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journal of gerontology biological sciences copyright 1998 by the gerontological society of america 1998 vol 53a no 5 b362 b368 comparison of cross sectional and longitudinal designs in the study ...

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             Journal of Gerontology: BIOLOGICAL SCIENCES                                                 Copyright 1998 by The Gerontological Society of America
              1998. Vol. 53A, No. 5, B362-B368
                      Comparison of Cross-Sectional and Longitudinal
                                           Designs in the Study of Aging
                                        of Upper Extremity Performance
                                                        12                   12                12                         1
                               Johanne Desrosiers,  Rejean Hebert,  Gina Bravo,  and Annie Rochette
                                                                                                                                                   Downloaded from https://academic.oup.com/biomedgerontology/article/53A/5/B362/588231 by guest on 19 August 2022
                    'Centre de Recherche en G6rontologie et Geriatrie, Sherbrooke Geriatric University Institute, Sherbrooke, Qu6bec, Canada.
                                         Taculte" de Me*decine, University de Sherbrooke, Sherbrooke, Quebec, Canada.
                            The purpose of the study was to compare two research designs, namely the cross-sectional design and the longitudi-
                            nal design, in the context of upper extremity performance and age-related changes. Upper extremity performance of
                            360 randomly recruited, healthy, community-dwelling elderly persons was evaluated with reliable and valid sensori-
                            motor tests. Three years later, survivors (n = 264) were reevaluated with the same tests. In many tests, cross-sec-
                            tional and longitudinal designs were comparable for estimating the changes in upper extremity performance with
                            age. However, in some tests, the decline with age using a cross-sectional design was underestimated. The upper
                            extremity performance decline observed with the longitudinal design was larger than the decline predicted with the
                            cross-sectional design. The withdrawal and survivor biases related to the longitudinal design and the cohort bias
                            associated with the cross-sectional design may, in part, explain these results.
                N the study of age-related changes, two major research         used by clinicians to compare the performance of their
             I designs may be used: the cross-sectional design and the         patients to that of a normal population. These data are
             longitudinal design. Both designs have particular advan-          important in gerontology because it is important to differ-
             tages and disadvantages. Even though the cross-sectional          entiate between the difficulties attributable to normal aging
             design is less expensive and frequently used in the devel-        and those attributable to pathologic aging.
             opment of normative data, this design may have an impor-             The objective of the present study was to compare cross-
             tant limitation in the study of aging. This limitation is the     sectional and longitudinal designs in the context of upper
             cohort bias in that people born at the beginning of the cen-      extremity performance changes with age. The method-
             tury have not experienced the same events nor under the           ologic relevance of the study is based on the appropriate-
             same conditions as younger people, which may influence            ness of the cross-sectional design for studying age-related
             their performance.                                                changes. The clinical relevance of the study is based on the
                In addition to being longer and more expensive, the            durability of the normative data developed with a cross-
             study of aging with a longitudinal design presents other          sectional design. If the performance decline predicted by
             possible biases related to withdrawal (refusals) and to sur-      the cross-sectional design is equivalent to the decline ob-
             vival (deaths or ineligibility factors). The bias associated      served with the longitudinal design, normative data may be
             with withdrawal was studied by Hubert et al. (1) with 500         applied to successive cohorts. If not, they should be regu-
             subjects aged 75 years and older, followed on a 3-year            larly revised.
             period. Men had more tendency to drop out, but no health-
             related variables were associated with withdrawal from the        METHODS
             study. Mihelic and Crimmins (2) found that withdrawal
             (nonresponse) was associated, among other variables, with         Subjects
             age (older people), living situation (alone), and functional         During 1992-1993, a random sample of 360 subjects (179
             impairments (more), but not with gender. The survival bias        women and 181 men), aged 60 and older (mean, 73.9; SD,
             was more serious because people who died during a study           8.0), and living at home was drawn from the electoral list of
             were those whose health was more affected (3-5).                  the city of Sherbrooke, Quebec, Canada. The purpose of this
                Upper extremity performance is an important prerequi-          cross-sectional study was to develop reference values for
             site to functional independence in older people (6-9). With       many upper sensorimotor parameters (10). The eligibility
             the aging of the population, more and more people may             criteria were lucidity (clinical judgment), independence in
             have a decline in upper extremity performance secondary           activities of daily living (eating, washing, dressing, groom-
             to age-related sensorimotor deficits. Therefore, sensorimo-       ing, and toiletting), and absence of upper extremity impair-
             tor parameters related to good upper extremity perfor-            ments (neurologic or orthopedic). The participation rate in
             mance, such as gross and fine dexterity, motor coordina-          this study was 78% and statistical analyses revealed no dif-
             tion, global performance, grip strength and sensibilities, are    ference between those who refused to participate and those
             often measured in clinical settings to monitor their evolu-       who accepted in terms of age, gender, height, weight, domi-
             tion. Reference values or normative data are frequently           nance, self-perceived health, and current activity level (11).
