633 | 384 134 | 0.0016 |
Taoyuan | 2678 | 1 911 161 | 0.0014 | 2889 | 1 934 968 | 0.0015 | 2979 | 1 958 686 | 0.0015 | 3034 | 1 978 782 | 0.0015 | 3091 | 2 002 060 | 0.0015 |
Hsinchu | 832 | 882 449 | 0.0009 | 900 | 894 846 | 0.0010 | 967 | 908 644 | 0.0011 | 989 | 922 469 | 0.0011 | 1020 | 928 359 | 0.0011 |
Miaoli | 466 | 559 986 | 0.0008 | 491 | 560 163 | 0.0009 | 498 | 560 397 | 0.0009 | 497 | 561 744 | 0.0009 | 500 | 560 968 | 0.0009 |
Taichung | 3693 | 2 587 558 | 0.0014 | 4112 | 2 606 794 | 0.0016 | 4419 | 2 624 072 | 0.0017 | 4623 | 2 635 761 | 0.0018 | 4806 | 2 648 419 | 0.0018 |
Changhua | 1472 | 1 315 034 | 0.0011 | 1587 | 1 314 354 | 0.0012 | 1503 | 1 312 935 | 0.0011 | 1726 | 1 312 467 | 0.0013 | 1743 | 1 307 286 | 0.0013 |
Nantou | 500 | 535 205 | 0.0009 | 531 | 533 717 | 0.0010 | 535 | 531 753 | 0.0010 | 558 | 530 824 | 0.0011 | 568 | 526 491 | 0.0011 |
Yunlin | 603 | 728 490 | 0.0008 | 696 | 725 672 | 0.0010 | 734 | 723 674 | 0.0010 | 774 | 722 795 | 0.0011 | 819 | 717 653 | 0.0011 |
Chiayi | 1130 | 826 205 | 0.0014 | 1181 | 824 420 | 0.0014 | 1284 | 822 524 | 0.0016 | 1313 | 821 577 | 0.0016 | 1346 | 815 638 | 0.0017 |
Tainan | 2409 | 1 866 727 | 0.0013 | 2534 | 1 870 061 | 0.0014 | 2648 | 1 875 757 | 0.0014 | 2748 | 1 875 406 | 0.0015 | 2823 | 1 873 794 | 0.0015 |
Kaohsiung | 4172 | 2 760 180 | 0.0015 | 4504 | 2 764 868 | 0.0016 | 4650 | 2 769 054 | 0.0017 | 4751 | 2 770 887 | 0.0017 | 4950 | 2 773 483 | 0.0018 |
Pingtung | 892 | 880 731 | 0.0010 | 929 | 876 911 | 0.0011 | 961 | 872 288 | 0.0011 | 978 | 870 020 | 0.0011 | 986 | 861 209 | 0.0011 |
Taitung | 214 | 229 062 | 0.0009 | 218 | 226 607 | 0.0010 | 236 | 224 668 | 0.0011 | 238 | 224 859 | 0.0011 | 228 | 222 816 | 0.0010 |
Yilan | 497 | 460 426 | 0.0011 | 471 | 460 398 | 0.0010 | 570 | 460 902 | 0.0012 | 576 | 461 625 | 0.0012 | 594 | 460 486 | 0.0013 |
Hualien | 646 | 345 303 | 0.0019 | 694 | 343 311 | 0.0020 | 694 | 341 433 | 0.0020 | 715 | 340 964 | 0.0021 | 719 | 338 805 | 0.0021 |
Total | 30 351 | 22 679 487 | 0.0013 | 32 758 | 22 754 771 | 0.0014 | 34 107 | 22 832 965 | 0.0015 | 35 606 | 22 899 582 | 0.0016 | 36 640 | 22 937 740 | 0.0016 |
Phy means the number of physicians. p/p means the the number of physicians divided by the population.
. | 2001 . | 2002 . | 2003 . | 2004 . | 2005 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 7810 | 2 633 802 | 0.0030 | 7976 | 2 641 856 | 0.0030 | 7840 | 2 627 138 | 0.0030 | 6183 | 2 622 472 | 0.0024 | 6342 | 2 616 375 | 0.0024 |
NewTaipei | 2636 | 3 610 252 | 0.0007 | 2779 | 3 641 446 | 0.0008 | 2856 | 3 676 532 | 0.0008 | 2934 | 3 708 099 | 0.0008 | 2996 | 3 736 677 | 0.0008 |
Keelung | 518 | 390 966 | 0.0013 | 541 | 391 450 | 0.0014 | 565 | 392 242 | 0.0014 | 510 | 392 337 | 0.0013 | 475 | 391 727 | 0.0012 |
Taoyuan | 2654 | 1 762 963 | 0.0015 | 2592 | 1 792 603 | 0.0014 | 2847 | 1 822 075 | 0.0016 | 2783 | 1 853 029 | 0.0015 | 2561 | 1 880 316 | 0.0014 |
Hsinchu | 762 | 819 596 | 0.0009 | 792 | 831 476 | 0.0010 | 846 | 842 174 | 0.0010 | 868 | 854 196 | 0.0010 | 785 | 868 369 | 0.0009 |
Miaoli | 465 | 560 640 | 0.0008 | 471 | 560 766 | 0.0008 | 471 | 560 903 | 0.0008 | 469 | 560 643 | 0.0008 | 451 | 559 944 | 0.0008 |
