Objectives. Sagittal alignment of the lumbosacral spine, and specifically pelvic incidence (PI), has been implicated in the development of spine pathology, but generally ignored with regards to diseases of the hip. We aimed to determine if increased PI is correlated with higher rates of hip osteoarthritis (HOA). The effect of PI on the development of knee osteoarthritis (KOA) was used as a negative control. Methods. We studied 400 well-preserved cadaveric skeletons ranging from 50 to 79 years of age at death. Each specimen’s OA of the hip and knee were graded using a previously described method. PI was measured from standardised lateral photographs of reconstructed pelvises. Multiple regression analysis was performed to determine the relationship between age and PI with HOA and KOA. Results. The mean age was 60.2 years (standard deviation (. sd. ) 8.1), and the mean PI was 46.7° (. sd. 10.7°). Multiple regression analysis demonstrated a significant correlation between increased PI and HOA (standardised beta = 0.103, p = 0.017). There was no correlation between PI and KOA (standardised beta = 0.003, p = 0.912). Conclusion. Higher PI in the younger individual may contribute to the development of HOA in later life. Cite this article: Dr J. J. Gebhart. Relationship between pelvic incidence and osteoarthritis of the hip. Bone Joint Res 2016;5:66–72. DOI: 10.1302/2046-3758.52.2000552

Many different designs of total hip arthroplasty (THA) with varying performance and cost are available. The identification of those which are the most cost-effective could allow significant cost-savings. We used an established Markov model to examine the cost effectiveness of five frequently used categories of THA which differed according to bearing surface and mode of fixation, using data from the National Joint Registry for England and Wales. Kaplan–Meier analyses of rates of revision for men and women were modelled with parametric distributions. Costs of devices were provided by the NHS Supply Chain and associated costs were taken from existing studies. Lifetime costs, lifetime quality-adjusted-life-years (QALYs) and the probability of a device being cost effective at a willingness to pay £20 000/QALY were included in the models.

The differences in QALYs between different categories of implant were extremely small (<  0.0039 QALYs for men or women over the patient’s lifetime) and differences in cost were also marginal (£2500 to £3000 in the same time period). As a result, the probability of any particular device being the most cost effective was very sensitive to small, plausible changes in quality of life estimates and cost.

Our results suggest that available evidence does not support recommending a particular device on cost effectiveness grounds alone. We would recommend that the choice of prosthesis should be determined by the rate of revision, local costs and the preferences of the surgeon and patient.

Cite this article: Bone Joint J 2015;97-B:449–57.

Aims. This study aimed to investigate the incidence of ≥ 5 mm asymmetry in lower and whole leg lengths (LLs) in patients with unilateral osteoarthritis (OA) secondary to developmental dysplasia of the hip (DDH-OA) and primary hip osteoarthritis (PHOA), and the relationship between lower and whole LL asymmetries and femoral length asymmetry. Methods. In total, 116 patients who underwent unilateral total hip arthroplasty were included in this study. Of these, 93 had DDH-OA and 23 had PHOA. Patients with DDH-OA were categorized into three groups: Crowe grade I, II/III, and IV. Anatomical femoral length, femoral length greater trochanter (GT), femoral length lesser trochanter (LT), tibial length, foot height, lower LL, and whole LL were evaluated using preoperative CT data of the whole leg in the supine position. Asymmetry was evaluated in the Crowe I, II/III, IV, and PHOA groups. Results. The incidences of whole and lower LL asymmetries were 40%, 62.5%, 66.7%, and 26.1%, and 21.7%, 20.8%, 55.6%, and 8.7% in the Crowe I, II/III, and IV, and PHOA groups, respectively. The incidence of tibial length asymmetry was significantly higher in the Crowe IV group (44.4%) than that in the PHOA group (4.4%). In all, 50% of patients with DDH-OA with femoral length GT and LT asymmetries had lower LL asymmetry, and 75% had whole LL asymmetry. The incidences of lower and whole LL asymmetries were 20% and 42.9%, respectively, even in the absence of femoral length GT and LT asymmetries. Conclusion. Overall, 43% of patients with unilateral DDH-OA without femoral length asymmetry had whole LL asymmetry of ≥ 5 mm. Thus, both the femur length and whole LL should be measured to accurately assess LL discrepancy in patients with unilateral DDH-OA. Cite this article: Bone Jt Open 2024;5(2):79–86