             B362
                                      COMPARISON OF CROSS-SECTIONAL AND LONGITUDINAL DESIGNS                                               B363
                Three years later (1995-1996), the same subjects were            Statistical Analyses
             recontacted to replicate the study. The same eligibility crite-        To simplify the results presentation, the terms time 1 and
             ria were applied and subjects who no longer satisfied these         time 2 will be used respectively for the first evaluation in
             criteria were excluded. As in the cross-sectional study, peo-       1992-1993 and the second in 1995-1996. t test and chi-
             ple who refused to participate, although eligible, were             square analyses were used to compare, at time 1, personal
             asked to reply to a short telephone questionnaire in order to       characteristics and upper extremity performance of subjects
             estimate the refusal bias.                                          who did not participate in the second measurement with
                                                                                 those who participated in both measurements. The same sta-
             Procedure                                                           tistical tests were used to verify if those who refused to par-
                The same evaluation procedure was followed for the two           ticipate were comparable in personal characteristics, at time         Downloaded from https://academic.oup.com/biomedgerontology/article/53A/5/B362/588231 by guest on 19 August 2022
             measurement periods. To avoid an information bias in the            2, to those who agreed. Paired t tests were used to verify if
             second measurement, data from the first assessment were             the changes between time 1 and time 2 were significant.
             not available to the examiner. For both measurements, each             The main analysis of this study focused on comparing
             subject was evaluated once at the Upper Limb Function               upper extremity changes predicted with the cross-sectional
             Measurement Laboratory at the Centre de Recherche en                design (predicted difference: PREDDIF) to changes ob-
             Ge'rontologie et G6riatrie or at their home under the same          served by the longitudinal design (observed difference:
             conditions, but not by the same examiner who took the first         OBSDIF). The observed difference is defined by the ob-
             measurement. The duration of each measurement varied                served score at time 1 minus the observed score at time 2.
             between VA and 2 hours, depending on the subject, includ-           The predicted difference is calculated by subtracting the
             ing a rest. This study was submitted to and accepted by the         predicted score at time 2 from the score at time 1. The pre-
             Research Ethics Committee of the Sherbrooke Geriatric               dicted score at time 2 was estimated using simple linear
             University Institute.                                               regression analyses developed with time 1 data (cross-sec-
                Anthropometric data were first collected, followed by a          tional design), where age was the independent variable and
             structured interview in order to quantify personal characteris-     the upper extremity test score was the dependent variable.
             tics potentially related to upper extremity performance: age,       In some tests, a high score indicates a low performance
             living situation (living alone, living with somebody else, liv-     whereas in others, the scoring system is reversed. Conse-
             ing in a senior's residence), self-perceived health status, and     quently, in order to facilitate the data interpretation, the pre-
             activity level. Regarding self-perceived health status, the         dicted and observed differences were standardized so that
             subject was asked: "Compared to other people your age, how          positive numbers represent a decline.
             would you describe your present health? Excellent, good,               For each upper extremity test, a t score was attributed to
             fair, or poor." Activity level was evaluated using questions        each subject. These t scores were defined by
             regarding the frequency of physical activities. Based on this                            (OBSDIF-PREDDIF)
             information, the evaluator estimated the level of activity on a
             global scale: very active, active, slightly active, or sedentary.
