Imperfect Accuracy Research Articles

Association between covariates and disease occurrence in the presence of diagnostic error

Identification of covariates associated with disease is a key part of epidemiological research. Yet, while adjustment for imperfect diagnostic accuracy is well established when estimating disease prevalence, similar adjustment when estimating covariate effects is far less common, although of important practical relevance due to the sensitivity of such analyses to misclassification error. Case-study data exploring evidence for seasonal differences in Salmonella prevalence using serological testing is presented, in addition simulated data with known properties are analysed. It is demonstrated that: (i) adjusting for misclassification error in models comprising continuous covariates can have a very substantial impact on the resulting conclusions which can then be drawn from any analyses; and (ii) incorporating prior knowledge through Bayesian estimation can provide potentially more informative assessments of covariates while removing the assumption of perfect diagnostic accuracy. The method presented is widely applicable and easily generalized to many types of epidemiological studies.

Macrophages and Mast Cells Infiltration Are Biomarkers of Primary Refractory Hodgkin's Lymphoma

AbstractAbstract 3881Classical Hodgkin's lymphoma is a highly curable lymphoma and about 80% of patients can be cured with modern treatment strategies. In spite of great clinical progress, a significant minority of classical Hodgkin's lymphoma experiences treatment failure after primary chemotherapy including a first line of anthracyclin-based regimen. Patients with refractory Hodgkin's lymphoma represent 5 to 10% of classical Hodgkin's Lymphoma. Many of these patients have a poor overall survival estimated at 25% at 5 years. A better biological characterization of such primary refractory patients might allow the use of early therapeutic intervention including targeted therapy. It remains, however, a challenge to identify patients whose disease will not be eradicated by standard therapy. Current prognostic models predict the outcome of treatment with imperfect accuracy, and clinically relevant biomarkers have not yet been established to improve the International Prognostic Score. For these reasons, reliable biomarkers for predicting long term survival at diagnosis are needed for such patients. Steidl et al. (Nejm,2010) recently reported the prognostic value of tumor-associated macrophages in patients with classical Hodgkin's lymphoma, showing that higher infiltration is associated with a shortened survival.The value of tumor-associated macrophages in primary refractory Hodgkin's lymphomas has not been specifically assessed. In a retrospective study (Canioni et al., Plos one 2009), we previously evaluated 59 patients (18 with primary refractory or early relapse disease and 41 responders) collected from 1997 to 2004 in two hematology centres (Necker Hospital and Gustave Roussy Institute, Paris France) for c-kit expression by immunohistochemical analysis as a marker of mast cell infiltration and correlated the results with the response to treatment. All available poor prognosis patients were first identified (18 patients with primary refractory disease or early relapse (< 1year)) and the control group (47 responders) was randomly selected. Patients received conventional chemotherapy-based treatments [(MOPP (mechlorethamine, vincristine, procarbazine, and prednisone), ABVD (doxorubicine, bleomycine, vinblastine, and dacarbazine) or the combination of both or BEACOPP (bleomycine, etoposide, doxorubicine, cyclophosphamide, vincristine, procarbazine, prednisone)] and radiotherapy in stages I and II. Most patients presented a nodular sclerosis subtype of Hodgkin's lymphoma regardless whether they were refractory (17/18cases, 94.5%) or responders (37/41cases, 90%). In this cohort, 44 (75%) patients had a localized stage, whereas 19 (25%) had a disseminated disease. The results showed that refractory Hodgkin's lymphoma were associated with an excess of mast cells infiltration in the tumor cells microenvironment. The number of mast cells stained was significantly higher in refractory Hodgkin's lymphoma (c-kit+ mast cells > 6 per field) than in responders (c-kit+ mast cells ≤ 6) (p=0.001 and 0.0194 in univariate and multivariate analysis, respectively). In this cohort of patients, using CD68 staining we also found a statistically significant higher proportion of tumor-associated macrophages in refractory Hodgkin's lymphoma as compared to responders in univariate and multivariate analyses (p=0.0048 and p=0.0041, respectively). Therefore, we confirmed a strong correlation between the number of CD68 positive macrophages in the tumor stroma and clinical outcome. The use of such markers (CD68 and c-kit) in combination with well-established clinical risk factors could improve on the predictive value of a single biomarker used alone.Therefore, in addition to mast cells, macrophages are also important players in refractory Hodgkin's lymphoma that may confer drug resistance to Hodgkin Reed Sternberg cells. Taken together, these data strongly suggest that microenvironment should be targeted in Hodgkin's lymphomas. In this regard, the use of kinase inhibitors that target both c-kit and M-CSF receptors could restore chemotherapy sensitivity in refractory Hodgkin's lymphoma and should be evaluated in clinical trials. Disclosures:No relevant conflicts of interest to declare.

