Analysis of case-control studies of screening: impact of misspecifying the duration of detectable preclinical pathologic changes

Exposure Definition in Case-Control Studies of Cervical Cancer Screening: A Systematic Literature Review

The first step in evaluating the effectiveness of cervical screening is defining exposure to screening. Our aim was to describe the spectrum of screening exposure definitions used in studies of the effectiveness of cervical screening. This systematic review included case-control studies in a population-based screening setting. Outcome was incidence of cervical cancer. Three electronic databases were searched from January 1, 2012 to December 6, 2018. Articles prior to 2012 were identified from a previous review. The qualitative synthesis focused on describing screening exposure definitions reported in the literature and the methodologic differences that could have an impact on the association between screening and cervical cancer. Forty-one case-control studies were included. Six screening exposure definitions were identified. Cervical cancer risk on average decreased by 66% when screening exposure was defined as ever tested, by 77% by time since last negative test, and by 79% after two or more previous tests. Methodologic differences included composition of the reference group and whether diagnostic and/or symptomatic tests were excluded from the analysis. Consensus guidelines to standardize exposure definitions are needed to ensure evaluations of cervical cancer screening can accurately measure the impact of transitioning from cytology to human papillomavirus-based screening and to allow comparisons between programs.

Screening is associated with a lower risk of hepatocellular carcinoma-related mortality in patients with chronic hepatitis B

BACKGROUND & AIMS

Patients with chronic hepatitis B (CHB) infection routinely undergo screening for hepatocellular carcinoma (HCC), but the efficacy of screening remains unclear. We aimed to evaluate the impact of screening with ultrasound and/or serum alpha-fetoprotein (AFP) on HCC-related mortality in patients with CHB.

METHODS

We performed a matched case-control study of patients with CHB receiving care through the Veterans Affairs (VA) health administration. Cases were patients who died of HCC between 01/01/2004 and 12/31/2017, while controls were patients with CHB who did not die of HCC. Cases were matched to controls by CHB diagnosis date, age, sex, race/ethnicity, cirrhosis, antiviral therapy exposure, hepatitis B e antigen status, and viral load. We identified screening ultrasound and AFPs obtained in the 4 years preceding HCC diagnosis in cases and the equivalent index date in controls. Using conditional logistic regression, we compared cases and controls with respect to receipt of screening. A lower likelihood of screening in cases corresponds to an association between screening and reduced risk of HCC-related mortality.

RESULTS

We identified 169 cases, matched to 169 controls. Fewer cases than controls underwent screening with either screening modality (33.7% vs. 58.6%) or both modalities (19.5% vs. 34.4%). In multivariable conditional logistic regression, screening with either modality was associated with a lower risk of HCC-related mortality (adjusted odds ratio [aOR] 0.21, 95% CI 0.09-0.50), as was screening with both modalities (aOR of 0.13; 95% CI 0.04-0.43).

CONCLUSIONS

HCC screening was associated with a substantial reduction in HCC-related mortality in VA patients with CHB.

LAY SUMMARY

Patients with hepatitis B infection have a high risk of developing liver cancer. It is therefore recommended that they undergo frequent screening for liver cancer, but whether this leads to a lower risk of dying from liver cancer is not clear. In this study, we show that liver cancer screening is associated with a reduction in the mortality from liver cancer in patients with hepatitis B infection.

Case-Control Studies of the Efficacy of Screening Tests That Seek to Prevent Cancer Incidence: Results of an Approach That Utilizes Administrative Claims Data That Do Not Provide Information Regarding Test Indication

Case-control studies evaluating a screening test's efficacy in reducing cancer mortality require accurate classification of test indication to obtain a valid result. However, for analogous studies of cancer incidence, determination of test indication is not as critical because, to define exposure, we need consider only tests that can identify precursor lesions whose treatment might prevent cancer, not tests leading to cancer diagnosis. This study utilizes US Surveillance, Epidemiology, and End Results (SEER)-Medicare data, which do not include information about colonoscopy indication, to evaluate the efficacy of colonoscopy in preventing colorectal cancer (CRC) incidence. Cases were Medicare enrollees diagnosed with CRC between 1996 and 2013; up to 3 controls were matched to each case. Colonoscopy receipt prior to presumed onset of occult cancer was associated with an approximately 60% reduction in CRC incidence (odds ratio = 0.41, 95% confidence interval: 0.40, 0.42). The association was robust to differing exposure windows and estimates of occult cancer duration and is similar to those from CRC incidence studies in which exam indication was available. Our results suggest that, when it is impractical/impossible to determine whether tests were conducted for screening, the efficacy of a test in preventing cancer incidence can still be estimated using a case-control study design.

