Guidelines for the descriptive presentation and statistical analysis of contact allergy data

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1 Contact Dermatitis 2004: 51: Copyright # Blackwell Munksgaard 2004 Printed in Denmark. All rights reserved CONTACT DERMATITIS Review Article Guidelines for the descriptive presentation and statistical analysis of contact allergy data WOLFGANG UTER 1,AXEL SCHNUCH 2 AND OLAF GEFELLER 1 1 Department of Medical Informatics, Biometry and Epidemiology, University of Erlangen-Nu rnberg, Erlangen, and 2 Information Network of Departments of Dermatology (IVDK), University of Go ttingen, Go ttingen, Germany On behalf of the ESCD working group: European Surveillance System on Contact Allergies (ESSCA) The present guidelines aim to support clinical researchers in adequately presenting data on contact allergy, and to use statistical tests appropriate for their data. A description of the mode of selection of patients, and of their relevant demographic details, is an essential prerequisite for the correct interpretation of study results. Proportions and rates, if regarded as estimate of these parameters of a target populations, should normally be supplemented with confidence intervals to address precision. Concordance, i.e., agreement between two ratings in a dependent sample, must be quantified with a chance-corrected measure such as Cohen s kappa coefficient. If the diagnostic quality of an outcome is being assessed, standard measures like sensitivity and specificity, as well as the prevalence-dependent positive and negative predictive values should be calculated. Often, contact allergy to a certain substance depends on several factors. In this situation, depending on the research question, techniques like stratification, standardization or multifactorial analysis should be employed. With increasing complexity of statistical description and analysis, consulting with a biostatistician is often mandatory. Key words: contact allergy; clinical epidemiology; statistics; review # Blackwell Munksgaard, Accepted for publication 21 April 2004 Adequate design and performance of experiments and collection of standardized, valid clinical data are well-recognized prerequisites of high-quality studies. However, only if the statistical analysis and the presentation of its results is also of a sufficiently high standard will authors fully exploit the potential of their study and will readers fully be able to evaluate and appreciate its results. The present review aims at providing clinical researchers in the field of contact allergy (CA) with guidelines on selecting those descriptive measures and statistical methods which are most appropriate for their problem. Research questions regarding CA typically comprise the profile of a certain allergen (e.g. pattern of reactions, probably under different test conditions, demographicvariables of sensitized patients, spectrum of cosensitization) or address certain subpopulations with their spectrum of allergens. Owing to the complexity of some research questions, however, the instruments included in this toolbox might not suffice. Direct consultation and liasing with biostatisticians is always advisable. Outcomes and Factors Visual evaluation of type, extent and severity of clinical dermatitis and patch test reactions is still the mainstay of patient management and of clinical CA research. This, combined with the patient s history, including information on occupation, possible sources of allergen exposure and, if possible, the relevance of positive patch test reactions, can be subject to statistical analysis. Hence, the present guidance focuses on such categorical outcomes. Instrument-based measurements, such as those for transepidermal water loss and other non-invasive techniques, microdialysates, (immuno-)histological slides, etc., have their own repertoire of statistical analysis methods, which would exceed the scope of this paper, and have partly been dealt with in other reviews or textbooks. As yet, there are no commonly accepted measurement scales to quantify extent and severity of (allergic) contact dermatitis, which could be comparable to the SCORAD, the EASI, the SASSAD and other instruments used in atopiceczema research (1), but only a few suggestions (2, 3). In

2 48 UTER ET AL. contrast, the grading of patch test reactions to allergens has largely been standardized on an international level (4), with partial refinement by national contact dermatitis groups, e.g. in central Europe (5). Usually, not only the number or percentage of positive reactions should be given, but also the numbers of doubtful and irritant reactions, to obtain a complete view of the reaction profile of the allergen in question. If there is uncertainty about the interpretation of reactions recorded as þ (erythema, infiltrate, possibly papules), these should be presented and analysed separately from stronger positive reactions. Concerning supplementary test methods, useful suggestions for the scoring of repeated open application test (ROAT) results (6) and of reactions to occlusively tested SLS (7), which has recently been advocated as a useful supplement to allergen patch testing (8), are