Measuring changes in logarithmic data, with special reference to bronchial responsiveness

doi:10.1016/0895-4356(94)90096-5

Journal of Clinical Epidemiology

Volume 47, Issue 10, October 1994, Pages 1099-1108

https://doi.org/10.1016/0895-4356(94)90096-5 Get rights and content

Abstract

Bronchial provocation tests with agents such as histamine and methacholine are commonly used in clinical and epidemiological studies of respiratory illness because bronchial hyperresponsivenes is a non-specific abnormality of the airways which is characteristic of asthma. However, measurements of bronchial responsiveness are log-normally distributed. As a result, special considerations need to be given to reporting within-subject changes in these measurements in longitudinal studies as, for example, in clinical trials or in any study in which a before-and-after experimental design is used. In these types of experiments, changes in bronchial responsiveness should not be simply expressed in the units of the measurement, such as dose of provoking agent, but must be expressed in units based on a logarithmic scale. The appropriate log-based units for measuring within-subject changes are doubling dose, fold difference or percent change. This paper explains the methods for calculating changes in these units in a statistically correct manner. All three units represent different ways of expressing the same change on a logarithmic scale. However, ‘doubling dose’ is only appropriate when it relates directly to the method of administering the provoking agent in doubling concentrations and ‘fold difference’ or ‘percent change’ are both appropriate for expressing any log-based changes. The methods for calculating changes in these units also apply to calculations of repeatability within test methods and to calculations of comparability and agreement between test methods. The methods are described solely for reporting changes in units of bronchial responsiveness but are applicable to other log-normally distributed measurements.

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Cited by (31)