Aims. The aim of this study was to determine the clinical outcomes and factors contributing to failure of transposition osteotomy of the acetabulum (TOA), a type of spherical periacetabular osteotomy, for advanced osteoarthritis secondary to hip dysplasia. Methods. We reviewed patients with Tönnis grade 2 osteoarthritis secondary to hip dysplasia who underwent TOA between November 1998 and December 2019. Patient demographic details, osteotomy-related complications, and the modified Harris Hip Score (mHHS) were obtained via medical notes review. Radiological indicators of hip dysplasia were assessed using preoperative and postoperative radiographs. The cumulative probability of TOA failure (progression to Tönnis grade 3 or conversion to total hip arthroplasty) was estimated using the Kaplan-Meier product-limited method. A multivariate Cox proportional hazards model was used to identify predictors of failure. Results. This study included 127 patients (137 hips). Median follow-up period was ten years (IQR 6 to 15). The median mHHS improved from 59 (IQR 52 to 70) preoperatively to 90 (IQR 73 to 96) at the latest follow-up (p < 0.001). The survival rate was 90% (95% CI 82 to 95) at ten years, decreasing to 21% (95% CI 7 to 48) at 20 years. Fair joint congruity on preoperative hip abduction radiographs and a decreased postoperative anterior wall index (AWI) were identified as independent risk factors for failure. The survival rate for the 42 hips with good preoperative joint congruity and a postoperative AWI ≥ 0.30 was 100% at ten years, and remained at 83% (95% CI 38 to 98) at 20 years. Conclusion. Although the overall clinical outcomes of TOA in patients with advanced osteoarthritis are suboptimal, favourable results can be achieved in selected cases with good preoperative joint congruity and adequate postoperative anterior acetabular coverage. Cite this article: Bone Joint J 2024;106-B(8):783–791

Aims. The aim of this study was to determine whether total hip arthroplasty (THA) for chronic hip pain due to unilateral primary osteoarthritis (OA) has a beneficial effect on cognitive performance. Methods. A prospective cohort study was conducted with 101 patients with end-stage hip OA scheduled for THA (mean age 67.4 years (SD 9.5), 51.5% female (n = 52)). Patients were assessed at baseline as well as after three and months. Primary outcome was cognitive performance measured by d2 Test of Attention at six months, Trail Making Test (TMT), FAS-test, Rivermead Behavioural Memory Test (RBMT; story recall subtest), and Rey-Osterrieth Complex Figure Test (ROCF). The improvement of cognitive performance was analyzed using repeated measures analysis of variance. Results. At six months, there was significant improvement in attention, working speed and concentration (d2-test; p < 0.001), visual construction and visual memory (ROCF; p < 0.001), semantic memory (FAS-test; p = 0.009), verbal episodic memory (RBMT; immediate recall p = 0.023, delayed recall p = 0.026), as well as pain (p < 0.001) with small to large effect sizes. Attention, concentration, and visual as well as verbal episodic memory improved significantly with medium effect sizes over η. 2. partial. = 0.06. In these cognitive domains the within-group difference exceeded the minimum clinically important difference. Conclusion. THA is associated with clinically relevant postoperative improvement in the cognitive functions of attention, concentration, and memory. These data support the concept of a broad interaction of arthroplasty with central nervous system function. Cite this article: Bone Joint J 2022;104-B(3):331–340

Aims. The gluteus minimus (GMin) and gluteus medius (GMed) have unique structural and functional segments that may be affected to varying degrees, by end-stage osteoarthritis (OA) and normal ageing. We used data from patients with end-stage OA and matched healthy controls to 1) quantify the atrophy of the GMin and GMed in the two groups and 2) describe the distinct patterns of the fatty infiltration in the different segments of the GMin and GMed in the two groups. Methods. A total of 39 patients with end-stage OA and 12 age- and sex frequency-matched healthy controls were prospectively enrolled in the study. Fatty infiltration within the different segments of the GMin and the GMed was assessed on MRI according to the semiquantitative classification system of Goutallier and normalized cross-sectional areas were measured. Results. The GMin was smaller in the OA-group (p < 0.001) compared to the control group, but there was no group difference in the size of the GMed (p = 0.101). Higher levels of fatty infiltration were identified in the anterior segment of the GMin (p = 0.006) and the anterior (p = 0.006) and middle (p = 0.047) segments of the GMed in the OA group. All subjects in the control group had fatty infiltration of the anterior segment of the GMin, but all except one had no fatty infiltration in the entire GMed. Conclusion. End-stage OA was associated with significant atrophy of the GMin and higher levels of fatty infiltration, particularly in the anterior segments of the GMin and GMed. Minor fatty infiltration of the anterior segment of GMin appears to be a normal part of ageing. Our study has demonstrated different patterns of atrophy and fatty infiltration between patients with end-stage OA and healthy matched peers. Cite this article: Bone Jt Open 2021;2(1):40–47