available. To give further aggregated information on the reaction profile of a certain allergen, in addition to the usual proportions of certain types of patch test reactions [doubtful, irritant, (weak/strong) positive], the following parameters have been suggested: (1) The reaction index (RI), introduced by Brasch and Henseler (9): (number of positive reactions number of doubtful or irritant reactions)/(number of positive reactions þ number of doubtful or irritant reactions). Values close to 1 indicate that the proportion of þ to þþþ reactions is much larger than the proportion of doubtful or irritant reactions, values close to 1 the opposite. (2) The positivity ratio (PR) (10) which is simply the proportion of þ reactions among all positive reactions (þ to þþþ). A value of greater than 80% is considered indicative of a problematicallergen. (3) The time pattern in terms of the proportion of crescendo, plateau or decrescendo reactions, e.g. from day 1 (D1) of patch test or D2 to D3 or D4. Comparisons between the types of time patterns have been found particularly useful in photopatch testing (11). However, this may also provide interesting perspectives in the evaluation of conventional patch test results, as with problematicallergens (12) or different concentrations of a marginal irritant. The RI and the PR (i) provide concise information on a certain allergen patch test preparation and (ii) may help to put solitary information on % positive into a more balanced perspective. As an example: octyl gallate [0.3% petrolatum (pet.)], tested in patients, caused 3.5% positive reactions. However, the RI was 0.4 and the PR 92% (10), casting severe doubts on the validity of the majority of positive test results, and also on the suitability of the patch test preparation, for that matter. Patient Selection As a clear prerequisite for meaningful interpretation of research results in terms of CA frequency in a certain group of patients, the denominator must be described clearly in terms of the number of subjects included (if all persons are not tested with all allergens of a panel of allergens, the number tested must be stated for each allergen), the period analysed, the indication for patch testing (aimed testing versus testing consecutive patients) and important demographic characteristics which may have a profound impact on the observed spectrum of CA, e.g. according to the MOAHLFA index (13). Clearly, the proportion of missing data for these items must be kept low by appropriate quality control of routine or study documentation. The MOAHLFA index is an extension of the well-known MOHL (14) and the later MOAHL index (15), which lists the proportions of certain demographicvariables, namely M for male sex, O for occupational causation of dermatitis, A for atopy, H for hand, L for leg, F for face as affected site and the last A for the proportion of patients aged 40 and above. Considering these factors, which all may have an influence on the frequency of sensitization, will help to explain differing results from different centres (13). With regard to the first A, it should be mentioned that this stood for atopy in general in the MOAHL index, i.e. the presense of either atopiceczema, allergic rhinoconjuncitivits or allergic bronchial asthma (15). In contrast, in the MOAHLFA index as suggested, only atopic eczema is considered, because according to current evidence, there seems to be no reason to assume (i) an aetiologically relevant association between CA and mucosal atopicsymptoms and (ii) a relevant impact of the presence of these types of atopic symptoms on the indication for patch testing. Hence, the inclusion of these diseases will render this A in the index less specific, while the proportion of patch tested patients with underlying previous or current atopic eczema will have some impact on the spectrum of CA, either due to presumptive immunological abnormalities or due to disease-specific exposures to topical medicaments, ointment base ingredients, etc., similar to leg dermatitis as underlying condition. While these considerations refer to the presentation of results, appropriate discussion of selection processes, as far as these are known, and their

3 STATISTICS IN CONTACT ALLERGY 49 potential effect on CA frequencies or risk estimates, as appropriate, should supplement the epidemiological interpretation of results. It is often a major criticism of patient-based studies (i.e. clinical epidemiology) that prevalences found in a particular group of patients are (mis-)interpreted as prevalences on a population level. Hence, the results found, if discussed epidemiologically, which may not always be necessary, depending on the research question, should be put into the proper perspective. Delineating the recruitment process for the study subjects, and (where appropriate) quantifying dropouts or non-respondents from the initial study population that could not be included in the analysis, are prerequisites for such an assessment. Probability Number of events 20 Proportions and Rates Very often, proportions (%) are the measure of an outcome of interest, such as the percentage of irritant, doubtful and positive reactions to a certain allergen, or the frequency