Methacholine PC<inf>20</inf> in African Americans and whites with asthma with homozygous genotypes at ADRB2 codon 16
2013, Pulmonary Pharmacology and Therapeutics
Citation Excerpt :
Model assumptions were checked before the analysis and an appropriate measure was taken in case of violation. A factorial ANOVA was performed to analyze the log10 transformed PC20 [36]. Race, genotype, and interaction of race and genotype were used in the initial model.
African Americans have worse asthma outcomes compared to whites. Adrenoceptor beta 2, surface gene (ADRB2) Gly16Arg genotypes have been associated with β₂-agonist bronchodilator response, asthma exacerbation rate, response to methacholine, and lung function decline but not specifically in African Americans.
We sought to compare the provocative concentration of methacholine that causes a 20% fall in FEV₁ (PC₂₀) in African Americans and whites with asthma who were ADRB2 homozygous at codon 16 (Arg16Arg or Gly16Gly).
African Americans and whites whose parents and grandparents were of the same race, aged ≥10 years, with baseline FEV₁ of ≥60% predicted, and no upper or lower respiratory tract infection within the previous 2 weeks meeting genotype criteria were enrolled. PC₂₀ was measured after withholding short-acting and long-acting β₂-agonists for 8 and 12 h respectively, montelukast for 24 h, ipratropium bromide and inhaled corticosteroids for 12 h, and antihistamines for 72 h.
423 participants were screened and 88 had a positive challenge. Participants were 32 yrs ± 19 yrs (mean ± SD), 70% female, 51% White (vs. African American), 6% Hispanic. Similar numbers of participants were using inhaled corticosteroids by race and genotype. There were significant differences in log PC₂₀ between race/genotype groups (p = 0.012). African American Arg16Arg participants had a lower log PC₂₀ than White Gly16Gly (p = 0.009) and African American Gly16Gly (p = 0.041) participants. Both race and genotype contributed significantly to the model (p = 0.037 and p = 0.014, respectively) but there was no interaction between race and genotype on log PC₂₀.
Airway hyperresponsiveness is influenced by race and the ADRB2 codon 16 polymorphism. African Americans with the Arg16Arg genotype have increased airway reactivity and may be at risk for worse asthma outcomes. Inclusion of genetic information as an additional clinical tool may aid in the personalization of asthma management decisions.
[ClinicalTrials.gov Identifier: NCT00708227]
Protection by budesonide and fluticasone on allergen-induced airway responses after discontinuation of therapy
2005, Journal of Allergy and Clinical Immunology
Citation Excerpt :
PC20 was calculated by means of linear interpolation of log dose-response curves and log transformed to fit a normal distribution before analysis. A fold difference change was calculated to assess the change in PC20 caused by allergen challenge.15 A multiplicative ANOVA model with the factors of subject, treatment order, response (isolated early and dual), and treatment was used to compare the effects of a 7-day treatment with budesonide, fluticasone propionate, and placebo on allergen-induced early and late airway bronchoconstriction (maximum percentage decrease in FEV1 and AUC), airway hyperresponsiveness, and sputum eosinophilia.
Treatment with inhaled steroids is an effective method of reducing bronchoconstriction and airway inflammation after allergen challenge. However, the durationof the protective effects of inhaled steroids after discontinuation of therapy has not been established.
We sought to evaluate the protective effect of 1 week of inhaled steroid therapy against inhaled allergen challenge 12 hours after discontinuation of therapy.
In this randomized, double-blind, placebo-controlled crossover trial, 26 asthmatic subjects (>18 years old) not using inhaled steroids were administered 200 μg of budesonide twice daily, 200 μg of fluticasone twice daily, or placebo twice daily for 1 week. Twelve hours after discontinuation of therapy, subjects were administered an inhaled allergen challenge. Each treatment period was separated by a 3-week washout period.
When compared with placebo (26% ± 14%), there was a slight but significant protection against the allergen-induced early response after fluticasone treatment (19% ± 10%, P = .001) but not after budesonide treatment (23% ± 13%, P = .08). However, when the area under the curve for the early airway response was examined, there was no difference between the 2 drugs in the amount of protection (P = .62). Partial protection was demonstrated against the late-response allergen-induced sputum eosinophilia with both treatments (P = .001). By contrast, no protection was observed against allergen-induced airway hyperresponsiveness for either treatment.
The protective effects of inhaled steroids against allergen-induced early responses, airway eosinophilia, and allergen-induced airway hyperresponsiveness are partially or completely lost as early as 12 hours after discontinuation of therapy.
Effect of specific immunotherapy added to pharmacologic treatment and allergen avoidance in asthmatic patients allergic to house dust mite
2004, Journal of Allergy and Clinical Immunology
Citation Excerpt :