“Early-FDG-PET” but Not Macrophage Infiltration In Diagnostic Specimen Seems to Predict Clinical Course of Hodgkin Lymphoma

AbstractAbstract 4826 Background:Hodgkin Lymphoma (HL) is a highly curable malignancy that mostly affects young adults; currently, considering all patients more than 75% of them will be cured and the ones diagnosed with early stage disease have a chance of cure over 90%. However, despite these very satisfactory results, about 20% of patients still die from progressive disease and non-specific related Hodgkin's mortality, mostly due to late toxic effects, continues to rise with time. Consequently, the optimal treatment should be designed based on prognostic models, but currently all of them predict the outcome of treatment with imperfect accuracy. Since from recent studies “early FDG–PET” and lately tissue macrophages infiltration seem to be powerful predictors, we hypothesized that macrophage infiltration could be the shadow of the inflammatory microenvironment that FDG-PET identifies in HL and that persist at early assessment in patients who will fail to respond to treatment. Consequently we decided to verify this hypothesis analyzing a group of patients with HL diagnosed and treated at our institution. Patients and methods:on the basis of availability of paraffin embedded diagnostic specimen and “early PET” assessment, we selected a cohort of 24 patients (M/F: 12/12) with Hodgkin Lymphoma, diagnosed and treated at our institution between February 2007 and February 2010. Before starting treatment all patients completed staging with whole body CT scan, FDG-PET and bone marrow biopsy. Ten patients had stage II disease, 10 patient stage III and 4 patients stage IV; median age was 33 years. Programmed treatment consisted of 4–6 cycles of ABVD and, if indicated, involved-field radiation therapy. Patients repeated CT scan and FDG-PET after two cycles and after completion of therapy. Macrophage infiltration in paraffine-embedded diagnostic specimen was retrospectively determined by immunohostochemistry. Results:After two cycles of ABVD, FDG-PET was negative in 18/24 patients (75%), while FDG-PET was positive in the six remaining patients (25%). Overall 20 out of 24 patients (83%) achieved a CR, however two of them had an early relapse (within 6 months), so they underwent 2nd line therapy plus autologous stem cell transplantation (ASCT), both obtaining a second CR. Among the four remaining patients, one achieved only a PR and entered salvage protocol with 2nd line treatment plus ASCT, two achieved a CR after second line treatment and the last one was refractory to 3 lines of treatment and finally was enrolled in an investigational protocol. With a median follow up of 18.5 months, 21 out of 24 patients are alive in CR, a patient is alive in PR and two patients died, due respectively to pulmonary thromboembolism and ARDS (after mediastinal irradiation). Five out six patient (83%) with persistent positive “early FDG-PET” failed their first line treatment. About macrophage percentage in the diagnostic specimen, evaluated and classified according to the criteria reported in the recent paper by Dr Steidl and coworkers, one patient (4%) was classified with score 1, twelve (50%) with score 2 and eleven (46%) with score 3. Among the six patients with persistent positive “early-FDG-PET”, one of them had score 1 (and never obtained CR), three had score 2 and two score 3. Conclusions:with the limitation of a small cohort of patients and the lack of gene-expression assays, our data do not seem to support our hypothesis neither to confirm the recently reported prognostic impact of macrophage infiltration in diagnostic specimen. Disclosures:No relevant conflicts of interest to declare.

Bayesian estimation of the true prevalence of Mycobacterium avium subsp. paratuberculosis infection in Cypriot dairy sheep and goat flocks