of selected population characteristics such as sex, occupation, atopy, etc., in the subset of patients testing positive to a certain allergen. Primarily, proportions are descriptive of the study population. Often, however, researchers may want to communicate these results as typical or representative of other persons or patients sharing the characteristics defining their study group. Hence, the study group is regarded as a sample. This implies that the observed proportion is an estimate of the result which would theoretically be observed if all eligible persons in the target population were included in the study. Consequently, the precision of this estimate must be addressed by supplementing the point estimate (the observed proportion) with a confidence interval (CI), usually, but not necessarily, a 95% CI. The extremely useful concept of CI in general can be interpreted as follows: if 100 samples from a given target population were drawn, or 100 groups of patients sharing the same characteristics were assessed, the observed proportion would, in 95 (90, 99) of these 100 samples, lie within the limits indicated by the 95% (90, 99%) CI. Count data such as proportions often follow a binomial distribution: B (n, P); for more details on this classical sampling distribution see textbooks such as (16). The 2 parameters of the binomial distribution are the probability of a single event (P) and the number of experiments or subjects measured (n). Assuming a binomial distribution, the probability that 0, 1, 2, 3, etc. events are observed in the n subjects studied can be calculated. An illustrative example is given in Fig. 1 for an event which has a 0.1 (or 10%) probability Fig. 1. Examples of binomially distributed data, with the parameter probability held constant at 0.1 and n ¼ 10 (dotted lines) and 100 (solid lines). of occurring. The 1st plot shows with dashed lines the probability that 0, 1, 2, etc. events are observed in 10 subjects, the 2nd plot with solid lines shows the corresponding probabilities for a group of 100 subjects. As can be seen from Fig. 1, the binomial distribution, with increasing n, more and more resembles the well-known symmetrical, bellshaped form of the normal distribution. Hence, a normal approximation to the binomial distribution can be used to calculate a CI according to formula (1). This formula exploits the fact that, given a normal distribution, the proportions of events within or beyond a certain span around the mean can be determined. Typically, a 5% error (a) is regarded as acceptable, i.e. 2.5% of measurements may lie below and 2.5% above the CI. Hence, the symmetrical 2.5 and 97.5 percentiles (Z a/2 for a ¼ 0.05) of the standard normal distribution are of interest in determining the CI, i.e and þ1.96 (as can be taken from statistical tabulations). rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^pð1 ^pþ CIð^pÞ ¼^p Z 2 SEð^pÞ; SEð^pÞ ¼ n where Z a/2 is the 100 (1 a/2) percentile of the standard normal distribution, n is the total number of subjects and ^p is the observed proportion (the estimate). The larger the study sample [n in formula (1)], the smaller the standard error [SE in formula (1)] will be, and hence the more precise the estimate, i.e. the narrower the CI. As an example: the point estimate 10% as 10 of 100 is accompanied by a 95% CI of , while for 100 of 1000, the corresponding CI is % according to formula (1). ð1þ

4 50 UTER ET AL. However, for small samples (e.g. n < 30), the exact CI based directly on the binomial distribution is preferable, because the above normal approximation to the binomial distribution, or other types of approximations, may not hold. In summary, CIs provide a valuable measure of the precision of observed proportions, which may help to dispel over-interpretation of results obtained, especially with very small samples. Most statistical software packages offer the calculation of a CI to a proportion. If less than 100 cases are analysed, the use of percentage to describe proportions becomes questionable, while a sample size of less than 10 renders percentage meaningless. While proportions simply quantify the frequency of a certain condition among those examined, rates are measures of the occurrence of events with reference to time such as the heart rate (beats/min) or cancer incidence rate (new cases per persons per year). Thus their unit contains time. In the general field of epidemiology, incidence is the most important rate. However, for CA epidemiology, incidence in terms of the rate of newly sensitized persons has rarely been assessed on a population level [one exception is the Copenhagen Allergy Study (17)]. In the clinical (patient-based) epidemiology of CA, incidence can only be approximately estimated (18). Such computations must be regarded as point estimates just like observed proportions and should also be supplemented with CIs to address precision [see epidemiological textbooks (19)]. Often, the supplementation of CIs to proportions or rates will make formal statistical testing unnecessary. For instance, if CIs of proportions of different subgroups do not overlap, significant difference is already evident. If proportions or rates are statistically tested for differences, the following situations may arise: (1) Comparison of the proportions observed in 2 independent groups of patients (e.g. those with a certain occupation versus those with other occupations or male versus female). The statistical null hypothesis would be equality of proportions, or, in other words, that the 2 samples are derived from the same target population. This hypothesis can be tested with the chi-square test, which examines the departure of observed n ij from expected e ij cell frequencies, summed up over each cell of the k l contingency table, deriving a test statistic with a chi-squared distribution and (k 1)(l 1) degrees of freedom. 