No Association Between Screening for Hepatocellular Carcinoma and Reduced Cancer-Related Mortality in Patients With Cirrhosis

BACKGROUND & AIMS

Screening patients with cirrhosis for hepatocellular carcinoma (HCC) has been recommended. We conducted a matched case-control study within the US Veterans Affairs (VA) health care system to determine whether screening by abdominal ultrasonography (USS) and/or by measuring serum level of α-fetoprotein (AFP) was associated with decreased cancer-related mortality in patients with cirrhosis.

METHODS

We defined cases (n = 238) as patients with cirrhosis who died of HCC from January 1, 2013 through August 31, 2015 and had been in VA care with a diagnosis of cirrhosis for at least 4 years before the diagnosis of HCC. We matched each case to 1 control (n = 238), defined as a patient with cirrhosis who did not die of HCC and had been in VA care for at least 4 years before the date of the matched case's HCC diagnosis. Controls were matched to cases by year of cirrhosis diagnosis, race and ethnicity, age, sex, etiology of cirrhosis, Model for End-Stage Liver Disease score, and VA medical center. We identified all USS and serum AFP tests performed within 4 years before the date of HCC diagnosis in cases or the equivalent index date in controls and determined by chart extraction (blinded to case or control status) whether these tests were performed for screening.

RESULTS

There were no significant differences between cases and controls in the proportions of patients who underwent screening USS (52.9% vs 54.2%), screening measurement of serum AFP (74.8% vs 73.5%), screening USS or measurement of serum AFP (81.1% vs 79.4%), or screening USS and measurement of serum AFP (46.6% vs 48.3%) within 4 years before the index date, with or without adjusting for potential confounders. There also was no difference in receipt of these screening tests within 1, 2, or 3 years before the index date.

CONCLUSIONS

In a matched case-control study of the VA health care system, we found that screening patients with cirrhosis for HCC by USS, measurement of serum AFP, either test, or both tests was not associated with decreased HCC-related mortality. We encourage additional case-control studies to evaluate the efficacy of screening for HCC in other health care systems, in which available records are sufficiently detailed to enable identification of the indication for USS and AFP tests.

Annual surveillance mammography after early-stage breast cancer and breast cancer mortality

BACKGROUND

After treatment for early-stage breast cancer (bca), annual surveillance mammography (asm) is recommended based on the assumption that early detection of an invasive ipsilateral breast tumour recurrence or subsequent invasive contralateral primary bca reduces bca mortality.

METHODS

We studied women with unilateral early-stage bca treated by breast-conserving surgery from 1994 to 1997 who subsequently developed an ipsilateral recurrence or contralateral primary more than 24 months after initial diagnosis, without prior regional or distant metastases. Annual surveillance mammography was defined as 2 episodes of bilateral mammography 11-18 months apart during the 2 years preceding the ipsilateral recurrence or contralateral primary. The association between asm and bca death was evaluated using a Cox proportional hazards model.

RESULTS

We identified 669 women who experienced invasive ipsilateral recurrence (n = 455) or a contralateral primary (n = 214) at a median interval of 53 months [interquartile range (iqr): 37-72 months] after initial diagnosis, 64.7% of whom had received asm during the preceding 2 years. The median interval between the 2 bilateral mammograms was 12.3 months (iqr: 11.9-13.0 months), and the median interval between the 2nd mammogram and histopathologic confirmation of ipsilateral recurrence or contralateral primary was 1.5 months (iqr: 0.8-3.9 months). Median followup after ipsilateral recurrence or contralateral primary was 7.76 years (iqr: 3.68-9.81 years). The adjusted hazard ratio for bca death associated with asm was 0.86 (95% confidence limits: 0.63, 1.16).

CONCLUSIONS

Annual surveillance mammography was associated with a modestly lowered hazard ratio for bca death.