             Subsequently, upper extremity tests were administered.              where Spred is the standard deviation of the predicted score
                                                                                 model. A t test was then used to check if, on average, these
             Measurement Instruments                                             t scores were null. If the longitudinal and cross-sectional
                Many tests were chosen in order to reflect upper extrem-         designs described the aging effect in the same way, then the
             ity function. These tests are all reliable and valid. Gross         observed difference from the longitudinal design and the
             manual dexterity was measured with the Box and Block                predicted difference from the cross-sectional design should
             Test (12-14) whereas fine manual dexterity was measured             be equivalent. In order to confirm the null hypothesis that
             with the Purdue Pegboard (15-17). Global upper extremity            no difference was observed between the observed upper
             performance was estimated with the TEMPA (Test Evaluant             extremity performance decline (longitudinal design) and
             la performance des Membres superieurs des Personnes                 the predicted decline (cross-sectional design), the differ-
             Ag6es) (18-20).                                                     ences should be near 0. To take into account the high num-
                Upper extremity motor coordination was estimated with            ber of statistical analyses done, the level of p < .01 was
             the Finger-Nose Test (21-23). Grip strength was measured            retained.
             with two apparatuses: the Jamar dynamometer (11,24) and
             the Martin vigorimeter (25,26). The Jamar dynamometer               RESULTS
             was set at the second position and the large bulb of the               Of the original 360 subjects in the cross-sectional study,
             Martin vigorimeter was selected for all subjects.                   264 (128 women and 136 men) with a mean age of 75.0
                Tactile recognition was estimated with the Pick-Up Test          (SD = 7.4) participated in the second measurement. There-
             (27), modified by Dellon (28,29). Static and moving two-            fore, 96 subjects were not reevaluated: 26 had died, 15
             point discriminations were measured on the palmar face of           were not located, 29 refused, and 26 were no longer eligible
             the distal phalanx of the index and little finger of both           because of the development of impairment.
             hands, using the Mackinnon-Dellon disk-criminator (30).                When characteristics at time 1 of the 96 drop-out subjects
             Touch/pressure thresholds (31) were estimated at the distal         were compared to those who participated, drop-outs were
             phalanx of the index of the dominant hand using the                 older (p < .001), had a lower body mass index (p = .006), per-
             Semmes-Weinstein monofilaments (32). Finally, the same              ceived themselves in poorer health (p = .001), were less
             filaments were used for the tactile localization test (33).         active (p = .001), and were more likely to live in a senior's
                         B364                                                                                                 DESROSIERS ETAL.
                         residence (p = .04). From the phone questionnaire at time 2,                                                                         Table 1 presents the results related to the objective of the
                         the subjects who refused to participate in the second mea-                                                                      study. For each test, when significant differences were found
                         surement (n = 29) were older (p = .01), perceived themselves                                                                    between the upper extremity performance of the women and
                         in poorer health (p < .01), and were less active {p < .001) than                                                                the men, the results are presented by gender. If not, they
                         those who participated. In addition, the subjects who partici-                                                                  were combined. The first two columns of the table report
                         pated in both measurements showed, at time 1, significantly                                                                     upper extremity scores obtained at the time 1 measurement
                         higher performance on all upper extremity tests (p < .01) than                                                                  (1992-1993) and at the time 2 measurement (1995-1996).
                         those who participated in only one measurement, with the                                                                        The third column shows the result of the difference between
                         exception of the tactile localization of the left index (p = . 14).                                                             the two measurements (time 1 minus time 2), which corre-
                                                                                                                                                                                                                                                                                             Downloaded from https://academic.oup.com/biomedgerontology/article/53A/5/B362/588231 by guest on 19 August 2022
                                                                                           Table 1. Comparison of the Observed and Predicted Differences
                                                                                                                                                             OBSDIF                        T                     PREDDIF                     OBSDIF -
                                                                                                                       1                         2             1                                                                             PRFnniF                      n