2 ¼ Xk i¼1 X l j¼1 ðn ij e ij Þ 2 e ij ð2þ Fisher s exact test is an alternative preferable in case of small samples, e.g. if any of the expected cell counts are less than 5. These 2 tests must not be applied in dependent sample situations [see Measures of Concordance and (20)]. (2) A test for trend of proportions, e.g. over time. Although similar to the previous test problems in terms of the statistical null hypothesis of homogeneity, trend tests take the ordering of the (time) scale into account. One example of a trend test is the chi-squared test for trend (16). Another possibility is the Cochran Armitage trend test. This trend test is based upon the regression coefficient for the weighted linear regression of the binomial proportions on the scores of the levels of the ordered explanatory variable (e.g. time). Risk Estimates Estimates of individual risk all address the question of how much the frequency or likelihood of disease (or other conditions) is increased if a certain factor is present, relative to the frequency or likelihood if this factor is not present. These measures essentially comprise the absolute or relative risk difference, the relative risk (RR), the odds ratio (OR) and the prevalence ratio. The interpretation of a difference in risk between exposed and unexposed heavily depends on the baseline risk (incidence) of the disease and is thus uninformative if communicated alone. The RR, in contrast, is a quotient and thus quantifies the factor by which risk is increased in the exposed independent from baseline frequency. It is typically an incidence-based measure, namely, the incidence found in those exposed divided by the incidence observed in the non-exposed and can thus directly be estimated only in longitudinal (cohort) studies, which are rarely performed in the field of CA, as previously mentioned. Hence, the most commonly used measures are the OR and the prevalence ratio, which are explained in this section. Both can be calculated in crosssectional designs, to which clinical assessment of successive patients (who are seen just once during a certain time frame) bears a similarity. In the simplest, and often simplistic, case of a 2 2 contingency table (Table 1), cross-tabulating the dichotomized outcome with the dichotomized exposure variable, the prevalence ratio is easily calculated just by dividing the proportion (prevalence) of the study group by that of the comparison group: (a/ n E ¼ 1 )/(c/n E ¼ 0 ). The most common measure of risk, however, is the OR, by virtue of several advantages which will not be discussed in depth here. In contrast

5 STATISTICS IN CONTACT ALLERGY 51 Table 1. Different risk estimates illustrated with a 2 2 contingency table. D ¼ disease with D ¼ 1 being the diseased and D ¼ 0 the healthy, E ¼ exposure (risk factor) with E ¼ 1 being the exposed, E ¼ 0 the nonexposed D ¼ 1 D¼ 0 E ¼ 1 a b n E ¼ 1 E ¼ 0 c d n E ¼ 0 n D ¼ 1 n D ¼ 0 n Total to the prevalence ratio (and the RR), the OR is a quotient of 2 odds, i.e. [a/(n E ¼ 1 a)]/[c/(n E ¼ 0 c)] or (a/b)/(c/d). With decreasing risk of a disease (which can be translated into decreasing prevalence here) P, the risk of that disease and its odds P/(1 P) become more and more similar, because 1 P asymptotically approaches 1. Consequently, the quotients based on risk versus odds become more and more similar, i.e. the OR becomes a valid approximation of the RR when the rare disease assumption holds. There are no strict rules as to when a disease can be regarded rare enough; however, if the disease prevalence does not exceed 1%, the numerical discrepancy between OR and RR is negligible. Asymptotic95% CIs to the OR, based on an approximation of the normal distribution already introduced, can be calculated according to the following formula: ORÞ; CI 95% ðorþ dor ¼e In OR c Z2 SEðInc OR rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SEðIn cse ORÞ dor ¼ a þ 1 b þ 1 c þ 1 d Some statistical software packages offer the calculation of exact CIs, which are preferable especially in the case of small sample sizes. However, while a valid description of the precision of a crude (unadjusted) risk estimate by exact CIs is an important issue, the risk estimate itself may critically depend on other factors, the so-called confounders. As an example: the prevalence of nickel allergy has often been found to be very high in hairdressers, compared to other occupations, raising the suspicion that nickel is an occupational allergen. However, if the young age and predominantly female sex of ð3þ hairdressers is