Aims. Rotational acetabular osteotomy (RAO) has been reported to be effective in improving symptoms and preventing osteoarthritis (OA) progression in patients with mild to severe develomental dysplasia of the hip (DDH). However, some patients develop secondary OA even when the preoperative joint space is normal; determining who will progress to OA is difficult. We evaluated whether the preoperative cartilage condition may predict OA progression following surgery using T2 mapping MRI. Methods. We reviewed 61 hips with early-stage OA in 61 patients who underwent RAO for DDH. They underwent preoperative and five-year postoperative radiological analysis of the hip. Those with a joint space narrowing of more than 1 mm were considered to have 'OA progression'. Preoperative assessment of articular cartilage was also performed using 3T MRI with the T2 mapping technique. The region of interest was defined as the weightbearing portion of the acetabulum and femoral head. Results. There were 16 patients with postoperative OA progression. The T2 values of the centre to the anterolateral region of the acetabulum and femoral head in the OA progression cases were significantly higher than those in patients without OA progression. The preoperative T2 values in those regions were positively correlated with the narrowed joint space width. The receiver operating characteristic analysis revealed that the T2 value of the central portion in the acetabulum provided excellent discrimination, with OA progression patients having an area under the curve of 0.858. Furthermore, logistic regression analysis showed T2 values of the centre to the acetabulum’s anterolateral portion as independent predictors of subsequent OA progression (p < 0.001). Conclusion. This was the first study to evaluate the relationship between intra-articular degeneration using T2 mapping MRI and postoperative OA progression. Our findings suggest that preoperative T2 values of the hip can be better prognostic factors for OA progression than radiological measures following RAO. Cite this article: Bone Joint J 2021;103-B(9):1472–1478

Although the association between femoroacetabular impingement and osteoarthritis is established, it is not yet clear which hips have the greatest likelihood to progress rapidly to end-stage disease. We investigated the effect of several radiological parameters, each indicative of a structural aspect of the hip joint, on the progression of osteoarthritis. Pairs of plain anteroposterior pelvic radiographs, taken at least ten years apart, of 43 patients (43 hips) with a pistol-grip deformity of the femur and mild (Tönnis grade 1) or moderate (Tönnis grade 2) osteoarthritis were reviewed. Of the 43 hips, 28 showed evidence of progression of osteoarthritis. There was no significant difference in the prevalence of progression between hips with initial Tönnis grade 1 or grade 2 osteoarthritis (p = 0.31). Comparison of the hips with and without progression of arthritis revealed a significant difference in the mean medial proximal femoral angle (81° vs 87°, p = 0.004) and the presence of the posterior wall sign (39% vs 7%, p = 0.02) only. A logistic regression model was constructed to predict the influence of these two variables in the development of osteoarthritis. Mild to moderate osteoarthritis in hips with a pistol-grip deformity will not progress rapidly in all patients. In one-third, progression will take more than ten years to manifest, if ever. The individual geometry of the proximal femur and acetabulum partly influences this phenomenon. A hip with cam impingement is not always destined for end-stage arthritic degeneration