Comparison between means was performed with the Student t test for unpaired data. Subjects who did not undergo methacholine challenge because of bronchoconstriction were given a PD20FEV1 arbitrary value of 0.16 Logarithmic transformation of PD20FEV1 was used for the analysis, and PD20FEV1 data were presented as geometric means.
Although several studies support the efficacy of specific immunotherapy in allergic asthma, its benefit compared with that of standardized pharmacologic intervention remains unknown.
A double-blind, placebo-controlled trial in 72 patients with mild-to-moderate asthma and allergy to house dust mite (HDM; Dermatophagoides species) was conducted to assess the effects of specific immunotherapy added to guideline-adjusted pharmacologic treatment and allergen avoidance.
After 1 observational year of pharmacologic treatment and standard measures of HDM avoidance, 2 groups of asthmatic subjects were randomly assigned to receive specific immunotherapy consisting of subcutaneous injections of either a mixture of Dermatophagoides pteronyssinus and Dermatophagoides farinae vaccine (n = 41) or placebo (n = 31) for 3 years. Medications were adjusted every 3 months according to the Global Initiative for Asthma guidelines.
The adjustment of treatment was associated with a reduction in asthma symptom scores in all subjects. The addition of specific immunotherapy was associated with a decrease in the number of subjects requiring rescue bronchodilators, an increase in morning and evening peak expiratory flow, and a reduced skin sensitivity to HDM extracts. The addition of specific immunotherapy had no significant effects on the cumulative dose of inhaled corticosteroids, asthma symptoms, lung volumes, or bronchial responsiveness to methacholine.
These results suggest that specific immunotherapy added to pharmacologic treatment and HDM avoidance provides marginal but statistically significant clinical benefits, possibly by reducing the allergic response of asthmatic patients sensitized to HDM.
A pre-seasonal birch/hazel sublingual immunotherapy can improve the outcome of grass pollen injective treatment in bisensitized individuals. A case-referent, two-year controlled study
2003, Allergologia et Immunopathologia
The study tests the hypothesis of a reduction of priming due to tree allergy in patients sensitised to both birch/hazel and grass pollen undergoing an associated preseasonal Sublingual/Injective immunotherapy
36 out of 49 bisensitized candidates were pair-matched into 18 case-referent couples. During two years all patients were administered preseasonal grass-SIT and one patient in each couple received also birch/hazel-SLIT. Diary cards were fulfilled for three consecutive grass pollen seasons. Specific Nasal Provocation Test (NPT) for grass and aspecific bronchial challenge were done; sera were analyzed for specific IgE and IgG
During the peak of the grass pollen season both groups showed a significant improvement in total symptom-score. Conjunctivitis and cough improved significantly more in patients with associated therapies. While antihistamine score decreased significantly in both groups, antiasthmatics did only in the SLIT-SIT group. The follow-up documented a significant increase in grass- and birch-specific IgG and a decrease in grass-specific IgE. Grass-NPT threshold was clearly higher in SLIT-SIT-group (p = 0.01) and only in this group PD20 methacholine improved significantly (p < 0.05)
Combined birch/hazel-SLIT and grass-SIT are safe and improve clinical outcomes of SIT alone in young bisensitized patients. Priming reduction is supported by specific NPT and bronchial hyperresponsiveness
El estudio comprueba la hipótesis de la reducción de la sensibilidad a polen de árboles en pacientes sensibilizados tanto a polen de abedul/avellano como de gramíneas, que reciben inmunoterapia preestacional asociada por vía sublingual/vía subcutánea
36 de 49 pacientes bisensibilizados se distribuyeron en 18 parejas. A todos los pacientes se les administró durante dos años inmunoterapia preestacional subcutánea (SIT) con extracto de polen de gramíneas y a uno de los pacientes de cada pareja se le administró además inmunoterapia sublingual (SLIT) de polen abedul/avellano. Durante tres estaciones polínicas de gramíneas consecutivas, los pacientes rellenaron fichas de puntuación de síntomas/uso de medicamentos. Se realizaron pruebas específicas de provocación nasal con gramíneas y provocación bronquial inespecífica con metacolina. Se valoraron la IgE e IgG séricas específicas
Durante el pico de la estación polínica de gramíneas, ambos grupos mostraron una mejoría significativa de la puntuación total de síntomas. La conjuntivitis y la tos mejoraron significativamente más en los pacientes del grupo SLIT + SIT. Aunque a la necesidad de antihistamínicos disminuyó significativamente en ambos grupos, el uso de medicamentos antiasmáticos sólo disminuyó en el grupo SLIT + SIT. Se observó un incremento significativo de la IgG específica a abedul y gramíneas y una disminución en la IgE específica a gramíneas. El umbral del test de provocación nasal a gramíneas fue claramente superior en el grupo SLIT + SIT (p = 0,01) y sólo en este grupo mejoró significativamente el PD20 con metacolina
La combinación de inmunoterapia sublingual con extracto de polen de abedul/avellano con la inmunoterapia subcutánea con extracto de gramíneas es segura y da una respuesta clínica mejor que la inmunoterapia subcutánea sola en pacientes jóvenes bisensibilizados. La reducción del estímulo lo apoya el test de provocación nasal específico y el de hiperreactividad bronquial con metacolina