We estimated the prevalence of Mycobacterium avium subsp. paratuberculosis (MAP) infected sheep and goats, older than 2 years, reared in the region effectively controlled by the Government of the Republic of Cyprus, in September 2005. The sera collected from 8011 animals (3429 sheep and 4582 goats) from 83 flocks, non-vaccinated against MAP, were examined for antibodies with a commercially available enzyme linked immunosorbent assay (Pourquier ® paratuberculosis antibody screening ELISA). The true prevalence of MAP infection was calculated, in a Bayesian framework, separately in sheep and goats, with models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. The within-flock mean seroprevalence in sheep and goats was 9.9% (95% CI: 8.9; 10.9%) and 7.9% (7.2; 8.7%), respectively. There was at least one seropositive sheep in 52% (38; 66%) of flocks with sheep and one seropositive goat in 50% (39; 62%) of flocks with goats. Within the seropositive flocks the mean seroprevalence was 12.1% (10.9; 13.4%) and 10.3% (9.3; 11.4%) in sheep and goats, respectively. The calculated mean true prevalence of infected sheep and goats was 15.0 and 11.1%, respectively. There was at least one infected sheep in 60.8% (95% credible interval: 42.3; 78.8%) and at least an infected goat in 48.6% (30.4; 68.5%) of the flocks. In the infected flocks, the mean within flock true prevalence of infection in sheep and goats was estimated at 24.6% (16.3; 33.3%) and 23.1% (15.5; 33.6%), respectively.

Internally Generated Error Signals in Monkey Frontal Eye Field during an Inferred Motion Task

An internal model for predictive saccades in frontal cortex was investigated by recording neurons in monkey frontal eye field (FEF) during an inferred motion task. Monkeys were trained to make saccades to the extrapolated position of a small moving target that was rendered temporarily invisible and whose trajectory was altered. On approximately two-thirds of the trials, monkeys made multiple saccades while the target was invisible. Primary saccades were correlated with extrapolated target position. Secondary saccades significantly reduced residual errors resulting from imperfect accuracy of the first saccade. These observations suggest that the second saccade was corrective. Because there was no visual feedback, corrective saccades could only be driven by an internally generated error signal. Neuronal activity in the frontal eye field was directionally tuned before both primary and secondary saccades. Separate subpopulations of cells encoded either saccade direction or direction error before the second saccade. These results suggest that FEF neurons encode the error after the first saccade, as well as the direction of the second saccade. Hence, FEF appears to contribute to detecting and correcting movement errors based on internally generated signals.

Tumor-Associated Macrophages and Survival in Classic Hodgkin's Lymphoma

Despite advances in treatments for Hodgkin's lymphoma, about 20% of patients still die from progressive disease. Current prognostic models predict the outcome of treatment with imperfect accuracy, and clinically relevant biomarkers have not been established to improve on the International Prognostic Score. Using gene-expression profiling, we analyzed 130 frozen samples obtained from patients with classic Hodgkin's lymphoma during diagnostic lymph-node biopsy to determine which cellular signatures were correlated with treatment outcome. We confirmed our findings in an independent cohort of 166 patients, using immunohistochemical analysis. Gene-expression profiling identified a gene signature of tumor-associated macrophages that was significantly associated with primary treatment failure (P=0.02). In an independent cohort of patients, we found that an increased number of CD68+ macrophages was correlated with a shortened progression-free survival (P=0.03) and with an increased likelihood of relapse after autologous hematopoietic stem-cell transplantation (P=0.008), resulting in shortened disease-specific survival (P=0.003). In multivariate analysis, this adverse prognostic factor outperformed the International Prognostic Score for disease-specific survival (P=0.003 vs. P=0.03). The absence of an elevated number of CD68+ cells in patients with limited-stage disease defined a subgroup of patients with a long-term disease-specific survival of 100% with the use of current treatment strategies. An increased number of tumor-associated macrophages was strongly associated with shortened survival in patients with classic Hodgkin's lymphoma and provides a new biomarker for risk stratification.

Genome-Wide Expression Profiling Predicts Treatment Outcome in Classical Hodgkin Lymphoma