Aims. The modified Dunn procedure has the potential to restore the anatomy in hips with severe slipped capital femoral epiphyses (SCFE). However, there is a risk of developing avascular necrosis of the femoral head (AVN). In this paper, we report on clinical outcome, radiological outcome, AVN rate and complications, and the cumulative survivorship at long-term follow-up in patients undergoing the modified Dunn procedure for severe SCFE. Patients and Methods. We performed a retrospective analysis involving 46 hips in 46 patients treated with a modified Dunn procedure for severe SCFE (slip angle > 60°) between 1999 and 2016. At nine-year-follow-up, 40 hips were available for clinical and radiological examination. Mean preoperative age was 13 years, and 14 hips (30%) presented with unstable slips. Mean preoperative slip angle was 64°. Kaplan–Meier survivorship was calculated. Results. At the latest follow-up, the mean Merle d’Aubigné and Postel score was 17 points (14 to 18), mean modified Harris Hip Score was 94 points (66 to 100), and mean Hip Disability and Osteoarthritis Outcome Score was 91 points (67 to 100). Postoperative slip angle was 7° (1° to 16°). One hip (2%) had progression of osteoarthritis (OA). Two hips (5%) developed AVN of the femoral head and required further surgery. Three other hips (7%) underwent implant revision due to screw breakage or change of wires. Cumulative survivorship was 86% at ten-year follow-up. Conclusion. The modified Dunn procedure for severe SCFE resulted in a low rate of AVN, low risk of progression to OA, and high functional scores at long-term follow-up. The slip deformities were mainly corrected but secondary impingement deformities can develop in some hips and may require further surgical treatment. Cite this article: Bone Joint J 2019;101-B:403–414

Aims. Recently, there has been considerable interest in quantifying the associations between bony abnormalities around and in the hip joint and osteoarthritis (OA). Our aim was to investigate the relationships between acetabular undercoverage, acetabular overcoverage, and femoroacetabular impingement (FAI) with OA of the hip, which currently remain controversial. . Materials and Methods. A total of 545 cadaveric skeletons (1090 hips) from the Hamann-Todd osteological collection were obtained. Femoral head volume (FHV), acetabular volume (AV), the FHV/AV ratio, acetabular version, alpha angle and anterior femoral neck offset (AFNO) were measured. A validated grading system was used to quantify OA of the hip as minimal, moderate, or severe. Multiple linear and multinomial logistic regression were used to determine the factors that correlated independently with the FHV, AV, and the FHV/AV ratio. . Results. Female cadavers had smaller FHVs (standardised beta -0.382, p < 0.001), and AVs (standardised beta -0.351, p < 0.001), compared with male patients, although the FHV/AV ratio was unchanged. Every 1° increase in alpha angle increased the probability of having moderate OA of the hip compared with minimal OA by 7.1%. Every 1 mm decrease in AFNO increased the probability of having severe or moderate OA of the hip, compared with minimal OA, by 11% and 9%, respectively. The relative risk ratios of having severe OA of the hip compared with minimal OA were 7.2 and 3.3 times greater for acetabular undercoverage and overcoverage, respectively, relative to normal acetabular cover. . Conclusion . Acetabular undercoverage and overcoverage were independent predictors of increased OA of the hip. The alpha angle and AFNO had modest effects, supporting the hypothesis that bony abnormalities both in acetabular dysplasia and FAI are associated with severe OA. Cite this article: Bone Joint J 2017;99-B:432–9

Objectives. The purpose of this study was to assess N-acetyl aspartate changes in the thalamus in patients with osteoarthritis of the hip using proton magnetic resonance spectroscopy. Methods. Nine patients with osteoarthritis of the hip (symptomatic group, nine women; mean age 61.4 years (48 to 78)) and nine healthy volunteers (control group, six men, three women; mean age 30.0 years (26 to 38)) underwent proton magnetic resonance spectroscopy to assess the changes of N-acetyl aspartate in the thalamus. . Results. The ratio of N-acetyl aspartate to creatine plus phosphocreatine in the thalamus contralateral to the symptomatic hip in patients with osteoarthritis of the hip was significantly lower than the ratio of N-acetyl aspartate to creatine plus phosphocreatine in the thalamus in the control group (1.611 (1.194 to 1.882) vs 1.355 (1.043 to 1.502), p < 0.001). And, a strong negative correlation was detected between the ratio of N-acetyl aspartate to creatine plus phosphocreatine in the thalamus contralateral to the symptomatic hip in patients with osteoarthritis of the hip and pain duration (r = -0.83, p = 0.018). Conclusions. We evaluated the ratio of N-acetyl aspartate to creatine plus phosphocreatine in the thalamus of patients with osteoarthritis of the hip by using proton magnetic resonance spectroscopy. We concluded that the ratio of N-acetyl aspartate to creatine plus phosphocreatine in the thalamus contralateral to the symptomatic hip in patients with osteoarthritis of the hip were significantly lower than those in the thalamus of the control group, and that pain duration was strongly related to the decrease of the ratio of N-acetyl aspartate to creatine plus phosphocreatine