Taichung | 3858 | 2 485 968 | 0.0016 | 4058 | 2 508 495 | 0.0016 | 4205 | 2 499 763 | 0.0017 | 3908 | 2 547 332 | 0.0015 | 3783 | 2 566 220 | 0.0015 |
Changhua | 1286 | 1 313 994 | 0.0010 | 1350 | 1 316 179 | 0.0010 | 1464 | 1 316 443 | 0.0011 | 1476 | 1 316 762 | 0.0011 | 1377 | 1 315 826 | 0.0010 |
Nantou | 432 | 541 818 | 0.0008 | 436 | 541 292 | 0.0008 | 455 | 540 397 | 0.0008 | 500 | 538 953 | 0.0009 | 480 | 537 168 | 0.0009 |
Yunlin | 480 | 774 520 | 0.0006 | 499 | 742 797 | 0.0007 | 553 | 710 501 | 0.0008 | 600 | 736 772 | 0.0008 | 572 | 733 330 | 0.0008 |
Chiayi | 960 | 831 331 | 0.0012 | 1015 | 830 301 | 0.0012 | 1089 | 830 004 | 0.0013 | 1097 | 828 244 | 0.0013 | 1076 | 828 802 | 0.0013 |
Tainan | 3557 | 1 848 243 | 0.0019 | 2281 | 1 852 664 | 0.0012 | 2379 | 1 856 562 | 0.0013 | 2377 | 1 860 591 | 0.0013 | 2248 | 1 862 918 | 0.0012 |
Kaohsiung | 4184 | 2 731 415 | 0.0015 | 4315 | 2 742 905 | 0.0016 | 4371 | 2 746 819 | 0.0016 | 3873 | 2 751 602 | 0.0014 | 4024 | 2 753 486 | 0.0015 |
Pingtung | 810 | 894 879 | 0.0009 | 846 | 892 862 | 0.0009 | 847 | 890 557 | 0.0010 | 931 | 887 060 | 0.0010 | 847 | 885 011 | 0.0010 |
Taitung | 184 | 238 131 | 0.0008 | 191 | 237 231 | 0.0008 | 207 | 236 085 | 0.0009 | 245 | 233 584 | 0.0010 | 204 | 232 037 | 0.0009 |
Yilan | 455 | 465 799 | 0.0010 | 472 | 464 107 | 0.0010 | 490 | 463 285 | 0.0011 | 499 | 462 286 | 0.0011 | 487 | 461 586 | 0.0011 |
Hualien | 548 | 353 139 | 0.0016 | 567 | 352 154 | 0.0016 | 630 | 351 146 | 0.0018 | 693 | 349 149 | 0.0020 | 644 | 347 298 | 0.0019 |
Total | 31 599 | 22 257 456 | 0.0014 | 31 181 | 22 340 584 | 0.0014 | 32 115 | 22 362 626 | 0.0014 | 29 946 | 22 503 111 | 0.0013 | 29 352 | 22 577 090 | 0.0013 |
. | 2001 . | 2002 . | 2003 . | 2004 . | 2005 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 7810 | 2 633 802 | 0.0030 | 7976 | 2 641 856 | 0.0030 | 7840 | 2 627 138 | 0.0030 | 6183 | 2 622 472 | 0.0024 | 6342 | 2 616 375 | 0.0024 |
NewTaipei | 2636 | 3 610 252 | 0.0007 | 2779 | 3 641 446 | 0.0008 | 2856 | 3 676 532 | 0.0008 | 2934 | 3 708 099 | 0.0008 | 2996 | 3 736 677 | 0.0008 |
Keelung | 518 | 390 966 | 0.0013 | 541 | 391 450 | 0.0014 | 565 | 392 242 | 0.0014 | 510 | 392 337 | 0.0013 | 475 | 391 727 | 0.0012 |
Taoyuan | 2654 | 1 762 963 | 0.0015 | 2592 | 1 792 603 | 0.0014 | 2847 | 1 822 075 | 0.0016 | 2783 | 1 853 029 | 0.0015 | 2561 | 1 880 316 | 0.0014 |
Hsinchu | 762 | 819 596 | 0.0009 | 792 | 831 476 | 0.0010 | 846 | 842 174 | 0.0010 | 868 | 854 196 | 0.0010 | 785 | 868 369 | 0.0009 |
Miaoli | 465 | 560 640 | 0.0008 | 471 | 560 766 | 0.0008 | 471 | 560 903 | 0.0008 | 469 | 560 643 | 0.0008 | 451 | 559 944 | 0.0008 |
Taichung | 3858 | 2 485 968 | 0.0016 | 4058 | 2 508 495 | 0.0016 | 4205 | 2 499 763 | 0.0017 | 3908 | 2 547 332 | 0.0015 | 3783 | 2 566 220 | 0.0015 |
Changhua | 1286 | 1 313 994 | 0.0010 | 1350 | 1 316 179 | 0.0010 | 1464 | 1 316 443 | 0.0011 | 1476 | 1 316 762 | 0.0011 | 1377 | 1 315 826 | 0.0010 |
Nantou | 432 | 541 818 | 0.0008 | 436 | 541 292 | 0.0008 | 455 | 540 397 | 0.0008 | 500 | 538 953 | 0.0009 | 480 | 537 168 | 0.0009 |
Yunlin | 480 | 774 520 | 0.0006 | 499 | 742 797 | 0.0007 | 553 | 710 501 | 0.0008 | 600 | 736 772 | 0.0008 | 572 | 733 330 | 0.0008 |
Chiayi | 960 | 831 331 | 0.0012 | 1015 | 830 301 | 0.0012 | 1089 | 830 004 | 0.0013 | 1097 | 828 244 | 0.0013 | 1076 | 828 802 | 0.0013 |
