nonsteroidal anti - inflammatory drugs ( nsaids ) are the first - line treatment for osteoarthritis   and a cornerstone of pharmacologic management of other arthritic and rheumatologic illnesses . the dichotomous classification of patients into responders and nonresponders to nsaids began in the 1970s . walker et al . provided evidence of the validity of the responder / nonresponder thesis in rheumatoid arthritis and osteoarthritis . both the american college of rheumatology ( acr ) and the european league against rheumatism ( eular ) have developed response criteria for rheumatoid arthritis . eular response criteria are based on the multi - item disease activity score 28 ( das28 ) . a composite index of patient - reported pain , physical function , and global assessment appears to be as good as the entire acr core set or the das28 for determining response to treatment in clinical trials of rheumatoid arthritis . the most recent definition of response to nsaid treatment in osteoarthritis was determined by a joint task force comprising members of the outcome measures in rheumatology ( omeract ) committee and the osteoarthritis research society international ( oarsi ) . in the omeract - oarsi guidelines , response is a binary , composite endpoint based on three patient - reported core outcome measures : pain , physical function , and the patient global assessment . of these three , pain is considered the primary outcome measure of interest . in clinical trials , definitions of the effectiveness of analgesic therapies for arthritic pain are focused on response to treatment . in clinical practice , however , decisions to change the analgesic dose or drug for an individual patient are based on nonresponse to the existing treatment . we sought to develop a working definition of nonresponse to analgesic treatment , focusing on the measurement of pain with the 0100  mm visual analog scale ( vas ) . we posited that nonresponse could be measured in terms of ( i ) the smallest amount of change on the pain vas that can be reliably measured or ( ii ) the smallest change that the patients report as important . the first of these concepts , the smallest amount of change that can be reliably measured , is reported in the literature as either the smallest detectable difference ( sdd ) or the minimal detectable change ( mdc ) . searches were carried out for randomized clinical trials ( rcts ) of patient - reported measurement of chronic pain in arthritis . articles known to the authors were supplemented by searches of pubmed performed in june 2010 with the following algorithms : reliability and pain and vas ; * arthritis and  drug resistance  [ mesh terms ] and  anti - inflammatory agents , nonsteroidal  [ mesh terms ] and  humans  [ mesh terms ] ; nsaid - refractory ; nsaid * and ( non - respon * or nonrespon * ) ; refractory [ title word ] and osteoarthritis [ title word ] ; refractoriness [ title word ] and concept . articles were screened for those reporting parameters of the english 0100  mm pain vas : the sdd , the mcid , or the reliability , from which the mdc can be calculated . the sdd on a measurement scale is that amount of difference for which anything smaller can not be reliably distinguished from random error in the measurement . the first is the limits of agreement method , and the term sdd is usually used when the parameter is calculated by this method . the sdd is applicable to longitudinal data , and thus the limits of agreement method is often used to assess agreement between test and retest scores [ 12 , 13 ] . the mean difference between test and retest scores and its sd are calculated , and the sdd is the 95% confidence interval ( ci ) of the difference , that is , 1.96 times the sd of the difference between scores . the sdd reported in three rcts of rheumatoid arthritis , given as negative change or improvement , was 18.6 , 19.0 , and 20.0 ( table 1 ) . sdds of this magnitude constitute half or more of the mean baseline pain score in vas units , suggesting that a very large change in pain status is required before that change is detectable . the second method for calculating the sdd is from the standard error of the measurement ( sem ) [ 15 , 16 ] , and , when calculated in this way , it is usually termed the mdc ( it is also referred to as the  smallest real difference    and the  tolerance interval  ) . the sem is a function of the standard deviation ( sd ) of the study sample and the reliability of the measurement instrument . the reliability coefficient ( rc ) may be the test - retest reliability or an intraclass correlation coefficient . the sem is derived from the sd and the rc as follows : sem = sd(1-rc ) . hence , we calculated it for rcts reporting mean ( sd ) values from the pain vas . six rcts of rheumatoid arthritis patients ( the three in table 1 and three additional publications ) reported rcs of 0.74 , 0.75 , 0.88 , 0.88 , 0.94 , and 0.94 . we calculated the mdc for rheumatoid arthritis [ 10 , 11 , 20 , 21 , 23 , 24 ] and osteoarthritis [ 2530 ] rcts reporting mean pain vas score at baseline using three arbitrary rc values ( 0.75 , 0.85 , and 0.95 ) spanning the range found in the literature . as expected based on the above formulas , the mdc was smaller ( i.e. , a more precise measurement could be obtained ) for higher values of rc ( figure 1 ) . for example , in osteoarthritis , the median mdcs were 10.7 , 18.6 , and 24.0 for rcs of 0.95 , 0.85 , and 0.75 , respectively . in addition , the data appear to indicate a trend toward smaller mdcs at higher baseline pain scores ( figure 1 ) . by linear regression analysis , the slope of the line through all the data points ( osteoarthritis and rheumatoid arthritis ) with rc = 0.85 ( 0.28 ) was statistically significant at p = 0.005 ( as were the slopes at the other two rc values ) . this finding suggests that , when the patient 's pain is greater , the instrument can reliably detect smaller differences in pain . for a given rc , ( the median mdcs for rheumatoid arthritis were 15.8 , 27.3 , and 35.3 for rcs of 0.95 , 0.85 , and 0.75 , resp . ) linear regression analyses of rheumatoid arthritis and osteoarthritis trials as separate groups did not produce statistically significant correlations between baseline pain and mdc . rather than mdc being inversely correlated with baseline pain score , the data may be interpreted as a difference between osteoarthritis and rheumatoid arthritis , combined with the fact that the rheumatoid arthritis trials assessed here included patients with lower baseline pain scores than the patients in the osteoarthritis trials . distinct from the concepts of sdd and mdc is that of the minimal clinically important difference ( mcid ) . defined the mcid as  the smallest difference in score in the domain of interest which patients perceive as beneficial and which would mandate  a change in the patient 's management  . the measurement of the mcid for a scale requires a reference standard ( or  external criterion  ; also referred to as an  anchor  ) frequently the patient global assessment ( pga ) of treatment effect . the four rcts reporting the mcid on the pain vas used the pga as an anchor ( table 2 ) . although the mcid values for improvement reported in these rcts fall within a relatively narrow range ( 11.1 to 19.9 ) , there was no consensus on the definition of the mcid ( table 2 ) . for the purposes of this paper , the mcid is expressed as the amount of change on the pain vas corresponding to a specific degree of change on the pga . assessed only the improvement aspect of the mcid and defined the minimal clinically important improvement ( mcii ) as the minimum improvement ( on the pain vas ) reported by 75% of osteoarthritis patients who ranked their response as  good  on the pga . by this definition , the mcii was 15.3 for hip osteoarthritis and 19.9 for knee osteoarthritis ( table 2 ) . the mcid for osteoarthritis pain was also investigated in terms of the  minimal perceptible clinical improvement  ( mpci ) . this parameter was defined as the change in the pain vas score corresponding to a change from none  to  poor  in the pga , and the reported value was 11.1 . to achieve a direct comparison between the mpci and the mcii described above , we examined the 75th percentile of patients with a pga of  good  in ehrich et al .   and found that they had a minimum change of approximately 33 on the pain vas , a much larger change than that reported by tubach et al . . pope et al . anchored the pain score in a patient - reported overall assessment of disease status . their study and another on back pain   assessed the mcid for both improvement and worsening , and both rcts found that the mcid was larger for improvement than for worsening : 11.8 versus + 6.8 in the ra study and 18 versus + 8 in the back pain study ( table 2 ) . the mcid on the pain vas is not a fixed value ; it depends to some extent on the baseline pain score . to investigate this idea , tubach et al . when knee osteoarthritis patients were categorized according to their baseline pain scores , the mciis were 11 , 27 , and 37 units for the lowest , middle , and highest tertiles , respectively . for hip osteoarthritis patients , the study of back pain also reported mcids according to baseline pain score . in this study , baseline pain scores were divided into three categories : mean minus 2*sd , mean , and mean plus 2*sd , corresponding to scores of 35 , 64 , and 93 , respectively . these scores fit the tertiles described by tubach et al . as shown in figure 2 , the mcids for improvement in each tertile were 9 , 19 , and 29 , respectively . the mcid of 11.9 reported by pope et al .   at a mean baseline score of 42.3 also fits in well with the data in figure 2 . two of the sdds reported in the literature ( 18.6 and 19.0 ; table 1 ) fit well onto the graph of mdc values in figure 1 ( not shown ) . the corresponding rcs of 0.88   and 0.94 , respectively , may explain why the sdds fall squarely between the overall median values of mdc at rc = 0.95 ( 14.7 ) and rc = 0.85 ( 25.4 ) on the graph . the third sdd ( 20 ) , which had an rc of 0.75 , did not fit the graph for that mdc data set . the calculated values of mdc decreased with increasing baseline pain score , suggesting that small differences in pain can be measured more precisely at higher levels of pain . the mdc is a function of the sd of the mean group - level pain score . is the sd for patient - reported pain actually smaller at higher levels of pain ? according to these data , yes . linear regression analyses of the sd versus the baseline pain score yielded a statistically significant slope ( 0.26 ; p = 0.005 ) for the combined data set , but statistically nonsignificant slopes when osteoarthritis and rheumatoid arthritis were analyzed separately . there was also no linear relationship between the rc ( the other variable on which mdc depends ) and the baseline pain . we interpret this to mean that the relationship between the mdc and baseline pain is an inherent characteristic of the pain vas rather than a byproduct of physiologically different disease states or the statistical reliability of the scale . the trend of the mcid is opposite that of the mdc  it is larger at higher baseline pain levels . thus it appears that , although small differences in pain are reliably detectable in patients with severe pain , these patients require a larger amount of pain relief in order to report being satisfied with the change they experience . in the context of figure 2 , a patient with severe pain ( score > 65 ) needs a change to the moderate pain category ( 5065 ) to view it as clinically important .   