Excessive acetabular cover secondary to a retroverted acetabulum causes pincer impingement, which may cause early osteoarthritis of the hip. Our aim was to determine if there was a relationship between acetabular version and osteoarthritis of the hip. Using image processing and analysis software we studied 117 CT images of the hip in patients aged less than 65 years who had undergone a CT virtual colonoscopy. The mean CT joint space of the 18 hips with acetabular retroversion was narrower compared with the 99 hips with normal acetabular alignment (p < 0.0001). A correlation of r = 0.46 (p < 0.01) was found between right hip acetabular version and the mean right hip joint space and of r = 0.31 (p = 0.02) between left hip acetabular version and the mean left hip joint space. Acetabular retroversion is associated with radiological evidence of osteoarthritis of the hip. An understanding of the mechanical basis of osteoarthritis of the hip allows early treatment of the underlying structural abnormality and prevents progression of the degenerative condition

We evaluated the short-term of 0 to 90 days and the longer term, up to 12.7 years, mortality for patients undergoing primary total hip replacement (THR) in Denmark in comparison to the general population. Through the Danish Hip Arthroplasty Registry we identified all primary THRs undertaken for osteoarthritis between 1 January 1995 and 31 December 2006. Each patient (n = 44 558) was matched at the time of surgery with three people from the general population (n = 133 674). We estimated mortality rates and mortality rate ratios with 95% confidence intervals for THR patients compared with the general population. There was a one-month period of increased mortality immediately after surgery among THR patients, but overall short-term mortality (0 to 90 days) was significantly lower (mortality rate ratio 0.8; 95% confidence interval 0.7 to 0.9). However, THR surgery was associated with increased short-term mortality in subjects under 60 years old, and among THR patients without comorbidity. Long-term mortality was lower among THR patients than in controls (mortality rate ratio 0.7; 95% confidence interval 0.7 to 0.7). Overall, THR was associated with lower short- and long-term mortality among patients with osteoarthritis. Younger patients and patients without comorbidity before surgery may also experience increased mortality after THR surgery, although the absolute risk of death is small

There have been several studies examining the association between the morphological characteristics seen in acetabular dysplasia and the incidence of the osteoarthritis (OA). However, most studies focus mainly on acetabular morphological analysis, and few studies have scrutinised the effect of femoral morphology. In this study we enrolled 36 patients with bilateral acetabular dysplasia and early or mid-stage OA in one hip and no OA in the contralateral hip. CT scans were performed from the iliac crest to 2 cm inferior to the tibial tuberosity, and the morphological characteristics of both acetabulum and femur were studied. . In addition, 200 hips in 100 healthy volunteer Chinese adults formed a control group. The results showed that the dysplastic group with OA had a significantly larger femoral neck anteversion and a significantly shorter abductor lever arm than both the dysplastic group without OA and the controls. Femoral neck anteversion had a significant negative correlation with the length of the abductor lever arm and we conclude that it may contribute to the development of OA in dysplastic hips. Cite this article: Bone Joint J 2014; 96-B:1586–93

We retrospectively examined the long-term outcome of 96 asymptomatic hips in 96 patients with a mean age of 49.3 years (16 to 65) who had radiological evidence of femoroacetabular impingement. When surveillance commenced there were 17, 34, and 45 hips with cam, pincer, and mixed impingement, respectively. Overall, 79 hips (82.3%) remained free of osteoarthritis for a mean of 18.5 years (10 to 40). In contrast, 17 hips (17.7%) developed osteoarthritis at a mean of 12 years (2 to 28). No statistically significant difference was found in the rates of development of osteoarthritis among the three groups (p = 0.43). Regression analysis showed that only the presence of idiopathic osteoarthritis of the contralateral diseased hip was predictive of development of osteoarthritis on the asymptomatic side (p = 0.039). We conclude that a substantial proportion of hips with femoroacetabular impingement may not develop osteoarthritis in the long-term. Accordingly, in the absence of symptoms, prophylactic surgical treatment is not warranted