Tainan | 3557 | 1 848 243 | 0.0019 | 2281 | 1 852 664 | 0.0012 | 2379 | 1 856 562 | 0.0013 | 2377 | 1 860 591 | 0.0013 | 2248 | 1 862 918 | 0.0012 |
Kaohsiung | 4184 | 2 731 415 | 0.0015 | 4315 | 2 742 905 | 0.0016 | 4371 | 2 746 819 | 0.0016 | 3873 | 2 751 602 | 0.0014 | 4024 | 2 753 486 | 0.0015 |
Pingtung | 810 | 894 879 | 0.0009 | 846 | 892 862 | 0.0009 | 847 | 890 557 | 0.0010 | 931 | 887 060 | 0.0010 | 847 | 885 011 | 0.0010 |
Taitung | 184 | 238 131 | 0.0008 | 191 | 237 231 | 0.0008 | 207 | 236 085 | 0.0009 | 245 | 233 584 | 0.0010 | 204 | 232 037 | 0.0009 |
Yilan | 455 | 465 799 | 0.0010 | 472 | 464 107 | 0.0010 | 490 | 463 285 | 0.0011 | 499 | 462 286 | 0.0011 | 487 | 461 586 | 0.0011 |
Hualien | 548 | 353 139 | 0.0016 | 567 | 352 154 | 0.0016 | 630 | 351 146 | 0.0018 | 693 | 349 149 | 0.0020 | 644 | 347 298 | 0.0019 |
Total | 31 599 | 22 257 456 | 0.0014 | 31 181 | 22 340 584 | 0.0014 | 32 115 | 22 362 626 | 0.0014 | 29 946 | 22 503 111 | 0.0013 | 29 352 | 22 577 090 | 0.0013 |
. | 2006 . | 2007 . | 2008 . | 2009 . | 2010 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 6496 | 2 632 242 | 0.0025 | 7110 | 2 629 269 | 0.0027 | 7089 | 2 622 923 | 0.0027 | 7513 | 2 607 428 | 0.0029 | 7747 | 2 618 772 | 0.0030 |
NewTaipei | 3144 | 3 767 095 | 0.0008 | 3342 | 3 798 015 | 0.0009 | 3757 | 3 834 276 | 0.0010 | 3972 | 3 873 653 | 0.0010 | 4067 | 3 897 367 | 0.0010 |
Keelung | 507 | 391 633 | 0.0013 | 569 | 390 397 | 0.0015 | 583 | 388 979 | 0.0015 | 601 | 388 321 | 0.0015 | 633 | 384 134 | 0.0016 |
Taoyuan | 2678 | 1 911 161 | 0.0014 | 2889 | 1 934 968 | 0.0015 | 2979 | 1 958 686 | 0.0015 | 3034 | 1 978 782 | 0.0015 | 3091 | 2 002 060 | 0.0015 |
Hsinchu | 832 | 882 449 | 0.0009 | 900 | 894 846 | 0.0010 | 967 | 908 644 | 0.0011 | 989 | 922 469 | 0.0011 | 1020 | 928 359 | 0.0011 |
Miaoli | 466 | 559 986 | 0.0008 | 491 | 560 163 | 0.0009 | 498 | 560 397 | 0.0009 | 497 | 561 744 | 0.0009 | 500 | 560 968 | 0.0009 |
Taichung | 3693 | 2 587 558 | 0.0014 | 4112 | 2 606 794 | 0.0016 | 4419 | 2 624 072 | 0.0017 | 4623 | 2 635 761 | 0.0018 | 4806 | 2 648 419 | 0.0018 |
Changhua | 1472 | 1 315 034 | 0.0011 | 1587 | 1 314 354 | 0.0012 | 1503 | 1 312 935 | 0.0011 | 1726 | 1 312 467 | 0.0013 | 1743 | 1 307 286 | 0.0013 |
Nantou | 500 | 535 205 | 0.0009 | 531 | 533 717 | 0.0010 | 535 | 531 753 | 0.0010 | 558 | 530 824 | 0.0011 | 568 | 526 491 | 0.0011 |
Yunlin | 603 | 728 490 | 0.0008 | 696 | 725 672 | 0.0010 | 734 | 723 674 | 0.0010 | 774 | 722 795 | 0.0011 | 819 | 717 653 | 0.0011 |
Chiayi | 1130 | 826 205 | 0.0014 | 1181 | 824 420 | 0.0014 | 1284 | 822 524 | 0.0016 | 1313 | 821 577 | 0.0016 | 1346 | 815 638 | 0.0017 |
Tainan | 2409 | 1 866 727 | 0.0013 | 2534 | 1 870 061 | 0.0014 | 2648 | 1 875 757 | 0.0014 | 2748 | 1 875 406 | 0.0015 | 2823 | 1 873 794 | 0.0015 |
Kaohsiung | 4172 | 2 760 180 | 0.0015 | 4504 | 2 764 868 | 0.0016 | 4650 | 2 769 054 | 0.0017 | 4751 | 2 770 887 | 0.0017 | 4950 | 2 773 483 | 0.0018 |
Pingtung | 892 | 880 731 | 0.0010 | 929 | 876 911 | 0.0011 | 961 | 872 288 | 0.0011 | 978 | 870 020 | 0.0011 | 986 | 861 209 | 0.0011 |
Taitung | 214 | 229 062 | 0.0009 | 218 | 226 607 | 0.0010 | 236 | 224 668 | 0.0011 | 238 | 224 859 | 0.0011 | 228 | 222 816 | 0.0010 |