Cervical cancer incidence in British Columbia: Predicting effects of changes from Pap to human papillomavirus screening and of changes in screening participation

Objectives To estimate the impact of increased participation in screening, and of the proposed change from Pap to human papillomavirus screening on the incidence of cervical cancer in British Columbia. Methods For invasive cervical cancer cases diagnosed in British Columbia between 2002 and 2011, data were extracted on age and cancer morphology from the British Columbia Cancer Registry, and Pap screening history was obtained from the British Columbia Cervical Cancer Screening Program database. Only screening performed two to seven years prior to diagnosis was assumed to reduce subsequent risk of cancer. Results from randomized trials of human papillomavirus versus cytology screening and population based estimates of cytology screening were used to estimate the effect of a change in screening test and increases in participation. Results Between 2002 and 2011, there were 1663 cases of cervical cancer reported; 660 (367 squamous and 293 non-squamous) were eligible and screened two to seven years prior to diagnosis. The predicted reduction by changing to human papillomavirus screening was 363 (95% confidence interval = 124-496) representing 22% of all cases. If 50% of subjects not screened two to seven years prior had undergone Pap screening, it is projected that a further 268 cases (16%) could have been prevented; if they had undergone human papillomavirus screening, a further 365 cases (22%) could have been prevented. Conclusions For many women who develop cervical cancer, primary human papillomavirus testing could have substantially reduced their cancer risk. Human papillomavirus rather than Pap testing would further increase the gains from any increases in population screening participation.

Cervical screening and cervical cancer death among older women: a population-based, case-control study

Recent research suggests that cervical screening of older women is associated with a considerable decrease in cervical cancer incidence. We sought to quantify the efficacy of cervical cytology screening to reduce death from this disease. Among enrollees of 2 US health plans, we compared Papanicolaou smear screening histories of women aged 55-79 years who died of cervical cancer during 1980-2010 (cases) to those of women at risk of cervical cancer (controls). Controls were matched 2:1 to cases on health plan, age, and enrollment duration. Cytology screening during the detectable preclinical phase, estimated as the 5-7 years before diagnosis during which cervical neoplasia is asymptomatic but cytologically detectable, was ascertained from medical records. A total of 39 cases and 80 controls were eligible. The odds ratio of cervical cancer death associated with screening during the presumed detectable preclinical phase was 0.26 (95% confidence interval: 0.10, 0.63) after adjustment for matching characteristics, smoking, marital status, and race/ethnicity using logistic regression. We estimate that cervical cytology screening of all women aged 55-79 years in the United States could avert 630 deaths annually. These results provide a minimum estimate of the efficacy of human papillomavirus DNA screening-a more sensitive test-to reduce cervical cancer death among older women.

Prostate-specific antigen and prostate cancer mortality: a systematic review

CONTEXT

Although findings from recently published clinical trials and a review from the U.S. Preventive Services Task Force suggest that there is limited to no prostate cancer mortality benefit associated with prostate-specific antigen (PSA) screening, confusion remains as to whether the use of PSA as a screening tool for prostate cancer is warranted.

EVIDENCE ACQUISITION

A systematic literature review was done in 2012 to identify case-control studies from the past 20 years that focused on evaluating the association between screening for prostate cancer and prostate cancer mortality. Emphasis was put on synthesizing the results of these studies, evaluating their limitations, and identifying remaining questions and issues that should be addressed in future studies.

EVIDENCE SYNTHESIS

A total of seven studies were identified in this time period, with the majority suggesting that a reduction in prostate cancer mortality is associated with PSA screening. However, the findings may be limited by various biases inherent to case-control studies of screening tests, such as selection biases resulting from both case and control subject selection, exposure measurement issues, lead and length biases, and issues specific to prostate cancer screening such as the influence of digital rectal examinations.

CONCLUSIONS

Findings from existing case-control studies of PSA and prostate cancer mortality suggest that there is a mortality benefit from PSA screening. However, these studies may be limited by bias and must therefore be interpreted with caution. As uncertainty regarding PSA screening remains, future studies to evaluate the association between PSA and prostate cancer mortality should address these potential biases directly.

