Pharmacokinetic profiles of 5 mg/kg ibudilast, a phosphodiesterase inhibitor, orally administered to dogs in fasted and non-fasted states. A preliminary study

Ibudilast (AV-411) is a non-selective inhibitor of cyclic nucleotide phosphodiesterase (PDE). It is currently marketed for human use in Asian countries for the treatment of asthma, cerebrovascular disorders and ocular allergies. Ibudilast has also been found to have an analgesic action for neuropathic pain at doses 5-10 times higher than those used in asthma therapy. Six healthy Labrador dogs were randomly assigned to two treatment groups using an open, single-dose, two-treatment, two-phase, cross-over design (2x2 Latin-square). Dogs in group 1 (n=3) were fasted for at least 10 hours overnight before the beginning of the experiment and 4 h following dosing while dogs in group 2 (n=3) received food ad libitum. During the first phase, each dog in group 1 and 2 received a single dose of 5 mg/kg ibudilast administered orally. After 1-week washout period the groups were rotated and the experiment was repeated. The analytical method, validated for dog plasma, was shown to be linear in the range 0.10-20 μg/mL. The limit of detection (LOD) and quantification (LOQ) were 0.03 and 0.1 μg/mL, respectively. No behavioural or health alterations were observed in the animals during or after the study. Ibudilast was detectable in plasma for up to 24 h showing a wide variability between animals. Although no statistically significant differences were observed in the present study between the fed and fasted states, examination of the raw data suggests that an effect may be present. The wide degree of variation observed in area under the curve (AUC) suggests that the investigation of population pharmacokinetic modelling is warranted.

Data Processing Problems for Multidisciplinary, Mixed-Longitudinal Studies with Application to the Nijmegen Growth Study

As more complex, computer-oriented studies of growth and development are undertaken, it becomes increasingly important that investigators contemplating the initiation of such studies are aware of some of the data processing problems they are likely to encounter. The present paper discusses some of these problems in the context of multidisciplinary, mixed-longitudinal growth studies and the solutions implemented in the Nijmegen Growth Study are documented.

Pharmacokinetic profiles of the analgesic drug flupirtine in cats

Flupirtine (FLU) is a non-opioid analgesic drug with no antipyretic or antiphlogistic effects, used in the treatment of a wide range of pain states in human beings. There is a substantial body of evidence on the efficacy of FLU in humans but this is inadequate to recommend its off-label use in veterinary clinical practice. The aim of this study was to evaluate the pharmacokinetic profiles of FLU after IV and PO administration in healthy cats. Six mixed breed adult cats were randomly assigned to two treatment groups using an open, single-dose, two-treatment, two-phase, paired, cross-over design (2 × 2 Latin-square). Group 1 (n  =  3) received a single dose of 5 mg/kg of FLU injected IV into the jugular vein. Group 2 (n  =  3) received the same dose via PO route. The wash out period was 1 week. Blood samples (1 mL) were collected at assigned times and plasma was then analysed by a validated HPLC method. No adverse effects at the point of injection and no behavioural changes or alterations in health parameters were observed in the animals during or after the study (up to 7 days after the full study). After IV administration, FLU was detectable in plasma up to 36 h. After PO administration, FLU plasma concentrations were lower than those following IV administration, but they were detectable over the same time range. The terminal part of both mean pharmacokinetic curves showed a similar trend of elimination. The oral bioavailability was approximately 40%. This is the first study of FLU in an animal species of veterinary interest and it could pave the way for the use of this active ingredient in the veterinary field.

Sulfachlorpyrazine residues depletion in turkey edible tissues

Sulfachlorpyrazine (SCP) is currently used to treat coccidian infections in turkeys; however, there is no information available about the withdrawal period necessary for the turkey to be safe for human consumption. A high performance liquid chromatography method with ultraviolet-visible light detection was adapted and validated for the determination of SCP in turkey tissues. The procedure is based on isolation of the (SCP sodium) compound from edible turkey tissues (muscles, liver, kidneys, and fat with skin) with satisfactory recovery (72.80 +/- 1.40) and specificity. The residue depletion of SCP in turkeys was conducted after a dose of 50 mg/kg body weight/day had been administrated orally for 3 days. After treatment has been discontinued residue concentrations were detected in tissues on the 7th day. The highest SCP concentrations were measured in muscles. Based on the results presented in this study, it could be assumed that a withdrawal period of 21 days, before medicated turkeys could be slaughtered, would be sufficient to ensure consumer safety.

Greater disability with increased pain involvement, pain intensity and depressive preoccupation

Persistent pain is often accompanied by functional disability. This study investigated the effect of pain extent and the involvement of specific pain sites on pain-related disability, as determined by the Pain Disability Index (PDI). Complete data were available from 278 persistent facial pain (PFP) patients. Patients were divided into one of two groups based on drawings of their pain distribution. When the patient's pain drawing was limited to the region supplied by the trigeminal nerves (Nn. V(1) V(2), and/or V(3)), with or without the inclusion of any combination of the cervical dermatomes C2, C3 and C4, the patient was assigned to the local/regional pain group. If the pain extended beyond this area, the patient was allocated to the group exhibiting widespread pain. In addition to the PDI, patients filled out the Beck Depression Inventory (BDI) and the State-Trait Anxiety Inventory (STAI). The local/regional pain group had significantly lower scores on the PDI, the BDI and STAI state than cases with widespread pain. Patients with widespread pain who indicated pain locations in any one or more of the extremities plus the lower back scored significantly higher on the PDI and the BDI than patients with no such combined involvement. Multiple regression analysis revealed that depressive preoccupation, pain extent and pain intensity were significant predictors of pain-related disability, whereas the STAI was not. If controlled for pain extent and pain intensity, the presence of high as opposed to low depressive scores added almost 11 points to the PDI score. These results showed that pain distribution, pain intensity and depressive mood are significant predictors of pain-related disability.