Yilan | 497 | 460 426 | 0.0011 | 471 | 460 398 | 0.0010 | 570 | 460 902 | 0.0012 | 576 | 461 625 | 0.0012 | 594 | 460 486 | 0.0013 |
Hualien | 646 | 345 303 | 0.0019 | 694 | 343 311 | 0.0020 | 694 | 341 433 | 0.0020 | 715 | 340 964 | 0.0021 | 719 | 338 805 | 0.0021 |
Total | 30 351 | 22 679 487 | 0.0013 | 32 758 | 22 754 771 | 0.0014 | 34 107 | 22 832 965 | 0.0015 | 35 606 | 22 899 582 | 0.0016 | 36 640 | 22 937 740 | 0.0016 |
. | 2006 . | 2007 . | 2008 . | 2009 . | 2010 . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | Phy . | Population . | p/p . | |
Taipei | 6496 | 2 632 242 | 0.0025 | 7110 | 2 629 269 | 0.0027 | 7089 | 2 622 923 | 0.0027 | 7513 | 2 607 428 | 0.0029 | 7747 | 2 618 772 | 0.0030 |
NewTaipei | 3144 | 3 767 095 | 0.0008 | 3342 | 3 798 015 | 0.0009 | 3757 | 3 834 276 | 0.0010 | 3972 | 3 873 653 | 0.0010 | 4067 | 3 897 367 | 0.0010 |
Keelung | 507 | 391 633 | 0.0013 | 569 | 390 397 | 0.0015 | 583 | 388 979 | 0.0015 | 601 | 388 321 | 0.0015 | 633 | 384 134 | 0.0016 |
Taoyuan | 2678 | 1 911 161 | 0.0014 | 2889 | 1 934 968 | 0.0015 | 2979 | 1 958 686 | 0.0015 | 3034 | 1 978 782 | 0.0015 | 3091 | 2 002 060 | 0.0015 |
Hsinchu | 832 | 882 449 | 0.0009 | 900 | 894 846 | 0.0010 | 967 | 908 644 | 0.0011 | 989 | 922 469 | 0.0011 | 1020 | 928 359 | 0.0011 |
Miaoli | 466 | 559 986 | 0.0008 | 491 | 560 163 | 0.0009 | 498 | 560 397 | 0.0009 | 497 | 561 744 | 0.0009 | 500 | 560 968 | 0.0009 |
Taichung | 3693 | 2 587 558 | 0.0014 | 4112 | 2 606 794 | 0.0016 | 4419 | 2 624 072 | 0.0017 | 4623 | 2 635 761 | 0.0018 | 4806 | 2 648 419 | 0.0018 |
Changhua | 1472 | 1 315 034 | 0.0011 | 1587 | 1 314 354 | 0.0012 | 1503 | 1 312 935 | 0.0011 | 1726 | 1 312 467 | 0.0013 | 1743 | 1 307 286 | 0.0013 |
Nantou | 500 | 535 205 | 0.0009 | 531 | 533 717 | 0.0010 | 535 | 531 753 | 0.0010 | 558 | 530 824 | 0.0011 | 568 | 526 491 | 0.0011 |
Yunlin | 603 | 728 490 | 0.0008 | 696 | 725 672 | 0.0010 | 734 | 723 674 | 0.0010 | 774 | 722 795 | 0.0011 | 819 | 717 653 | 0.0011 |
Chiayi | 1130 | 826 205 | 0.0014 | 1181 | 824 420 | 0.0014 | 1284 | 822 524 | 0.0016 | 1313 | 821 577 | 0.0016 | 1346 | 815 638 | 0.0017 |
Tainan | 2409 | 1 866 727 | 0.0013 | 2534 | 1 870 061 | 0.0014 | 2648 | 1 875 757 | 0.0014 | 2748 | 1 875 406 | 0.0015 | 2823 | 1 873 794 | 0.0015 |
Kaohsiung | 4172 | 2 760 180 | 0.0015 | 4504 | 2 764 868 | 0.0016 | 4650 | 2 769 054 | 0.0017 | 4751 | 2 770 887 | 0.0017 | 4950 | 2 773 483 | 0.0018 |
Pingtung | 892 | 880 731 | 0.0010 | 929 | 876 911 | 0.0011 | 961 | 872 288 | 0.0011 | 978 | 870 020 | 0.0011 | 986 | 861 209 | 0.0011 |
Taitung | 214 | 229 062 | 0.0009 | 218 | 226 607 | 0.0010 | 236 | 224 668 | 0.0011 | 238 | 224 859 | 0.0011 | 228 | 222 816 | 0.0010 |
Yilan | 497 | 460 426 | 0.0011 | 471 | 460 398 | 0.0010 | 570 | 460 902 | 0.0012 | 576 | 461 625 | 0.0012 | 594 | 460 486 | 0.0013 |
Hualien | 646 | 345 303 | 0.0019 | 694 | 343 311 | 0.0020 | 694 | 341 433 | 0.0020 | 715 | 340 964 | 0.0021 | 719 | 338 805 | 0.0021 |
Total | 30 351 | 22 679 487 | 0.0013 | 32 758 | 22 754 771 | 0.0014 | 34 107 | 22 832 965 | 0.0015 | 35 606 | 22 899 582 | 0.0016 | 36 640 | 22 937 740 | 0.0016 |
Phy means the number of physicians. p/p means the the number of physicians divided by the population.