INTRODUCTION: Despite advances in Hodgkin lymphoma (HL) treatment about 20% of patients still die due to progressive disease. Current prognostic models predict treatment outcome with imperfect accuracy and clinically relevant biomarkers are yet to be established that improve upon the existing International Prognostic Scoring system.PATIENTS AND METHODS: We analyzed 113 fresh frozen lymph node specimens from classical HL patients by gene expression profiling (Affymetrix UA 133 2.0 Plus) focusing on correlations with treatment outcome. The cohort comprised 100 diagnostic pretreatment and 13 relapse biopsies. Treatment was considered a failure if the lymphoma progressed during therapy or relapsed at any time. Treatment success was defined as absence of progression or relapse. Gene expression findings were validated in paraffin embedded material using immunohistochemistry (IHC) for CD20 and CD56 in the original 100 cases, in an independent validation cohort of 166 cases and a set of 172 cases using flow cytometric assessment of CD20 and CD56. For our predictive model, we trained a classifier by Simultaneous Multinominal Logistic Regression (SMLR) and assessed relative feature importance using Random Forests.RESULTS: We found underexpression of genes representing a global B cell signature in 18 pretreatment biopsies of patients whose first line systemic chemotherapy failed (p=0.033). These results were independently validated using immunohistochemistry for CD20 in 166 patients. The presence of background B cells in the direct vicinity of Hodgkin Reed Sternberg (HRS) cells favorably affected progression-free survival (p=0.042) in a univariate analysis; however, in multivariate analysis only clinical stage and hemoglobin were independent prognostic factors. Furthermore, down-regulation of genes involved in T cell receptor signaling was associated with failure of first line systemic chemotherapy. In contrast to immunohistochemistry validation, flow cytometry was not sensitive to differences in T (CD3) or B cell (CD20) numbers (p=0.22 and p=0.35, respectively). Under-expression of genes of an NK cell signature in 6 relapse biopsies correlated with failure to secondary therapy with autologous stem cell transplantation (p=0.048). IHC accordingly showed complete lack of NK cells in these biopsies. To study the predictive power of gene expression in comparison to clinical risk factors, we identified 103 gene expression probe sets and Ann Arbor stage as the most important features. Importantly, we found 8 probe sets that were more influential than Ann Arbor stage. In comparison to either gene expression or clinical variables alone, combining of the two data sources achieved best performance values for predicting outcome of first line treatment (Receiver Operating Characteristics [ROC]: AUC(combined) = 0.76; AUC(gene expression) = 0.71; AUC(clinical) = 0.69).CONCLUSION: Clinical outcome correlates with the presence of B cells in pretreatment and NK cells in relapse biopsies verifying the importance of the microenvironment for outcome prediction in HL. We were able to validate these findings by IHC and showed that GEP adds to the predictive value of clinical prognostic scoring. Our data suggest that integration of further molecular data, especially those derived from HRS cell enriched specimens, will be of value in helping to inform novel predictive models in Hodgkin lymphoma.

Knowing how they feel: Perceiving emotions felt by outgroups

Individuals can often accurately perceive others’ emotions in a purely interpersonal context. However, when people identify with an important ingroup, they experience distinctive patterns of emotion [Smith, E. R., Seger, C. R., & Mackie, D. M. (2007). Can emotions be truly group-level? Evidence regarding four conceptual criteria. Journal of Personality and Social Psychology, 93, 431–446]. Thus, in three studies using a variety of meaningful groups, we examine how a salient distinction between groups might influence people’s ability to estimate the emotions of outgroup members. Participants demonstrated substantial though imperfect accuracy in estimating the emotions reported by outgroups. Specific biases affected their estimates, especially the overlap of perceived emotions of the outgroup with the ingroup’s own emotions. Furthermore, there was a general overprediction of outgroups’ negative emotions and underprediction of their positive emotions. Because of the importance of an outgroup’s emotions as potential causes of their behavior, accuracy and biases in group emotion estimation may be consequential for intergroup relations.

ROUGH PILOT DECISION‐SUPPORT ALGORITHM

In this paper, a new application for the theory of rough sets is proposed. The theory of rough sets has been introduced into one of the most complicated fields, military aviation. The problem is to generate a pilot's decision‐support algorithm for the task of dropping a bomb on a target located behind an obstacle detected during flight. The aim of this algorithm is to simultaneously facilitate the performance of this task for the pilot; it will minimize pilot error caused by imperfect accuracy in estimating the situation and limited experience in a given situation.

The effect of changing scatterer positions on acoustic time-reversal refocusing in a 2D urban environment at low frequencies

In a previous work, we considered time-reversal refocusing for localizing a sound source in a highly reverberant urban environment with non-line-of-sight (NLOS) receivers. The approach involved a virtual (computer-based) time-reversal propagation calculation using a priori knowledge of the receiver and scatterer positions. Among the errors that affect the quality of refocusing is the imperfect accuracy of the assumed scatterer locations. Some practical analogues of changing scatterer positions are (a) the building coordinate errors (or mistakes) and (b) the random movement of vehicles on the street of an urban setting. We address these issues by conducting a time-reversal analysis of a set of numerically generated synthetic acoustic pressure recordings after intentionally introducing errors by altering the position of the scatterers. The numerical experiment results indicate that, for a realistically complicated urban setting, coordinate errors in the position of only a few scatterers have little detrimental effect. The effect of coordinate errors in one or a few scatterers is suppressed by the constraints imposed by correct propagation features (both kinematic and dynamic) generated by multiple reflections and diffractions from other precisely located scatterers. The dependence of source localization accuracy on the relative error in scatterer coordinates, the relative number of scatterers with coordinate errors and the number of receivers is quantitatively assessed in this paper. In general, time-reversal refocusing with a large number of receivers can compensate for more severe errors. Even for only three non-line-of-sight receivers, building location errors in the order of 3 m still give good results. Adding small scatterers (like vehicles) close to a receiver is more critical than adding scatterers relatively far from the receivers.