                                                                                                         92-93 (T )               95-96 (T )                (T  score                Predicted                   (T' score                                               r
                                                                                                                       1                        2               2                                               2                                  p>rd
                                                                                                           Score T                  Score T                  T  score)                  score                T  pred. score)                      S                   value
                         Box and Block Test (No. of blocks)
                         Men and women
                             Right hand                                                                 68.9 (8.3)*               59.6 (7.6)*                9.3 (6.8)*             66.2 (4.7)*                  2.7 (7.3)*                  0.85 (0.9)*               <.001
                             Left hand                                                                  68.2 (8.7)                59.2 (7.5)                 9.0 (6.5)              65.6 (4.8)                   2.6 (7.6)                   0.80 (0.9)                <.001
                         Purdue Pegboard (No. of pins)
                         Women
                             Right hand                                                                  13.3(1.8)                12.4 (2.3)                0.9(1.9)                12.7(1.1)                    0.5(1.5)                    0.24(1.2)                   .03
                             Left hand                                                                   12.5(1.9)                11.7(2.3)                  0.9(1.6)               12.0(1.2)                    0.6(1.6)                    0.18(1.0)                   .05
                             Both hands                                                                  10.1 (1.9)                 9.3(1.9)                0.8(1.5)                  9.6(1.1)                   0.5(1.6)                    0.17(0.9)                   .04
                             Total                                                                      35.9 (5.0)                33.2 (6.0)                 2.6 (3.6)              34.3 (3.4)                   1.6(3.9)                    0.24(1.0)                   .01
                             Assembly                                                                   27.5 (6.3)                25.5 (6.5)                 2.0 (5.0)              25.5 (3.5)                   2.0 (5.5)                 -0.007 (0.9)                  .93
                         Men
                             Right hand                                                                  11.8(1.9)                10.8(2.1)                 0.9(1.7)                 11.1(1.1)                   0.7(1.8)                    0.16(1.0)                   .07
                             Left hand                                                                   11.5(2.0)                10.5 (2.2)                 1.0(1.7)               10.8(1.3)                    0.7(1.7)                    0.17(1.1)                   .08
                             Both hands                                                                   9.0(1.9)                  8.2 (2.0)               0.8(1.4)                  8.4(1.1)                   0.7(1.7)                    0.11 (1.1)                  .27
                             Total                                                                      32.3 (5.3)                29.5 (5.7)                2.8(3.1)                30.3 (3.5)                   2.0 (4.5)                   0.17(1.1)                   .07
                             Assembly                                                                   24.4 (6.0)                22.0 (6.0)                2.3 (4.0)               22.2 (3.8)                   2.1(5.1)                    0.03 (0.9)                  .73
                         TEMPA (log. sec.)
                         Pick up and move ajar
                         Women
                             Right hand                                                                   0.5 (0.2)                0.5 (0.2)                0.03 (0.2)                0.5(0.1)                   0.03 (0.2)                  0.03 (0.9)                  .75
                             Left hand                                                                    0.5 (0.2)                0.5 (0.2)                0.02 (0.2)                0.5(0.1)                   0.03 (0.2)                -0.02 (0.9)                   .79
                         Men
                             Right hand                                                                   0.4 (0.2)                0.4 (0.2)                0.05 (0.3)                0.4(0.1)                  0.04 (0.2)                   0.05 (0.8)                  .49
                             Left hand                                                                    0.4 (0.2)                0.4 (0.2)                0.04 (0.3)                0.4 (0.4)                  0.03 (0.2)                  0.06 (0.8)                  .38
                         Open ajar and take a spoonful of coffee
                         Women and men                                                                    2.2 (0.2)                2.3 (0.2)                0.11(0.2)                 2.2(0.1)                  0.06 (0.2)                   0.20(1.1)                   .004
                         Pick up a pitcher and pour water into a glass
                         Women and men
                             Right hand                                                                   2.1 (0.2)                2.1 (0.2)                0.04 (0.2)                2.1 (0.1)                 0.05 (0.2)                 -0.008(1.0)                   .89
                             Left hand                                                                    2.1 (0.2)                2.1 (0.2)                0.03 (0.2)               2.1 (0.1)                  0.05 (0.2)                 -0.13(0.9)                    .02
                         Unlock a lock and open a pill container