Measuring inequality in physician distributions: the Gini coefficient
Traditionally, the Gini coefficient is a measure of the inequality of a distribution. In the present study, we calculated the Gini coefficient for each year from 2001 to 2010, to evaluate the inequality of the distribution of physicians in Taiwan. First, we calculated the physician-to-population ratio, which is defined as the number of physicians divided by the local population in each subdivision. Subsequently, we ranked all the subdivisions by its physician-to-population ratio and plotted them on a graph, where the X- and Y-axis represented the cumulative proportion of the population and physicians, respectively. We then plotted each subdivision onto the coordinate plane according to its cumulative proportion of the population (X) and physicians (Y). The resulting curve is known as the Lorenz curve. The area between the Lorenz curve and the 45-degree line divided by the triangle under the equity 45-degree line is the Gini coefficient, which is a ratio with a value between 0 and 1. A Lorenz curve that equals the 45-degree straight line (diagonal line between (0, 0) and (1,1)) indicates complete equality in the physician-to-population distribution (Gini coefficient equals zero). On the contrary, the Gini coefficient equals to 1 indicates extreme inequality in physician distribution.
Spatially adjusted Gini coefficients
A drawback of using the Gini coefficient to assess inequality in physician distribution is that it ignores geographical relationships in data. This paper employs a geographical correlation to calculate spatially adjusted Gini coefficients. First, we adopted three methods based on neighborhood, travel distance and travel time adjustments to construct the spatial matrix. Using these three matrices, we estimated the spatially adjusted number of physicians. Subsequently, we calculated the spatially adjusted physician-to-population ratio, which is defined as the spatially adjusted number of physicians divided by the local population in each subdivision. Following this, we ranked all the subdivisions by the spatially adjusted physician-to-population ratio. The methodologies related to the spatial adjustments, cij, are described in the following subsections.
Neighborhood adjustment
Travel distance adjustment
Travel time adjustment
Results
As the terrain of Eastern Taiwan is mostly mountains and Western Taiwan has mostly gently sloping plains, the population concentrates in Western Taiwan, especially in the north region where nearly 9 million people live in Taipei, New Taipei and Taoyuan. Approximately 2 million people live in central Taiwan, Taichung and south of Taiwan, Kaohsiung, respectively.
Table 2 represents the summary statistics for the variables of the number of physicians, the population, the physician-to-population ratios, travel time and travel distance. Taiwan has 349 subdivisions. The median, mean and standard deviation for the number of physicians are respectively 15, 105 and 210, whereas the maximum and minimum numbers of physicians are, respectively, 1537 and 0 , thus implying an unequal distribution of physicians in Taiwan. Similarly, we observe this maldistribution phenomenon in the physician-to-population ratio. The mean and standard deviation for the physician-to-population ratio are, respectively, 0.00107 and 0.00157, whereas the maximum and minimum physician-to-population ratios are, respectively, 0.01618 and 0. This indicates that the physician-to-population ratio is extremely unequal, despite an increase in the number of physicians over the last decade. We use Google Maps to estimate the distance and travel time between the addresses of two administrative centers in the subdivisions. Thus, the distance and travel time imply the topography and transport network of 349 subdivisions in Taiwan. The distance and travel time of the route with complicated topography such as high mountains or large lakes would be longer than routes with sloping plains. Thus, the mean and standard deviation for travel distance are 33 km and 26 km, respectively, while for travel time they are 40 and 29 min, respectively.
. | Number of physicians . | Population . | Physician-to-population ratio . | Travel distance (km) . | Travel time (min) . |
---|---|---|---|---|---|
Median | 15 | 34 284 | 0.00051 | 27 | 34 |
Mean | 105 | 65 724 | 0.00107 | 33 | 40 |
Standard deviation | 210 | 81 277 | 0.00157 | 26 | 29 |
Maximum | 1537 | 554 596 | 0.01618 | 430 | 533 |
Minimum | 0 | 1874 | 0 | 0.4 | 1 |
Number of observations | 349 | 349 | 349 | 8696 | 8696 |