Evaluation of cancer service screening: case referent studies recommended

Various cancer screening trials, randomised or otherwise controlled, have demonstrated reductions in cancer mortality. As a consequence, population screening programmes have been implemented. In the mean time, major advances are being made in early detection and treatment modalities of specific cancers and pre-cancers. The impact of these improvements should have bearing on the beneficial effect of periodical screening in preventing cancer death. To monitor these dynamics in the effectiveness of screening, case-referent studies are designed. The effectiveness is estimated by calculating an odds ratio indicating the cancer death rate in screened versus not screened invitees. The major criticisms of case referent studies are potential selection bias and confounding bias of the odds ratio. By properly designing and applying sensitivity analyses these biases can be minimised.

Outcomes of surveillance mammography after treatment of primary breast cancer: a population-based case series

GOAL

To ascertain outcomes of surveillance mammography (SM) following treatment of early stage unilateral primary breast cancer (PBC) in a population based case series.

METHODS

Random samples from all 12,279 women having breast surgery within 4 months after diagnosis of PBC, between July 1991 and December 1993 in Ontario, were drawn from a database created by deterministic linkage of PBC files from the Ontario Cancer Registry (OCR) with episodes of breast surgery extracted from the hospital Discharge Abstract Database (DAD), and mammography from the Ontario physician billings database (OHIP). Among women having >or=1 episode(s) of breast surgery subsequent (SBS) to the date of diagnosis up to December 2000, a sample of 1,200/5,064 (23.7%) was drawn, and among women with no SBS, a sample of 400/7,215 (5.5%). Among these two samples, operative, pathology, and mammography reports were abstracted from original charts. Treatments were abstracted and categorized. Women with complete data for Stages 1 and 2 unilateral PBC were included. From the subsequent surgery sample, 609/1,200 (50.8%) were excluded because of simultaneous or sequential bilateral breast cancers or mastectomies within 6 months, missing stage information, Stage 3 or 4 PBC, or missing primary charts. From the no subsequent surgery sample, 90/400 (22.5%) were excluded by the same criteria. Episodes of bilateral 2-view X-ray mammography, beginning >or=6 months after the diagnosis of unilateral PBC, and if multiple, at least 11 months apart, and not prompted by a clinical concern or symptom, were classified as SM. We confirmed episodes of cancer recurrence within the ipsilateral conserved breast (CRICB) and metachronous contralateral primary breast cancer (CPBC) >or=6 months after the diagnosis of the unilateral PBC from original operative and pathology reports. We used Cox models to describe the association of exposure to >or=1 episode(s) of SM with the risk of death from breast cancer among the study population, and separately among women experiencing CRICB or CPBC.

RESULTS

Eligible women comprising 591/1,200 and 310/400 produced a combined case series of 901/1,600 (56.3%). Women with >or=1 episode(s) of SM numbered 721/901 (80.0%). We confirmed 84 CRICB events among 584 women initially treated by lumpectomy (14.4%), and 49 CPBC events among all 901 women in the study population (5.4%). Among women having >or=1 episode(s), the 25th percentile of observed follow up was 1,631 days, the 50th, 4,287 days, and the 75th 5,011 days. Among women without any SM, the 25th percentile of observed follow-up was 440 days, the 50th, 891 days, and the 75th, 1,849 days. Hazard ratio (HR) for death due to breast cancer associated with >or=1 episode of SM was 0.28 (95% CI 0.22-0.37), adjusted for age, stage, type of surgery, adjuvant chemotherapy, and tamoxifen. Among 84/584 women with CRICB, unadjusted HR = 0.36 (95%CI 0.13, 1.00) and among 49/901 women with CPBC, unadjusted HR = 0.86 (0.20-3.77).

CONCLUSION

SM was associated with a significant reduction in the hazard for breast cancer death. Among women who experienced CRICB, the reduction was of borderline significance, and the reduction was not significant among women who experienced CPBC.

Protection of mammography screening against death from breast cancer in women aged 40-64 years

OBJECTIVE

This study assessed the efficacy of community-based screening mammography in protecting against breast cancer death, asking whether age differences in efficacy persisted in the 1990s.

METHODS

In a case-control study with follow-up, odds ratios (OR) were used to estimate the relative mortality rates from invasive breast cancer among women with at least one screening mammogram in the two years prior to a baseline reference date compared to non-screened women, adjusting for potential confounding. The multicenter population-based study included 553 black and white women diagnosed during 1994-1998 who died in the following five years, and 4016 controls without breast cancer.