Different response to doubling and fourfold dose increases in methacholine provocation tests in healthy subjects
2000, Chest
Citation Excerpt :
A dose-response slope (DRS) was calculated as the percent change inFEV1 as a function of the cumulated methacholinedose and was calculated by linear regression using all measure points,the first point representing the mean value of the preexposure andpostdiluent values. This method differs from the previously reportedmethods when only the end point (ie, the last value) isconsidered.1415161718 All calculations of PC20,PD20, and DRS were made using appropriatealgorithms in a datasheet (Excel; Microsoft; Redmond, WA).
In a modified methacholine provocation testthat was used to study changes in airway responsiveness to occupationalirritants or sensitizers in healthy subjects, two protocols were used:a long protocol (doubling methacholine concentrations between dosesteps) or a short protocol (fourfold increases in concentration). Thismodified methacholine provocation allows measurements of theprovocative dose causing 20% decrease in FEV₁(PD₂₀) in a high proportion of a normal population.
The distribution of PD₂₀ wasinvestigated in healthy nonatopic men without history of allergy orasthma symptoms using the long protocol (n = 101) or the shortprotocol (n = 309). In addition, 30 healthy subjects underwentmethacholine provocation tests using both protocols.
PD₂₀ was defined in 79% of subjectswith the long protocol and in 48% of subjects with the short protocol.The provocative concentration of methacholine causing a 20% decline inFEV₁ (PC₂₀) and PD₂₀ weresignificantly lower using the long protocol: long-protocolPC₂₀ (median [25th to 75th percentile]), 19.9 mg/mL (3.9to > 32 mg/mL) compared with short-protocol PC₂₀, > 32mg/mL (8.7 to >32 mg/mL; p < 0.0001); long-protocolPD₂₀, 4.2 mg (1.6 to 20 mg) compared with short-protocolPD₂₀, > 13.7 (2.6 to > 13.7 mg; p = 0.006). Thedifferences in PD₂₀ using short and long protocols wereconfirmed in a randomized trial of 30 healthy subjects tested with bothprotocols.
Using doubling concentrations,PC₂₀ and PD₂₀ could be defined in a higherproportion of healthy subjects than a protocol using fourfold doseincreases. Furthermore, the doubling protocol results in aPD₂₀ estimate that is less than half the value obtainedwhen using a protocol with fourfold concentrations between dose steps.The difference remains, whether the methacholine effect is regarded ascumulative or noncumulative. The explanation for the difference betweenthe protocols is unclear.
A 1-year study of salmeterol powder on pulmonary function and hyperresponsiveness to methacholine
1999, Journal of Allergy and Clinical Immunology
Background: Long-acting β₂-sympathomimetic agonists such as salmeterol have been proved safe and effective for the treatment of asthma. However, controversy still exists as to the appropriateness of scheduled long-term therapy with these agents. Objective: This study assessed the degree of bronchodilation provided by treatment with salmeterol for a period of 52 weeks and evaluated bronchial hyperresponsiveness to methacholine during and after the treatment period. Methods: Three hundred fifty-two patients with mild to moderate asthma were assessed by 12-hour serial spirometry and serial methacholine challenge tests. Results: The mean area under the FEV₁ curve above baseline over 12 hours after drug at day 1 was significantly greater with salmeterol powder compared with placebo (5.06 liter hours vs 0.77 L/h) and did not change significantly over 1 year. The mean increase in the log₂ of the provocative cumulative methacholine dose producing a 20% decrease in FEV₁ (PD₂₀FEV₁) during treatment was significantly higher in the salmeterol-treated patients than in the placebo group (1.02 doubling doses vs 0.43 doubling doses at week 4, 1.06 doubling doses vs 0.41 doubling doses at week 24). At week 52 the increase from baseline in log₂PD₂₀FEV₁ was not significantly different between salmeterol and placebo (1.08 vs 0.69 doubling doses). Seven days after treatment the log₂PD₂₀FEV₁ was –0.60 doubling doses lower than baseline for salmeterol compared with 0.10 doubling doses for placebo (P = .031). Long-term salmeterol use was not associated with a deleterious effect on asthma control during and after treatment. Conclusion: This study demonstrates that the bronchodilator properties of salmeterol are sustained over 52 weeks and that bronchial hyperresponsiveness to methacholine is decreased to a modest degree during treatment. Clinically significant increases in hyperresponsiveness did not develop after discontinuation of salmeterol treatment. (J Allergy Clin Immunol 1999;104:1189-97.)

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Original articleMeasuring changes in logarithmic data, with special reference to bronchial responsiveness

Abstract

Bronchial reactivity to inhaled histamine: a method and clinical survey

Clin Allergy

Tests of airway responsiveness in epidemiology

Bronchial hyperresponsiveness in two populations of Australian schoolchildren. I. Relation to respiratory symptoms and diagnosed asthma

Clin Allergy

Rapid method for measurement of bronchial responsiveness

Thorax

Original article
Measuring changes in logarithmic data, with special reference to bronchial responsiveness