Diagnostic accuracy of myocardial perfusion imaging in a study population without post-test referral bias

Most previous studies on the accuracy of myocardial perfusion imaging (MPI) are hampered by post-test referral bias, in that referral for coronary angiography was influenced by the MPI result. In this way, patients with a normal MPI result less frequently underwent catheterization, a tendency supposed to cause an underestimation of test specificity and an overestimation of test sensitivity. MPI by use of a gated dual-isotope protocol was undertaken before angiography in 357 patients referred for angiography for suspected stable angina pectoris. The MPI reports were kept secret to prevent post-test referral bias. The MPI study was normal in 215 patients (60%) and showed reversible perfusion abnormalities in 118 (33%) and fixed defects in 24 (7%). Angiography was normal in 231 patients (65%) and revealed 1 or more significant stenoses in 126 (35%). With angiography as the reference, the sensitivity and specificity of MPI for detecting significant coronary artery stenosis were 75% and 79%, respectively. In this prospective study without post-test referral bias, we found a lower sensitivity and slightly higher specificity than in studies with post-test referral bias. The imperfect accuracy may reflect differences between anatomic and physiologic imaging.

An Epidemiologic Critique of Current Microbial Risk Assessment Practices: The Importance of Prevalence and Test Accuracy Data

Data deficiencies are impeding the development and validation of microbial risk assessment models. One such deficiency is the failure to adjust test-based (apparent) prevalence estimates to true prevalence estimates by correcting for the imperfect accuracy of tests that are used. Such adjustments will facilitate comparability of data from different populations and from the same population over time as tests change and the unbiased quantification of effects of mitigation strategies. True prevalence can be estimated from apparent prevalence using frequentist and Bayesian methods, but the latter are more flexible and can incorporate uncertainty in test accuracy and prior prevalence data. Both approaches can be used for single or multiple populations, but the Bayesian approach can better deal with clustered data, inferences for rare events, and uncertainty in multiple variables. Examples of prevalence inferences based on results of Salmonella culture are presented. The opportunity to adjust test-based prevalence estimates is predicated on the availability of sensitivity and specificity estimates. These estimates can be obtained from studies using archived gold standard (reference) samples, by screening with the new test and follow-up of test-positive and test-negative samples with a gold standard test, and by use of latent class methods, which make no assumptions about the true status of each sampling unit. Latent class analysis can be done with maximum likelihood and Bayesian methods, and an example of their use in the evaluation of tests for Toxoplasma gondii in pigs is presented. Guidelines are proposed for more transparent incorporation of test data into microbial risk assessments.

Metapopulation Structure Favors Plasticity over Local Adaptation

We describe a model for the evolutionary consequences of plasticity in an environmentally heterogeneous metapopulation in which specialists for each of two alternative environments and one plastic type are initially present. The model is similar to that proposed by Moran (1992) but extends her work to two sites. We show that with migration between sites the plastic type is favored over local specialists across a broad range of parameter space. The plastic type may dominate or be fixed even in an environmentally uniform site, and even if the plasticity has imperfect accuracy or bears some cost such that a local specialist has higher fitness in that site, as long as there is some migration between sites with different distributions of environmental states. These results suggest that differences among taxa in dispersal and hence realized migration rates may play a heretofore unrecognized role in their patterns of adaptive population differentiation. Migration relaxes the thresholds for both environmental heterogeneity and accuracy of plastic response above which plasticity is favored. Furthermore, small changes in response accuracy can dramatically and abruptly alter the evolutionary outcome in the metapopulation. A fitness cost to plasticity will substantially reduce the range of conditions in which the plastic type will prevail only if the cost is both large and global rather than environment specific.