. | Number of physicians . | Population . | Physician-to-population ratio . | Travel distance (km) . | Travel time (min) . |
---|---|---|---|---|---|
Median | 15 | 34 284 | 0.00051 | 27 | 34 |
Mean | 105 | 65 724 | 0.00107 | 33 | 40 |
Standard deviation | 210 | 81 277 | 0.00157 | 26 | 29 |
Maximum | 1537 | 554 596 | 0.01618 | 430 | 533 |
Minimum | 0 | 1874 | 0 | 0.4 | 1 |
Number of observations | 349 | 349 | 349 | 8696 | 8696 |
. | Number of physicians . | Population . | Physician-to-population ratio . | Travel distance (km) . | Travel time (min) . |
---|---|---|---|---|---|
Median | 15 | 34 284 | 0.00051 | 27 | 34 |
Mean | 105 | 65 724 | 0.00107 | 33 | 40 |
Standard deviation | 210 | 81 277 | 0.00157 | 26 | 29 |
Maximum | 1537 | 554 596 | 0.01618 | 430 | 533 |
Minimum | 0 | 1874 | 0 | 0.4 | 1 |
Number of observations | 349 | 349 | 349 | 8696 | 8696 |
. | Number of physicians . | Population . | Physician-to-population ratio . | Travel distance (km) . | Travel time (min) . |
---|---|---|---|---|---|
Median | 15 | 34 284 | 0.00051 | 27 | 34 |
Mean | 105 | 65 724 | 0.00107 | 33 | 40 |
Standard deviation | 210 | 81 277 | 0.00157 | 26 | 29 |
Maximum | 1537 | 554 596 | 0.01618 | 430 | 533 |
Minimum | 0 | 1874 | 0 | 0.4 | 1 |
Number of observations | 349 | 349 | 349 | 8696 | 8696 |
. | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
2001 | 0.5128 | 0.4256 | 0.4408 | 0.4324 |
2002 | 0.4910 | 0.4078 | 0.4282 | 0.4174 |
2003 | 0.4880 | 0.4046 | 0.4259 | 0.4149 |
2004 | 0.4606 | 0.3779 | 0.4120 | 0.4004 |
2005 | 0.4670 | 0.3828 | 0.4170 | 0.4059 |
2006 | 0.4664 | 0.3806 | 0.4144 | 0.4030 |
2007 | 0.4751 | 0.3834 | 0.4166 | 0.4051 |
2008 | 0.4713 | 0.3783 | 0.4154 | 0.4040 |
2009 | 0.4693 | 0.3791 | 0.4165 | 0.4051 |
2010 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
Average | 0.4771 | 0.3899 | 0.4205 | 0.4095 |
. | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
2001 | 0.5128 | 0.4256 | 0.4408 | 0.4324 |
2002 | 0.4910 | 0.4078 | 0.4282 | 0.4174 |
2003 | 0.4880 | 0.4046 | 0.4259 | 0.4149 |
2004 | 0.4606 | 0.3779 | 0.4120 | 0.4004 |
2005 | 0.4670 | 0.3828 | 0.4170 | 0.4059 |
2006 | 0.4664 | 0.3806 | 0.4144 | 0.4030 |
2007 | 0.4751 | 0.3834 | 0.4166 | 0.4051 |
2008 | 0.4713 | 0.3783 | 0.4154 | 0.4040 |
2009 | 0.4693 | 0.3791 | 0.4165 | 0.4051 |
2010 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
Average | 0.4771 | 0.3899 | 0.4205 | 0.4095 |
Note: This table presents the traditional Gini coefficient and the three different kinds of spatially adjusted Gini coefficients for Taiwan from 2001 to 2010.
. | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
2001 | 0.5128 | 0.4256 | 0.4408 | 0.4324 |
2002 | 0.4910 | 0.4078 | 0.4282 | 0.4174 |
2003 | 0.4880 | 0.4046 | 0.4259 | 0.4149 |
2004 | 0.4606 | 0.3779 | 0.4120 | 0.4004 |
2005 | 0.4670 | 0.3828 | 0.4170 | 0.4059 |
2006 | 0.4664 | 0.3806 | 0.4144 | 0.4030 |
2007 | 0.4751 | 0.3834 | 0.4166 | 0.4051 |
2008 | 0.4713 | 0.3783 | 0.4154 | 0.4040 |
2009 | 0.4693 | 0.3791 | 0.4165 | 0.4051 |
2010 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
Average | 0.4771 | 0.3899 | 0.4205 | 0.4095 |
. | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
2001 | 0.5128 | 0.4256 | 0.4408 | 0.4324 |
2002 | 0.4910 | 0.4078 | 0.4282 | 0.4174 |
2003 | 0.4880 | 0.4046 | 0.4259 | 0.4149 |
2004 | 0.4606 | 0.3779 | 0.4120 | 0.4004 |
2005 | 0.4670 | 0.3828 | 0.4170 | 0.4059 |
2006 | 0.4664 | 0.3806 | 0.4144 | 0.4030 |
2007 | 0.4751 | 0.3834 | 0.4166 | 0.4051 |
2008 | 0.4713 | 0.3783 | 0.4154 | 0.4040 |
2009 | 0.4693 | 0.3791 | 0.4165 | 0.4051 |
2010 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
Average | 0.4771 | 0.3899 | 0.4205 | 0.4095 |
Note: This table presents the traditional Gini coefficient and the three different kinds of spatially adjusted Gini coefficients for Taiwan from 2001 to 2010.
Moreover, Table 3 shows the numerical results based on the traditional Gini coefficient and the spatially adjusted Gini coefficient. We compared different types of spatially adjusted Gini coefficients and found that the neighborhood-based spatially adjusted Gini coefficient is consistently smaller than those based on travel distance and time. Some areas, though adjacent, have a barrier on their territory border, making it very difficult for their populations to share medical resources. Therefore, the neighborhood-based spatially adjusted Gini coefficient may lead to an underestimation of inequality in physician distribution. Thus, computing the spatially adjusted Gini coefficients based on travel distance and time may be a more appropriate alternative. Overall, it is appropriate to use the travel distance and travel time in the estimation when calculating the Gini coefficients.