taken into account, both factors strongly associated with nickel allergy via age- and sex-characteristic fashion habits, nickel CA appears only slightly more common, if at all. In this and similar situations, a multifactorial analysis or other techniques adjusting for such confounding effects must be employed. Measures of Concordance The term concordance is colloquially used to describe simultaneous (concomitant) reactions to allergens. However, the concept of concordance in a stricter sense means agreement between ratings of 2 different observers, evaluating the same outcome in the same set of subjects. Beyond this original application, the concept of concordance as outlined below can be applied to describe test reactions observed during synchronous patch testing in the following situations: (1) Comparing test results obtained with different test methods, e.g. 24 versus 48 h patch test application, large versus small test chambers (20), water versus ethanol as test vehicle, or otherwise different preparations of the same allergen. (2) Comparing test results with mixes and any of their individual constituents. (3) Comparing test reactions to allergens which are structurally related, like fragrances (21) or para-amino compounds (22). The use of the concept of concordance to quantify agreement between test results is the only appropriate approach in the 1st situation and a useful additional measure in the other 2 situations. The sole consideration of the percentage of concordant ratings ( Table 2) P o : P O ¼ n 11 þ n 00 n and other measures based directly on these proportions will give a misleading, overly optimistic impression of concordance, because by chance Table contingency table illustrating a dependent sample situation with a left versus right comparison: Observed concordance Expected (random) concordance Right: positive Right: negative Right: total Left: positive n 11 n 10 n 11 þ n 10 n^p^q n^pð1 ^qþ n^p Left: negative n 01 n 00 n 01 þ n 00 nð1 ^pþ^q nð1 ^pþð1 ^qþ nð1 ^pþ Left: total n 11 þ n 01 n 10 þ n 00 n n^q nð1 ^qþ

6 52 UTER ET AL. alone a certain proportion of ratings P e will agree, with ^p being the probability of one positive rating, and ^q the probability of the other positive rating: P e ¼ ^p ^q þð1 ^pþð1 ^qþ Hence, only the agreement beyond chance should be considered. A well-known measure of chance-corrected agreement for categorical data such as patch test results is Cohen s kappa (23), either as simple k for 2 2 contingency tables (formula 4) or as weighted k for larger, symmetrically structured tables of ordinal data. ¼ P o P e 1 P e ð4þ The actual k value can be regarded as an estimate and should thus be supplemented with CIs. A refined interpretative scale has been proposed with k values of suggesting slight, fair, moderate, substantial and (almost) perfect agreement (24). However, the application of Cohen s kappa, or any other measure of concordance, for that matter, is not without pitfalls, e.g. similar k values may have an altogether different meaning in samples with very different prevalences of the outcome (25). Typical examples of the application of the k coefficient include the quantification of concordance between patch test results in a study with synchronous duplicate application of allergens (26), ranging between 0.86 (nickel sulfate 5% pet., p-phenylenediamine 1% pet.) and 0.56 (formaldehyde 1% aqueous) in this study or the evaluation of the pattern of c ross-sensitivity among different para-amino compounds (22). Statistical Testing in Dependent Samples Concordance, as described above, is a concept suitable for describing agreement between 2 outcomes observed in 1 set of patients, i.e. in dependent samples. Sometimes, beyond description, statistical analysis of such paired sample results may be an issue. Examples for this include statistically testing for differences between: (1) Test results obtained in the same patients with different concentrations, vehicles, exposure times, chamber sizes, etc. of an allergen. (2) Responses to allergen or irritant challenge before and after some therapeuticintervention in the same patients. In these and similar cases, it is not the concordant test results (using Table 2 for illustration purpose: n 00 and n 11 ) that are informative, but the discordant test results (n 01 and n 10 ), namely, the degree of asymmetry: if discordant results are essentially symmetrically distributed, it is reasonable to assume that they merely reflect chance variation, and not a systematicdifference. If, however, more discordant results are observed in a particular area of the contingency table, this may indicate a systematic difference. For 2 2 contingency tables (Table 2), McNemar s test, which is also available as an exact test based on the binomial distribution, is suitable to assess the null hypothesis of no difference. In quadratic contingency tables larger than 2 2, the Bowker test or a generalized Cochran Mantel Haenszel test can be applied. For an extensive explanation and discussion of the application of this class of statistical tests see (20). Assessment of Diagnostic Quality Diagnostictests are evaluated against a gold standard to examine their diagnosticproperties. These