Metapopulation Structure Favors Plasticity over Local Adaptation

We describe a model for the evolutionary consequences of plasticity in an environmentally heterogeneous metapopulation in which specialists for each of two alternative environments and one plastic type are initially present. The model is similar to that proposed by Moran (1992) but extends her work to two sites. We show that with migration between sites the plastic type is favored over local specialists across a broad range of parameter space. The plastic type may dominate or be fixed even in an environmentally uniform site, and even if the plasticity has imperfect accuracy or bears some cost such that a local specialist has higher fitness in that site, as long as there is some migration between sites with different distributions of environmental states. These results suggest that differences among taxa in dispersal and hence realized migration rates may play a heretofore unrecognized role in their patterns of adaptive population differentiation. Migration relaxes the thresholds for both environmental heterogeneity and accuracy of plastic response above which plasticity is favored. Furthermore, small changes in response accuracy can dramatically and abruptly alter the evolutionary outcome in the metapopulation. A fitness cost to plasticity will substantially reduce the range of conditions in which the plastic type will prevail only if the cost is both large and global rather than environment specific.

Discrete-Time Adaptive Control of Nonlinear Systems Using Neural Networks

A neural-adaptive control system for a class of discrete-time nonlinear plants is proposed. Neural networks and adaptation are required to ensure stability and asymptotic convergence of the tracking error, in spite of the nonlinear and unknown plant dynamics. An augmented error adaptive approach is taken. The effect of the inevitable imperfect approximation accuracy of the neural network on system stability is taken into consideration by using dead-zone adaptation. Stability and convergence proofs are presented together with a simulation example.

More talk, less paper: Predicting the accuracy of substituted judgments

purpose: To study the accuracy of substituted judgments regarding life-sustaining therapies and other therapies made by surrogate decision makers and to investigate factors associated with more accurate predictions. patients and methods: A total of 50 pairs of ambulatory patients and surrogates, chosen according to a legal hierarchy, underwent separate interviews in which surrogates were asked to predict the preferences of patients for eight modes of medical therapy in three clinical scenarios, given only yes or no as response options. Patient preferences, their surrogates' predictions, and the extent of agreement between the two were measured. The total number of correct predictions constituted the Surrogate Accuracy in Matching Patient Preferences Scale (SAMPPS). Sociodemographic factors associated with agreement were also assessed. results: Agreement between patients and surrogates ranged from 57% to 81%. The mean SAMPPS score was 17 of 24 correct. Kappa (k) coefficients, which measure inter-rater concordance, were positive for 23 of 24 items and were 0.3 or greater (P <0.05) for 14 of 24 items. Rates of agreement were not related to whether the surrogate interviewed (surrogate determined by state law) was the person the patient would have chosen as a surrogate or whether the patient had an advance directive. In multiple linear regression analysis, both prior discussions of preferences and nonchurchgoing behavior were significantly associated with patient-surrogate agreement, independent of religious denomination and race. conclusion: When pressed to choose, surrogates can predict the preferences of patients for life-sustaining therapies with an imperfect accuracy that nonetheless significantly exceeds the agreement expected due to chance alone. Exhorting surrogates to give their “best estimate” and encouraging prior discussions may improve accuracy. Houses of worship might be important target sites for campaigns to improve public awareness about advance directives.

An Examination of Negative Halo Error in Ratings

Several studies which have used correlational measures to compare levels of observed halo in ratings with true halo levels have found "negative halo error," or true halo that exceeds observed halo. The authors derived a causal model of halo error based on a widely accepted definition of halo error and, in the context of this model, formulated three hypotheses to explain findings of negative halo error. Reanalyses of data reported recently by Kozlowski and Kirsch (1987) and Murphy and Reynolds (1988) supported the hypothesis that "negative" halo error can be indicated when positive halo actually occurs along with imperfect correlational rating accuracy. It is suggested that positive halo rating error may be more pervasive a phenomenon than has recently been thought.

Precise Insertion Loss Measurements using Imperfect Square Law Detectors and Accuracy Limitations Due to Noise

Inaccuracies of insertion loss measurements caused by deviation of a square law detector from square law set a practical upper limit on the r.f. power which can be applied to a bolometer. The detection of the audio modulation after extraction from the carrier by a bolometer is limited by the behaviour of the second detector in the presence of noise and sets a lower limit. Since square law and synchronous detectors are superior to linear detectors at a low ``signal to noise ratio'', their behaviour is studied in more detail. It is shown that the bandwidth of the amplifier ahead of the second detector is not the controlling factor for the accuracy of the measurement. The concept of ``ratio of amplifier bandwidth to indicator bandwidth'' is introduced. Graphs are given for the indicator fluctuations as a function of this concept and of the ``signal to noise ratio'' at the amplifier output for both synchronous and square law detectors. A graph is furnished showing the range of insertion loss measurement as a function of the accuracy desired based upon the accuracy limitations at the high end low power end.