                         Women and men                                                                    2.4 (0.2)                2.6 (0.2)                0.17(0.2)                2.4 (0.2)                  0.05 (0.2)                   0.56 (0.9)               <.001
                         Tie a scarf around one's neck
                         Women and men                                                                    2.1 (0.3)                2.3 (0.3)                0.13(0.3)                2.2 (0.2)                  0.11(0.2)                    0.09(1.1)                   .34
                         Handle coins
                         Women
                             Right hand                                                                   2.0 (0.2)                2.2 (0.2)                0.15(0.2)                2.1 (0.1)                  0.04 (0.2)                   0.60(1.0)                <.01
                             Left hand                                                                    2.1(0.2)                 2.2 (0.2)                0.09 (0.2)               2.2(0.1)                   0.04 (0.2)                   0.30(1.1)                   .002
                         Men
                             Right hand                                                                   2.1 (0.2)                2.3 (0.2)                0.14(0.2)                2.1 (0.1)                  0.05 (0.2)                   0.50(1.3)                <.001
                            Left hand                                                                     2.2 (0.2)                2.3 (0.2)                0.11(0.2)                2.2(0.1)                   0.04 (0.2)                  0.37(1.3)                 <.001
                         Pick up and move small objects
                         Men
                            Right hand                                                                    2.1(0.2)                 2.2 (0.2)                0.06 (0.2)               2.1 (0.1)                  0.05 (0.2)                  0.04 (0.9)                   .60
                            Left hand                                                                     2.1(0.2)                 2.2 (0.2)                0.05 (0.2)               2.1 (0.1)                  0.05 (0.2)                  0.01 (0.9)                  .89
                                                                                                                                                                                                                                          Continued on next page
                                                COMPARISON OF CROSS-SECTIONAL AND LONGITUDINAL DESIGNS                                                                         B365
                                                      Table 1. Comparison of the Observed and Predicted Differences (Continued)
                                                                                                          OBSDIF             T2             PREDDIF           OBSDIF -
                                                                                                 2         1                                                   PREDDIF
                                                                      92-93 (T)        95-96 (T )        (T  score -     Predicted          (T score -                           P
                                                                                1                2         2                               2                      gpncd
                                                                        Score T          Score T          T  score)        score          T  pred. score)                       value
                 Finger-Nose Test (No. of movements)
                 Women
                    Right upper limb                                  22.3(4.1)        20.2 (3.8)        2.0(4.1)        21.2(2.1)          1.0(3.5)           0.27(1.1)         .004
                    Left upper limb                                   21.6(4.1)        19.4(3.7)         2.2 (3.6)       20.6(2.1)          1.0(3.6)           0.33(1.0)        <.001
                 Men                                                                                                                                                                          Downloaded from https://academic.oup.com/biomedgerontology/article/53A/5/B362/588231 by guest on 19 August 2022
                    Right upper limb                                  23.0 (3.9)       22.5 (4.0)        0.5 (3.6)       21.8(2.0)          1.2(3.5)         -0.18(1.0)          .03
                    Left upper limb                                   22.9 (4.2)       21.6(3.8)         1.3(3.3)        21.5(2.2)          1.3(3.7)         -0.01 (0.9)         .88
                 Jamar dynamometer (kg)
                 Women
                    Right hand                                        24.2 (4.9)       23.2 (4.9)        1.0(2.8)        22.8 (2.3)         1.4(4.6)         -0.08(1.0)          .35
                    Left hand                                         22.5 (4.7)       22.1 (5.0)        0.4 (2.8)       21.2(2.3)          1.4(4.4)         -0.21 (1.0)         .02
                 Men
                    Right hand                                        41.9(9.3)        38.9 (9.8)        3.0(4.1)        39.8 (4.9)         2.0 (8.2)          0.12(1.0)         .17
                    Left hand                                         40.2 (9.4)       38.1 (9.3)        2.1 (4.0)       37.7(5.1)          2.5(8.1)         -0.05(1.0)          .60
                 Martin vigorimeter (Kpa)
                 Women
                    Right hand                                        52.2(11.2)       51.0(11.9)        1.2(7.1)       49.7 (4.2)          2.5(10.8)        -0.12(1.1)          .18
                    Left hand                                         50.4(10.9)       48.3(11.3)        2.0 (7.7)      48.1 (4.1)          2.3(10.6)        -0.02(1.0)          .80
                 Men
                    Right hand                                        81.2(18.1)       75.5(17.6)        5.7 (9.7)      76.9(11.0)          4.4(15.7)          0.09 (0.9)        .24
                    Left hand                                         80.0(17.9)       74.0(17.7)        6.2(10.8)       75.3(10.3)         4.7(15.5)          0.09 (0.9)        .24
                 Pick-Up Test (log. sec.)