RESULTS

Efficacy for reducing the rate of breast cancer death within five years after diagnosis was greater at ages 50-64 years (OR = 0.47, 95% confidence interval (CI) 0.35-0.63) than at ages 40-49 (OR = 0.89, 95% CI 0.65-1.23), and greater among postmenopausal (OR = 0.45, 95% CI 0.33-0.62) than premenopausal women (OR = 0.74, 95% CI 0.53-1.04). Estimates of efficacy were conservative, as shown by sensitivity analyses addressing whether cancer was discovered by a screening mammogram, age at which screening was received, the length of the screening observation window, and years of follow-up after diagnosis.

CONCLUSIONS

Despite the persistence of age differences in efficacy of mammography screening, with greater observed benefit for women aged 50-64 years, these findings support current screening recommendations for women 40-64 years old.

Case–control prostate cancer screening studies should not exclude subjects with lower urinary tract symptoms

OBJECTIVE

Prostate-specific antigen (PSA)/digital rectal exam (DRE) screening for prostate cancer has become standard medical practice; however, its effectiveness in terms of reducing prostate cancer mortality remains undetermined. Case-control screening studies may help determine screening efficacy, though the proper disposition of symptomatic subjects is unclear. This paper presents a prostate cancer-specific methodological modification for analyzing symptomatic case-control screening subjects.

METHODS

Prostate cancer detection studies and case-control studies of PSA/DRE screening were reviewed, and the results for symptomatic and asymptomatic subjects were compared.

RESULTS

Most PSA/DRE detection studies have found that the prostate cancer detection rate among symptomatic patients is the same as or lower than that among asymptomatic patients. Lower urinary tract symptoms (LUTS), often referred to as early prostate cancer symptoms, occur more often in benign prostatic hyperplasia (BPH), a more commonly diagnosed, nonmalignant disease. Screened symptomatic subjects are usually removed from the "screened" category in case-control studies even though BPH-related symptoms do not confer increased prostate cancer risk and odds ratios do not change with inclusion of symptomatic subjects in the analysis.

CONCLUSION

Screened subjects with LUTS should remain in the "screened" category in case-control prostate cancer screening studies since these symptoms may not be associated with increased risk of prostate cancer or validity of the odds ratio.

Benefit of screening mammography in reducing the rate of late-stage breast cancer diagnoses (United States)

OBJECTIVE

We studied the benefit of modern mammography screening in community settings, evaluating age-related differences in rates of late-stage breast cancer detection.

METHODS

Our multicenter population-based case-control study included 931 black and white women with incident breast cancer (American Joint Commission on Cancer Stage IIB or higher) diagnosed 1994-1998 and 4,016 randomly sampled controls never diagnosed with breast cancer. Adjusted odds ratios (ORs) estimated the relative rate of late-stage diagnosis in screened and non-screened women.

RESULTS

Women aged 50-64 at diagnosis with at least one screening mammogram in the previous 2 years were significantly less likely to have late-stage diagnosis (OR = 0.41, 95% CI 0.33-0.52). Results for women aged 40-49 were consistent with a screening benefit, although the confidence interval marginally overlapped the null (OR = 0.81, 95% CI 0.64-1.02). Mammography screening was associated with lower rates of late-stage breast cancer among both premenopausal (OR = 0.64, 95% CI 0.50-0.81) and postmenopausal (OR = 0.44, 95% CI 0.35-0.56) women.

CONCLUSIONS

With modern mammography in the community, rates of late-stage breast cancer diagnoses are lower in screened compared to non-screened women ages 40 and older, but age-related differences persist.

Measuring screening intensity in case-control studies of the efficacy of mammography

Of great interest in studies of screening for breast cancer is the relative efficacy of different screening frequencies (intensities). Prior work has suggested that estimates of the association between screening intensity and outcome in case-control studies would not produce valid results and that only binary indicators (no screens vs. one or more) of exposure can be used. Using case-control studies drawn from simulated cohorts of 30,000-40,000 women, the authors found that biases demonstrated in prior studies can be explained by 1) misclassification of true exposure groups by observed screening history, and 2) differential exposure misclassification of cases and controls. Binary as well as ordered categorical and interval measures can be biased unless they account for misclassification. By combining measurements of screening history from multiple periods of observation of varying lengths and using repeated-measures logistic regression models, the effect of screening intensity can be estimated in the presence of misclassification. Assessing the effect of screening intensity in case-control studies of mammography is possible if principles and methods for misclassification and measurement error guide the analysis.