Discussion
Based on the analysis results after adopting the spatially adjusted Gini coefficients, we propose some alternative policies to reduce inequality in physician distributions. Our first proposed policy is to add a certain number of physicians to each county capital. As physicians tend to prefer to stay in urban areas, it is difficult to move physicians to rural areas directly [33–35]. However, it would likely be easier to appoint physicians to medium-sized cities (such as capitals of counties, provinces or states), which respects their preference for an urban environment. Table 4 presents the findings of a simulation in which a certain number of physicians were added to each of the 12 county capitals in Taiwan. The addition of more than 50 physicians to each county capital leads to a decrease in the spatially adjusted Gini coefficients; specifically, the coefficients based on neighborhood, travel distance and travel time decrease from 0.3785, 0.4178 and 0.4066, to 0.3765, 0.4152 and 0.4035, respectively. However, the addition of more than 50 physicians to each county capital leads to an increase in the traditional Gini coefficient. This worsening of the distribution of physicians observed upon adding more physicians to each county capital may occur because physicians are overly concentrated in the large-sized and medium-sized cities. However, as mentioned previously, the traditional Gini coefficient fails to consider geographical relationships. If the government uses the mandatory policies to increase the salary in the specific regions and appoint more physicians to medium-sized size cities, the spatially adjusted Gini coefficients will be refined. Our paper therefore shows that these policies could be useful for reducing inequality in physician distribution, when considering the geographical correlation. However, the effectiveness of the policies may hardly be evident if the geographical correlation is ignored. To reiterate, if we consider the spatial correlation, increasing physicians in the medium-sized cities by a certain number would help mitigate the maldistribution of physicians.
Number of physicians added in the county capital . | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
+0 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
+50 | 0.4691 | 0.3754 | 0.4139 | 0.4018 |
+100 | 0.4728 | 0.3736 | 0.4097 | 0.3978 |
+120 | 0.4749 | 0.3731 | 0.4083 | 0.3963 |
+150 | 0.4782 | 0.3727 | 0.4064 | 0.3942 |
Number of physicians added in the county capital . | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
+0 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
+50 | 0.4691 | 0.3754 | 0.4139 | 0.4018 |
+100 | 0.4728 | 0.3736 | 0.4097 | 0.3978 |
+120 | 0.4749 | 0.3731 | 0.4083 | 0.3963 |
+150 | 0.4782 | 0.3727 | 0.4064 | 0.3942 |
Note: This table presents the simulation results of increasing certain numbers of physicians in county capitals. The first column is the number of physicians added in the county capital. The second, third, fourth and fifth columns show the Gini coefficient and the three different kinds of spatially adjusted Gini coefficients derived after adding the corresponding number of physicians in the first column in the county capital.
Number of physicians added in the county capital . | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
+0 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
+50 | 0.4691 | 0.3754 | 0.4139 | 0.4018 |
+100 | 0.4728 | 0.3736 | 0.4097 | 0.3978 |
+120 | 0.4749 | 0.3731 | 0.4083 | 0.3963 |
+150 | 0.4782 | 0.3727 | 0.4064 | 0.3942 |
Number of physicians added in the county capital . | Gini coefficient . | Neighborhood adjustment . | Travel distance adjustment . | Travel time adjustment . |
---|---|---|---|---|
+0 | 0.4692 | 0.3785 | 0.4178 | 0.4066 |
+50 | 0.4691 | 0.3754 | 0.4139 | 0.4018 |
+100 | 0.4728 | 0.3736 | 0.4097 | 0.3978 |
+120 | 0.4749 | 0.3731 | 0.4083 | 0.3963 |
+150 | 0.4782 | 0.3727 | 0.4064 | 0.3942 |
Note: This table presents the simulation results of increasing certain numbers of physicians in county capitals. The first column is the number of physicians added in the county capital. The second, third, fourth and fifth columns show the Gini coefficient and the three different kinds of spatially adjusted Gini coefficients derived after adding the corresponding number of physicians in the first column in the county capital.
Our second proposed policy is to reduce patients’ travel time to reach physicians. The government could consider building new roads or expressways from rural areas (such as small towns or villages) to nearby cities. If transportation connectedness between rural and urban areas were improved, it would be easier for residents in rural areas to access the health-care services in the adjacent regions. Table 5 presents the findings of a simulation that reduces travel time. We suppose that people could save 5–30 min of travel time if the original travel time exceeded 120 min. As we only changed the travel time between two subdivisions, spatially adjusted Gini coefficients would change only based on travel time. We observe that a reduction in travel time leads to a decrease in the Gini coefficient adjusted for travel time. Specifically, if 30 min of travel time were saved, the travel time-based spatially adjusted Gini coefficient decreases from 0.4066 to 0.4062. Previous studies were restricted by only utilizing travel distance to measure the inequality in physician distribution. However, measurements based on travel distance could be misleading because it is difficult to shorten the direct distance between two locations. However, travel time could be reduced by building new roads, innovation in vehicles, and some improvements in public transportation. Our study demonstrates that improving the transportation network could be a possible solution for mitigating the maldistribution of physicians.
Time reduction | 120 min | 120–5 = 115 min | 120–10 = 110 min | 120–15 = 105 min |
Gini based on travel time adjustment | 0.4066 | 0.4063 | 0.4063 | 0.4062 |
Time reduction | 120–20 = 100 min | 120–25 = 95 min | 120–30 = 90 min | |
Gini based on travel time adjustment | 0.4062 | 0.4062 | 0.4062 |
Time reduction | 120 min | 120–5 = 115 min | 120–10 = 110 min | 120–15 = 105 min |
Gini based on travel time adjustment | 0.4066 | 0.4063 | 0.4063 | 0.4062 |
Time reduction | 120–20 = 100 min | 120–25 = 95 min | 120–30 = 90 min | |
Gini based on travel time adjustment | 0.4062 | 0.4062 | 0.4062 |
Note: This table presents the simulation results of reducing travel time. The results show the spatially adjusted Gini coefficient based on travel time: specifically, based on the assumption that people can save travel time from 5 to 30 min if the original travel time exceeds 120 min.