                 Eyes close-eyes open
                 Women
                    Right hand                                         2.6 (0.5)        2.7 (0.5)        0.13(0.6)        2.7(0.1)          0.06 (0.5)         0.13(0.9)
                    Left hand                                          2.6 (0.4)        2.6 (0.5)        0.03 (0.6)       2.6(0.1)          0.06 (0.4)       -0.07(1.0)          .42
                 Men
                    Right hand                                         2.8 (0.5)        3.1 (0.5)        0.20 (0.5)       3.0 (0.2)         0.11 (0.4)         0.21 (1.0)        .02
                    Left hand                                          2.8 (0.5)        3.0 (0.5)        0.15(0.5)        2.9 (0.3)         0.11 (0.5)         0.10(1.0)         .24
                 Two-point discrimination (mm)
                 Static
                 Women and men
                    Right index                                        4.9 (0.9)        4.7 (0.9)       -0.12(1.1)        5.0 (0.3)         0.18(0.9)        -0.30 (0.9)        <.001
                    Left index                                         4.9 (0.9)        4.8 (0.9)       -0.06(1.1)        5.0 (0.2)         0.14(0.9)        -0.21 (1.0)        <.001
                 Women
                    Right little finger                                5.1(1.1)         5.9(1.1)         0.76(1.4)        5.3 (0.3)         0.14(1.0)          0.59(1.0)        <.001
                    Left little finger                                 5.1 (0.8)        6.3(1.5)         1.23(1.5)        5.3 (0.3)         0.15(0.8)          1.21 (1.7)       <.001
                 Men
                    Right little finger                                5.4(1.1)         6.1 (1.4)        0.59(1.3)        5.6 (0.3)         0.16(0.9)          0.45(1.2)        <.001
                    Left little finger                                 5.5(1.0)         6.3(1.3)         0.77(1.4)        5.7 (0.2)         0.14(1.0)          0.64(1.3)        <.001
                 Moving
                 Women and men                                                                                                                                                   .02
                    Right index                                        4.4(1.0)         4.6(1.0)         0.27(1.1)        4.5 (0.2)         0.13(1.0)          0.13(0.9)
                 Women
                    Left index                                         4.1 (1.0)        4.6(1.0)         0.48(1.1)        4.3 (0.3)         0.18(0.9)          0.31 (1.0)        .001
                    Right little finger                                4.5(1.1)         5.3(1.0)         0.86(1.2)        4.6 (0.3)         0.15(1.0)          0.67(1.0)        <.001
                    Left little finger                                 4.5(1.0)         5.3(1.1)         0.81(1.1)        4.6 (0.4)         0.16(0.9)          0.70(1.1)        <.001
                 Men
                    Left little finger                                 4.3(1.0)         4.5(1.1)         0.20(1.2)        4.5 (0.2)         0.19(1.0)          0.01 (1.0)        .88
                    Right little finger                                4.8(1.0)         5.4(1.2)         0.57(1.3)        5.0 (0.3)         0.19(1.0)          0.37(1.1)        <.001
                    Left little finger                                 4.9(1.0)         5.3(1.3)         0.47(1.5)        5.0 (0.2)         0.12(1.0)          0.33(1.2)         .002
                 Touch/pressure threshold
                 (SW filaments number)
                 Women                                                 3.42 (0.4)       3.50 (0.3)       0.08 (0.4)       3.46(0.1)         0.04 (0.4)         0.12(0.9)         .13
                 Men                                                   3.56 (0.3)       3.61 (0.3)       0.05 (0.4)       3.62(0.1)         0.06 (0.3)       -0.05(1.0)          .58
                 Tactile localization (/12)
                 Women and men                                         9.2 (2.5)        8.3(2.1)         0.95 (2.7)       8.8 (0.4)         0.34 (2.5)         0.22 (0.8)       <.001
                    Note, p < .01, cross-sectional design differs significantly from the longitudinal design in estimating the age-associated decline. If the difference is posi-
                 tive, the cross-sectional design underestimates the decline. If negative, the cross-sectional design overestimates the decline,
                    •mean (SD).
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...Journal of gerontology biological sciences copyright by the gerontological society america vol a no b comparison cross sectional and longitudinal designs in study aging upper extremity performance johanne desrosiers rejean hebert gina bravo annie rochette downloaded from https academic oup com biomedgerontology article guest on august centre de recherche en grontologie et geriatrie sherbrooke geriatric university institute qubec canada taculte me decine quebec purpose was to compare two research namely design longitudi nal context age related changes randomly recruited healthy community dwelling elderly persons evaluated with reliable valid sensori motor tests three years later survivors n were reevaluated same many sec tional comparable for estimating however some decline using underestimated observed larger than predicted withdrawal survivor biases cohort bias associated may part explain these results major used clinicians their i be patients that normal population data are both have...

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