include (for an explanation of abbreviations see Table 3) (1) sensitivity (the proportion of diseased testing positive: a/n D ¼ present ), (2) specificity (the proportion of healthy persons testing negative, d/n D ¼ absent ), (3) the positive predictive value (PPV) [the proportion of persons testing positive being actually diseased (a/n T ¼ pos )], (4) the negative predictive value (NPV) (the proportion of persons testing negative being actually healthy (d/n T ¼ neg )]. The gold standard is a method with high, proven validity. In the field of CA, there is as yet no real gold standard that could diagnose CA at least as validly and reliably as the patch test itself. Hence, patch test results can only be evaluated against surrogates of a gold standard, such as a positive history of intolerance to the respective allergen, or the results of a provocative use test or ROAT. Conversely, for the time being, the patch test must be regarded as the gold standard against which new laboratory tests are evaluated. Table 3. Different measures of diagnosticperformance illustrated with a 2 2 contingency table. D ¼ disease (according to gold standard criterion), T ¼ test to be evaluated D ¼ present D ¼ absent T ¼ positive a b n T ¼ positive T ¼ negative cd n T ¼ negative n D ¼ present n D ¼ absent n Total

7 STATISTICS IN CONTACT ALLERGY 53 When assessing the sensitivity, specificity and other properties of allergen patch tests against the references mentioned, it should be kept in mind that these can only be as good as the gold standard chosen, which is as yet always far from ideal. However, despite the lack of a truly suitable external criterion for the validation of patch test results, the concepts used for the assessment of diagnostic properties can also be applied successfully within the realm of patch testing itself, e.g. for the evaluation (i) of mixes against reactivity to their constituents [e.g (27)] or (ii) of single marker allergens against reactivity to allergens that they are considered markers of. Note that when constituents are tested only in the case of a positive reaction to the mix used for screening, sensitivity and specificity cannot be calculated, as the row T ¼ negative is missing (Table 3), but only the PPV. Percentages such as sensitivity, specificity and PPV and NPV should be supplemented with (95%) CIs, to address the issue of precision. Being proportions, these can be calculated as described above. When interpreting the NPV, their dependency not only on sensitivity (Sens) and specificity (Spec) but also on the prevalence P of disease (of CA, in this context) must be considered (formula 5), which has also been illustrated by a recent paper in this journal (28): PPV ¼ NPV ¼ Sens P Sens P þð1 SpecÞ ð1 PÞ Spec ð1 PÞ Spec ð1 PÞþð1 SensÞ P According to this, the PPV of a positive patch test result is (much) higher, hence, the proportion of false-positives (much) lower, in a typical clinical setting, where patients with suspected CA are patch tested and the a priori likelihood of CA is high, relative to patch testing in the general population unselected for specific morbidity. This relationship seriously limits the value of patch test studies in the general population, at least concerning allergens which are not common. In contrast, in view of the relatively low prevalence even of common CAs even in patch test patients (with, e.g., nickel sulfate rarely exceeding 20%), the NPV is not so much of a problem, because it increases with decreasing prevalence. In the case of sensitivity and specifity both being 80% as an arbitrary assumption and a prevalence of 20%, the NPV is 94.1% (PPV ¼ 50%, i.e. every other test result is false-positive). If the prevalence is 10%, the NPV is 97.3% (PPV ¼ 30.8%), and if the prevalence is 1%, the NPV is further increased ð5þ to 99.7%, while the PPV decreases to a mere 3.9%. Hence, from a statistical perspective, a negative patch test result can confidently be interpreted as reflecting nonexistent CA, whereas a positive test result has to be interpreted cautiously. Clearly, in individual cases the a priori likelihood of CA to a range of allergens is highly variable, if the history of the patient is carefully taken into account. If the history is suggestive of a certain CA, a negative result, even with well-established test preparations such as nickel sulfate 5% pet. (29), should be challenged. The opposite, the evaluation of positive test reactions in the light of a possibly negative history, is the assessment of clinical relevance which will not be dealt with here. Stratification and Standardization The outcome of interest, such as CA to certain allergens, may occur more or less frequently in certain subgroups defined by age, sex, occupation or other characteristics. If these very differences in distribution are the main research interest, a stratified analysis, i.e. separate analyses for each subgroup, is usually performed and presented [for example (30)]. At the same time, stratification is one possible strategy of confounder control, by performing separate analyses for each different level of the confounding factor, such as sex (male versus female) or age (40 versus <40 or 10-year age strata) or other