Using radiography and computer tomography (CT) we studied the morphology of 83 hips in 69 Caucasian adults with osteoarthritis secondary to developmental dysplasia of the hip (DDH). A previously published series of 310 hips with primary osteoarthritis was used as a control group. According to the Crowe classification, 33 of the dysplastic hips were graded as class I, 27 as class II and 23 as class III or class IV. The intramedullary femoral canal had reduced mediolateral and anteroposterior dimensions in all groups compared with the control group. Only in Crowe class II hips was the femoral neck-shaft angle increased. The proximal femur had more anteversion in all the developmental dysplasia of the hip groups, ranging from 2° to 80°. Templated measurement of acetabular dimensions for plain radiography closely matched measurements taken by CT. The results of our study confirm the observations previously confined to the Japanese population

We compared 55 consecutive total hip replacements performed on 53 morbidly obese patients with osteoarthritis with a matched group of 55 total hip replacements in 53 non-obese patients. The groups were matched for age, gender, prosthesis type, laterality and preoperative Harris Hip Score. They were followed prospectively for five years and the outcomes were assessed using the Harris Hip Score, the Short-form 36 score and radiological findings. Survival at five years using revision surgery as an endpoint, was 90.9% (95% confidence interval 82.9 to 98.9) for the morbidly obese and 100% for the non-obese patients. The Harris Hip and the Short-form 36 scores were significantly better in the non-obese group (p < 0.001). The morbidly obese patients had a higher rate of complications (22% vs 5%, p = 0.012), which included dislocation and both superficial and deep infection. In light of these inferior results, morbidly obese patients should be advised to lose weight before undergoing a total hip replacement, and counselled regarding the complications. Despite these poorer results, however, the patients have improved function and quality of life

We evaluated the long-term results of 116 total hip replacements with a superolateral shelfplasty in 102 patients with osteoarthritis secondary to developmental dysplasia of the hip. After a mean follow-up of 19.5 years (11.5 to 26.0), 14 acetabular components (12%) had been revised. The cumulative survival at 20 years was 78%, with revision for loosening of the acetabular component as the end-point. All grafts were well integrated and showed remodelling. In six grafts some resorption had occurred under the heads of the screws where the graft was not supporting the socket. Apart from these 14 revisions, seven acetabular components had possible radiological signs of loosening at a mean follow-up of 14.5 years, one had signs of probable loosening, and five had signs of definite loosening. These results indicate that this technique of bone grafting for acetabular reconstruction in hip dysplasia is a durable solution for cemented acetabular components

We carried out radial MRI in 30 hips with moderate osteoarthritis and in ten normal hips. On a scout view containing the entire acetabular rim, 12 vertical radial slices were set at 15° intervals. Different appearances were observed in different parts of the joint. In the weight-bearing portion, from 45° anterosuperior to 45° posterosuperior, ‘attenuation’ (n = 16) and ‘disappearance’ (n = 25) were observed as abnormalities of the labrum with ‘capsular stripping’ (n = 29) and ‘extraosseous high signal lesion’ (n = 27) as capsular abnormalities, seen more often in the anterosuperior portion. In all 12 planes there were osteophytes on the acetabular edge (n = 24), femoral head (n = 22) and/or at the central acetabulum (n = 6), a bone cyst on the acetabulum (n = 18) and/or the femoral head (n = 9), irregularity of the articular cartilage (n = 30), and an effusion (n = 28). Our findings indicate that radial MRI may be a useful non-invasive diagnostic method for demonstrating pathology in moderate osteoarthritis of the hip

We measured the plasma 25-hydroxyvitamin D. 3. (25(OH)D. 3. ) levels in 62 consecutive Caucasian patients undergoing total hip replacement for osteoarthritis. The patients were divided into two groups based on whether they were vitamin D sufficient or deficient. The groups were matched for age, gender and the American Society of Anaesthesiologists (ASA) grade. The prevalence of vitamin D deficiency in our patients was comparable with recent population-based studies performed in the United Kingdom. Patients with vitamin D deficiency had lower pre-operative Harris hip scores (Mann-Whitney test, p = 0.018) and were significantly less likely to attain an excellent outcome from total hip replacement (chi-squared test, p = 0.038). Vitamin D levels were found to positively correlate with both pre- and post-operative Harris hip scores. These results warrant further study of vitamin D deficiency in patients undergoing joint replacement as it is a risk factor for a suboptimal outcome which is relatively simple and cheap to correct