Time reduction | 120 min | 120–5 = 115 min | 120–10 = 110 min | 120–15 = 105 min |
Gini based on travel time adjustment | 0.4066 | 0.4063 | 0.4063 | 0.4062 |
Time reduction | 120–20 = 100 min | 120–25 = 95 min | 120–30 = 90 min | |
Gini based on travel time adjustment | 0.4062 | 0.4062 | 0.4062 |
Time reduction | 120 min | 120–5 = 115 min | 120–10 = 110 min | 120–15 = 105 min |
Gini based on travel time adjustment | 0.4066 | 0.4063 | 0.4063 | 0.4062 |
Time reduction | 120–20 = 100 min | 120–25 = 95 min | 120–30 = 90 min | |
Gini based on travel time adjustment | 0.4062 | 0.4062 | 0.4062 |
Note: This table presents the simulation results of reducing travel time. The results show the spatially adjusted Gini coefficient based on travel time: specifically, based on the assumption that people can save travel time from 5 to 30 min if the original travel time exceeds 120 min.
Deaton [1] pointed out that people in rich countries are healthier and live longer than people in poor countries. Health systems in poor countries lack a sufficient number of physicians. In some poor or developing countries, the governments have insufficient funding to train sufficient physicians to work in their health-care system. However, our results indicate that the appropriate physician allocation and convenient transportation play an important role in mitigating the physician inequality problem. If poor countries can redistribute the physicians to suitable cities and improve the transportation network, they can mitigate the maldistribution of physicians and further reduce health inequality.
Huang et al. [36] analyzed the changes in geographic distribution for physicians in Taiwan from 1984–1998 and found that the traditional Gini coefficient for total physicians increased from 0.42 to 0.47, while the traditional Gini coefficient for clinic-based (office-based) physicians decreased from 0.30 to 0.25. Furthermore, Wu et al. [37] investigated the geographic distribution of physical therapy human resources in Taiwan from 1997–2006 and found that the traditional Gini coefficient for physical therapy reduced from 0.64 to 0.44, indicating that the geographic distribution of physical therapy improved during the sample period. Our paper compliments previous literature by measuring the inequality in Taiwan's physician distributions using the spatial method.
Limitations
This study has three limitations to consider when interpreting the spatially adjusted Gini coefficients results.
Quality of health care. Although the spatially adjusted Gini coefficient evaluates the inequality in physician distributions using the spatial method, it only measures the quantity of physicians. Previous studies have documented that the health quality provided by hospitals or physicians could influence patients’ preferences or choices for health-care services [38–41]. Furthermore, Yu et al. [41] stated that a disparity of quality of health care exists between urban and rural areas in Taiwan. While our study does not consider the quality of health care provided by physicians, the physicians or hospitals in rural areas have lower health-care quality and lack the technical expertise of physicians and the innovations of surgery equipment. Thus, the health inequality measurements for evaluating the quantity and quality of health care should be addressed.
Other measurement methods. This study only aimed to compare the spatially adjusted Gini coefficients; we did not check the need index or use other methods such as the concentration index to evaluate the inequality in physician distributions. Furthermore, this study excludes some health indicators, which measure the distribution of human resources for health. To evaluate health inequality accurately, future studies should include other measurements.
Access to health services. Although Taiwan's NHI program provides every citizen with equal access to health services, some other barriers to health services remain. For example, people living in rural areas face higher transportation costs to access health services in adjacent regions. The spatially adjusted Gini coefficients cannot measure this invisible barrier to the health services.
Conclusion
The purpose of this study was to assess the problem of physician maldistribution by analyzing spatial adjustments. To the best of our knowledge, existing literature has yet to estimate Gini coefficients by considering spatial adjustments. We measured the inequality in physician distribution in Taiwan as a whole using spatially adjusted Gini coefficients, which we adjusted based on neighborhood, travel distance and travel time. Using physician and population distribution data from 2001 to 2010, we calculated the traditional Gini coefficient and spatially adjusted Gini coefficients for Taiwan as a whole to measure the inequality in physician distribution. We found that the spatially adjusted Gini coefficient was consistently smaller than the traditional Gini coefficient over this period. Traditionally, the Gini coefficient fails to consider that people can access medical services in nearby areas. Therefore, our empirical results are consistent with those of previous studies [16–18], showing that the shortage of medical services in rural areas could be overestimated. Specifically, the spatially adjusted Gini coefficients based on travel time and travel distance could be more appropriate than the traditional Gini coefficient for measuring inequality in physician distributions.
Furthermore, from a policy perspective, this new measurement for inequality in physician distribution provides two feasible strategies for mitigating the maldistribution of physicians. First, appointing more physicians in each county, state or province's capital can mitigate the maldistribution. Second, improving transportation networks between rural areas and nearby cities can alleviate physician maldistribution. Health systems in low- and middle-income countries lack a sufficient number of physicians. Thus, allocating physicians to suitable areas to ensure efficient utilization, has become an important concern for their governments. Based on our results, we believe that increasing the number of physicians in medium-sized cities and improving transportation connectedness between medium-sized cities and nearby rural areas are appropriate solutions for the problems of physician maldistribution.
Acknowledgements
We thank all authors and investigators. We especially thank Professor Rachel Huang at National Central University in Taiwan for her meticulous comments.
Funding
This work was supported by grants from Ministry of Science and Technology of Taiwan (MST Project number: 103-2410-H-032-025-). The funding source had no role in this study.