factors. This will, however, lead to a multitude of stratumspecific prevalences, which may be hard to interpret as a whole. In this case, a unifying view may be achieved by suitably standardizing the prevalence by the confounders concerned. Standardization is a well-established technique to increase comparability of descriptive results such as incidence and prevalence data. With this aim in mind, it has been introduced to clinical CA research (31). There are essentially 2 methods of standardization: direct and indirect. To put it simply, indirect standardization involves calculating a quotient, in this context a standardized morbidity ratio (SMR), from the prevalence observed in the study sample P obs and the expected prevalence P exp. The expected prevalence P exp is the weighted sum of the stratum-specific prevalences P i * in the reference population (the asterisk indicating that this quantity is not directly observable in the study and has to be plugged in using external information). The weights are the relative sizes of each stratum in the study group h i (formula 6). SMR ¼ P obs P exp ; P ind ¼ X i h i P i ð6þ

8 54 UTER ET AL. In contrast, direct standardization involves calculating a weighted sum P dir of stratum-specific prevalences (of CA to a particular allergen) observed in the study group P i, the stratumspecific weights being the relative sizes of each stratum in the reference population h i * (formula 7). P dir ¼ X i h i P i ð7þ The advantage of direct standardization is that the proportion, in terms of an adjusted proportion, is preserved as an intuitively accessible absolute measure of morbidity, whereas the SMR is a relative measure, similar to the RR. The choice of the reference group for direct standardization is, in principle, arbitrary. Either an off-the-shelf population such as that proposed by Segi (32) or the standard population recently proposed by the WHO (33), or a self-defined reference population (31) can be used, as long as the combined distribution of all relevant factors is known or defined. The effect of direct standardization is well illustrated by a previous article in this journal (13). Approximative CIs can be calculated to standardized proportions, based on the weighted sum of the variances per stratum [see formula 15-7 (19)]. Control of Confounding Many research questions will address 1 particular factor of interest, such as a certain occupation (compared to other occupations), or a certain year of patch testing versus another reference year, if changes over time are an issue. In this situation, other factors associated both with the factor of interest and the outcome, i.e. potential confounders, may distort this comparison (Fig. 2). There are several ways of controlling for potential confounders: (1) Restriction: limiting analysis to a subset of persons who do not differ with regard to confounding variables, e.g. young females only, Exposure of interest: Work as hairdresser Confounding variable(s): (young) age (female) sex Fig. 2. Confounding: principle and an example. Outcome: Nickel allergy both in the study group and in the comparison group, in our nickel and hairdressing example. This, however, will impair generalizability of results and reduce the statistical power of the study due to the reduction in sample size; (2) Stratification: giving separate results for each subgroup defined by the (combined) confounding variable(s); (3) Matching: by study design, the comparison group is made similar to the study group regarding the distribution of confounding variables, e.g. similar proportions of young and old, males and females (frequency matching), or by matching 1 or more controls to each single case with regard to confounding variables (individual matching). In the analysis of matched study data, the matching variables must be duly considered, which is an issue of multifactorial analysis beyond the scope of this article; (4) Standardization (if descriptive measures are concerned); and (5) Adjustment techniques in terms of multifactorial analysis (see below). Multifactorial analysis plays an important role in the clinical epidemiology of CA [one of the 1st examples of its application was an analysis by the Danish Contact Dermatitis Group (34)]. Multifactorial Analysis Adjusted risk estimates may be derived from a stratified analysis, yielding separate risk estimates for each stratum, i.e. combinations of confounding factors. This estimate is the sum of all single stratum-specific estimates weighted by a weighting scheme, often reflecting the relative size of the stratum, given sufficient homogeneity across the strata. However, other multifactorial analyses are often preferable because they offer the added value of being able to derive risk estimates for several factors of interest at the same time, which are mutually adjusted. Multiple linear regression analysis is an expansion of simple linear regression (16, 35). In simple regression, a directional relationship between 1 independent factor X and 1 dependent outcome Y is postulated, estimated by fitting a regression line which optimally represents this relationship and quantified by a regression equation, which includes an intercept term and a slope coefficient b. Y ¼ þ X Multiple linear regression analysis is a wellknown means of analysing the association ð8þ