Glucose screening and the risk of complications in Type 2 diabetes mellitus

It is unknown whether glucose screening for Type 2 diabetes mellitus (DM2) reduces the risk of diabetic complications. We conducted a case-control study using 303 cases with DM2 and at least one symptomatic microvascular diabetic complication, matched 1:1 to control subjects. All subjects' blood glucose tests for the decade before the first clinical suspicion of DM2 were categorized as screening or not based on the presence of symptoms suggestive of DM2. Approximately 90% of case subjects and control subjects had been screened for diabetes. After adjusting for multiple covariates in a logistic regression model, the odds ratio of developing a complication associated with screening was 0.87 (95% confidence interval 0.38-1.98), suggesting that screening may be associated with a modest reduction in the risk of certain diabetic complications. However, the confidence limits were wide and consistent with no true benefit. Further studies are needed to establish whether the small reduction we observed is genuine.

Estimating the influence of rescreening interval on the benefits associated with cancer screening: approaches and limitations

ABSTRACT Randomized controlled trials that seek to measure the ability of a screening test to lower cancer mortality generally do not provide data that bear on the relative efficacy of different screening intervals. Guidance regarding the choice of a screening interval that achieves a high level of case-finding, without being excessively costly, can be obtained from one or more of several study designs that examine the subsequent occurrence of cancer in persons who have had a negative screening test. However, each of these can potentially provide a misleading result, and so their limitations must be considered before using the data they generate to develop a rational rescreening policy.

Visual inspection in oral cancer screening in Cuba: a case-control study

A case-control study was conducted to evaluate the efficacy of an on-going oral cancer screening programme in Cuba in preventing advanced oral cancer in Cuba. The cases for the study consisted of 200 oral cancer patients with stage III and IV disease. Three apparently healthy subjects per case, matched for sex, age (plus or minus 5 years) and residing within a perimeter of 200 m of the house with the case, and willing to be interviewed, were recruited as the controls. Information on socio-economic indicators, smoking, drinking, diet and screening history in the form of visits to the dentist were collected by personal interview with the subjects. Odds ratio (OR), with 95% confidence intervals (CI), of being diagnosed with an advanced oral cancer, in relation to the screening experience at the date of diagnosis of case, 1, 2, 3, 6, and 12 months prior to the date of diagnosis of case were estimated by conditional logistic regression for matched data. The odds ratio of advanced oral cancer associated with screening in relation to screening experience 3 months prior to the diagnosis of the case was 0.67 (95% CI: 0.46-0.95). The odds ratio was 0.91 (95% CI: 0.60-1.37) for a single screening test and 0.41 (95% CI: 0.24-0.68) for two or more tests. The protection offered by screening persisted up to 3 years since the last test. The results of a descriptive evaluation of the programme also revealed limited evidence towards a shift from advanced to early stages after the introduction of the programme. Nonetheless, the results should be interpreted with caution in view of the several limitations in the study, particularly the fact that screening history was established indirectly by interviews and advanced oral cancers constituted the cases, rather than those who died from the disease.

Reducing colorectal cancer mortality by repeated faecal occult blood test: a nested case-control study

Randomised trials have shown the efficacy of faecal occult blood testing (FOBT) in reducing colorectal cancer mortality, but observational studies are needed to monitor such efficacy in population programmes. We conducted a nested case-control study on a cohort of 21,879 subjects who participated in a colorectal screening programme from 1978 to 1995, undergoing at least one FOBT test. 95 fatal cases of colorectal cancer were eligible for the study. For each fatal case, 5 non-fatal matched controls were randomly selected from the cohort. FOBT screening history was less common among cases than controls. The odds ratio of colorectal cancer mortality among 'attenders' (defined as those who underwent a second FOBT within 2 years of study entry) with respect to 'non-attenders' was 0.64 (95% confidence interval 0.36-1.15). We also computed odds ratios defining exposure as one or more tests in the detectable preclinical period, hypothesising various lengths for the latter, which, however, yielded an efficacy estimate biased towards the null. A strong inverse relationship was observed between mortality and the number of tests, but this phenomenon is interpretable as 'healthy screenee bias'. The results suggest that the potential efficacy in preventing colorectal cancer mortality through annual FOBT screening may be of the order of one third.