the relationship between mcid and baseline severity may apply to other measures in addition to the pain vas . the rcts included in our analysis often reported physical function and pga as well and in tubach et al . , for instance , the mcid for both the womac physical function score and the pga increased with increasing baseline scores . future analyses should investigate the relationship between baseline pain and these other measures of patient response . the omeract - oarsi criteria for response to treatment include both absolute and relative changes on the pain vas . as described by pham et al . , a responder experiences either ( i ) 50% improvement on the pain vas , defined as at least 20  units , or ( ii ) 20% improvement , defined as at least 10  units , in combination with above - threshold improvements on at least one other measure of patient response , that is , physical function or the pga . the acr criteria have a similar definition of response , graded by percentage improvements ( 20% , 50% , and 70% ) in tender and swollen joint counts and 3 of the 5 other outcome measures ( of which pain is one ) . however , the acr20 , acr50 , and acr70 response levels are not linked to absolute unit improvements on the pain vas . the question is whether the pain vas is sensitive enough to detect the amount of change required for a definition of  response ' under either set of criteria . at rc = 0.85 , the median mdc on the pain vas is 25.4  units ( for osteoarthritis and rheumatoid arthritis combined ) , which is greater than the minimum of 1020  units required to be considered a responder in the omeract - oarsi criteria . as a percentage of the baseline pain , the median mdc is 46.1% ( at rc = 0.85 ) , which is within the threshold of improvement required for a response by definition ( i ) above , but outside the range required in definition ( ii ) . similarly , the sdds in patients with ra , as shown in table 1 ( 48% , 49% , and 76% ) , indicate that the smallest detectable change in pain is greater than the minimum amount considered necessary for a definition of  response  by both sets of criteria . the median values of mcid for each tertile in figure 2 are 9 , 24 , and 30  units overall and 9 , 25.5 , and 33.5  units for osteoarthritis only . whether the results are combined or osteoarthritis is considered separately , only patients attaining the mcid in the middle and highest tertiles can be classified as responders by the omeract - oarsi criteria . those in the lowest tertile might perceive an improvement in their pain as clinically important but still be classified as a nonresponder . taking the midpoint of each tertile in figure 2 as the baseline pain score and the overall median value of mcid of each tertile as the true mcid , the relative values of mcid are 22.5% , 47.0% , and 36.4% for baseline pain scores of 3049 , 5065 , and > 65 . thus the mcid for each tertile is less than the amount required for a response by omeract - oarsi definition ( i ) mentioned before . we have shown that the smallest decrease in pain that can be reliably measured , the mdc , is smaller than the mcid for scores of > 65 on the 0100  pain vas , but not for scores of < 50 . improvements in the middle of the pain vas may or may not be measurable depending on the type of pain , the baseline score , and the rc of the pain vas . we conclude that , for baseline pain scores above 65 , nonresponse can be defined as any change on the pain vas that is smaller than the mcid . for patients with scores below 65 , a change less than the mdc can be considered nonresponse ; however , improvements that are greater than the mdc but not considered clinically important by the patient may also justify a change in therapy .
our objective was to develop a working definition of nonresponse to analgesic treatment of arthritis , focusing on the measurement of pain on the 0100  mm pain visual analog scale ( vas ) . 
 we reviewed the literature to assess the smallest detectable difference ( sdd ) , the minimal detectable change ( mdc ) , and the minimal clinically important difference ( mcid ) . 
 the sdd for improvement reported in three studies of rheumatoid arthritis was 18.6 , 19.0 , and 20.0 . 
 the median mdc was 25.4 for 7 studies of osteoarthritis and 5 studies of rheumatoid arthritis ( calculated for a reliability coefficient of 0.85 ) . 
 the mcid increased with increasing baseline pain score . for baseline vas tertiles defined by scores of 3049 , 5065 , and > 65 , 
 the mcid for improvement was , respectively , 711 units , 1927 units , and 2937 units . 
 nonresponse can thus be defined in terms of the mdc for low baseline pain scores and in terms of the mcid for high baseline scores .