9 STATISTICS IN CONTACT ALLERGY 55 between a metricresponse (outcome) variable and several, categorical or metric, explanatory (risk) factors. In this type of analysis, the b coefficient is an indicator of the strength of association between the outcome and the respective factor, adjusted for the impact of all other factors. This useful approach can be generalized to accommodate modelling of binary outcome data, like the presence of a certain disease, or a positive reaction to a certain contact allergen. Furthermore, dependent longitudinal data can be analysed employing generalized estimating equations. A comprehensive discussion of all aspects of these complex statistical tools can be found in textbooks [e.g. (19, 36] and exceeds the scope of this article. Conclusion The recommendations given above are by no means an exhaustive review or cover all statistical methods potentially relevant to CA reseach. However, according to our experience, they do address the most common problems and might thus be useful to researchers in the clinical epidemiology of CA when preparing, performing and analysing a study, and when eventually writing a manuscript. We hope that due consideration of these recommendations will further improve the quality of CA research papers. References 1. Charman C, Williams H. Outcome measures of disease severity in atopiceczema. Arch Dermatol 2000: 136: Smit H A, Coenraads P J, Lavrijsen A P M, Nater J P. Evaluation of a self-administered questionnaire on hand dermatitis. Contact Dermatitis 1992: 26: Uter W, Pfahlberg A, Gefeller O, Schwanitz H J. Hand eczema in a prospectively followed cohort of office-workers. Contact Dermatitis 1998: 38: Wahlberg J E. Patch testing. In: Textbook of Contact Dermatitis, Rycroft R J G, Menne T, Frosch P J, Leppoittevin J-P (eds), Berlin: Springer, 2001: Schnuch A, Aberer W, Agathos M, Brasch J, Frosch P J, Fuchs T, Richter G. 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Contact Dermatitis 1985: 12: Altman D G. Practical Statistics for Medical Research. London: Chapman & Hall; Nielsen N H, Linneberg A, Menne T, Madsen F, Frølund L, Dirksen A, Jørgensen T. Incidence of allergic contact sensitization in Danish adults between 1990 and 1998; the Copenhagen Allergy Study, Denmark. Br J Dermatol 2002: 147: Schnuch A, Uter W, Geier J, Gefeller O. Epidemiology of contact allergy: an estimation of morbidity employing the clinical epidemiology and drug-utilization research (CE-DUR) approach. Contact Dermatitis 2002: 47: Rothman K J, Greenland S. Modern Epidemiology. Philadelphia: Lippincott-Raven, Gefeller O, Pfahlberg A, Geier J, Brasch J, Uter W. The association between size of test chamber and patch test reaction: a statistical reanalysis. Contact Dermatitis 1999: 40: Schnuch A, Lessmann H, Geier J, Frosch P J, Uter W. Contact allergy to fragrances: frequencies of sensitization from 1996 to Results of the IVDK. Contact Dermatitis 2004: 50: Uter W, Lessmann H, Geier J, Becker D, Fuchs T, Richter G. Die Epikutantestung mit Parastoffen. Dermatol Beruf Umwelt 2002: 50: Fleiss J L. Statistical Methods for Rates and Proportions. New York: Wiley, Landis J R, Koch G G. The measurement of observer agreement for categorical data. Biometrics 1977: 33: Thompson W D, Walter S D. A reappraisal of the kappa coefficient. J Clin Epidemiol 1988: 41: Uter W, Pfahlberg A, Brasch J. Zur Reproduzierbarkeit der Epikutantestung Die Bewertung der Konkordanz bei synchroner Applikation. Allergologie 2002: 25: Geier J, Gefeller O. Sensitivity of patch tests with rubber mixes: results of the Information Network of Departments of Dermatology From 1990 to Am J Contact Dermat 1995: 6: Diepgen T L, Coenraads P J. Sensitivity, specifity and positive predictive value of patch testing: the more you test, the more you get? Contact Dermatitis 2000: 42: Dooms-Goossens A, Naert C, Chrispeels M T, Degreef H. Is a 5% nickel sulphate patch test concentration adequate? Contact Dermatitis 1980: 6: Buckley D A, Rycroft R J, White I R, McFadden J P. The frequency of fragrance allergy in patch-tested patients increases with their age. Br J Dermatol 2003: 149: Schnuch A. PAFS: population-adjusted frequency of sensitization. (I). Influence fo sex and age. Contact Dermatitis 1996: 34: Segi M. Cancer mortality for selected sites in 24 countries ( ). Sendai: Tohoku University of Medicine, 1960.

10 56 UTER ET AL. 33. Bray F, Guilloux A, Sankila R, Parkin D M. Practical implications of imposing a new world standard population. Cancer Causes Control 2002: 13: Christophersen J, Menné T, Tanghoj P et al. Clinical patch test data evaluated by multivariate analysis. Danish Contact Dermatitis Group. Contact Dermatitis 1989: 21: Matthews D E, Farewell V T. Usingand Understanding Medical Statistics. Basel: Karger, Kleinbaum D G, Kupper L L, Morgenstern H. Epidemiologic Research. New York, USA: van Nostrand Reinhold, Address: Wolfgang Uter, MD Institut fu r Medizininformatik Biometrie und Epidemiologie Friedrich Alexander-Universita t Erlangen-Nu rnberg Waldstreet Erlangen Germany Tel: þ Fax: þ wolfgang.uter@rzmail.uni-erlangen.de