Generic pain intensity scores are affected by painful comorbidity

AIMS

To determine the degree to which the generic pain intensity rating (i.e., overall and without reference to a particular body site) of facial pain patients being seen in a specialty setting for facial pain is influenced by painful comorbidity in body parts other than the face.

METHODS

In this prospective study, 40 consecutive female temporomandibular pain patients rated their generic pain on a 100-mm visual analog scale. After marking all painful body sites on pain drawings, patients were asked to rate the pain intensity for each of the indicated pain sites; the patients did not have access to the generic pain intensity score. Pearson's correlation coefficient was used to correlate the generic pain intensity score with site-specific pain intensity ratings, their mean and maximum, and the number of pain sites.

RESULTS

The medians of the generic, maximum, and facial pain intensity scores were 49.5, 53, and 45.5, respectively. The generic pain intensity rating correlated more highly with the intensity scores reported for the most painful body site (r2 = 0.82; P < 0.001) than with the average rating across all painful sites (r2 = 0.62; P < 0.001), or the pain intensity score in the face (r2 = 0.61; P < 0.001). The number of pain sites did not correlate to any statistically significant degree with the generic pain intensity rating (r2 = 0.006; P = 0.65).

CONCLUSION

The results of this study suggest that the maximum visual analog scale pain intensity score, observed in any body location, is a better reflection of the generic pain intensity rating than the corresponding score of the face. To avoid over-rating or underrating of facial pain intensity, patients should be instructed to provide site-specific pain intensity scores if painful comorbidity is present.

Habituation of the early pain-specific respiratory response in sustained pain

Neurokinin-1 receptor and mu-opioid receptor agonists affect respiratory rhythm when injected directly into the preBötzinger brainstem complex, which is the hypothesized site for respiratory rhythmogenesis in mammals (Science 286 (1999) 1566). Early stress-induced analgesia (SIA) is naloxone-insensitive and as such considered independent of the activation of the mu-opioid system. Prolonged application of electrical shocks, however, produces analgesia that is mediated by the mu-opioid system (Science 208 (1980) 623). Together these findings suggest that any early pain-specific increased respiration should be attenuated in the tonic state of pain. Ten healthy, pain-free female volunteer subjects participated in this experimental study involving deep acute and tonic pain. The experimental design included three conditions: (1) baseline; (2) pain; and (3) a placebo control stimulus. Experimental pain was induced by the infusion of hypertonic saline into the masseter muscle. Infusion of isotonic saline in the contralateral masseter was used as a control. Blinded subjects were randomly assigned to a particular sequential order of the experimental stages, i.e. hypertonic saline infusion preceded the isotonic saline infusion or vice versa. Respiration rate, mean peak inspiratory and expiratory flow rates, and the minute ventilation volume quantified breathing. Results indicate that effects on respiration were pain-specific and that the early effects on respiration were significantly attenuated in sustained pain. In the early stage of pain, all monitored variables (respiration rate, minute ventilation volume, and inspiratory and expiratory flow rates) were elevated to statistically significant degrees when compared to measurements taken at baseline or during control infusion. Only respiration rate continued to be significantly elevated in sustained pain. We concluded that rhythmogenic neurons in the preBötzinger brainstem complex appear as the likely target for pro-nociceptive and anti-nociceptive input, explaining both the observed initial facilitation and subsequent habituation of respiration in early and sustained pain.

Humoral immunity to stress proteins and periodontal disease

BACKGROUND

There is evidence that microbial heat shock (stress) proteins (Hsp) are immunodominant antigens of many microorganisms. Immunity to these proteins has been shown in non-oral infections to contribute to protection. This study was undertaken to assess the relationship(s) between immunity to human and microbial heat shock proteins, periodontal disease status, and colonization by periodontal disease-associated microorganisms.

METHODS

Subgingival plaque and blood samples obtained from 198 patients during an earlier clinical study were examined for the presence of specific periodontal disease-associated microorganisms and antibodies to selected human and microbial heat shock proteins (Hsp70, Hsp90, DnaK, and GroEL). Particle concentration immunofluorescence assay (PCFIA) was used to detect anti-Hsp antibodies and slot immunoblot assay (SIB) was used to detect subgingival plaque species. Regression models were used to examine the contribution of age, gender, gingival index, probing depth, attachment loss, calculus index, plaque index, and microbial colonization to the anti-Hsp antibody concentrations.

RESULTS

Our studies demonstrated that, when evaluated by ANOVA, patients with higher anti-Hsp (Hsp90, DnaK, and GroEL) antibody concentrations tended to have significantly (P< or =0.05) healthier periodontal tissues. This was most obvious when the relationship between mean probing depths and antibody concentrations were studied. For Hsp90 antibodies, 2 variables (probing depth and P. gingivalis concentration) were found to have significant contributions (R = 0.293, P<0.0002). The equation derived from the regression model was y = 12558-2070*PD +1842*PG. This confirmed the inverse relationship with probing depth and the positive relationship with colonization by P. gingivalis. Attempts to model the other stress protein antibodies were not successful.

CONCLUSIONS

We believe that the present observations reflect the presence of protective anti-Hsp antibodies, rather than simply the presence of the microorganism in the gingival sulcus. The clinical significance of these observations lies in the potential of identifying patients who are at risk for developing periodontal disease based on their inability to mount an immune response to specific Hsp or Hsp epitopes, as well as the development of vaccines based on Hsp epitopes.

Spatial and temporal summation of sensory and affective dimensions of deep somatic pain

There is considerable evidence in support of differential information processing of the sensory-discriminative and motivational-affective meanings of pain. The purpose of this work was to examine whether temporal (acute, tonic, persistent) and spatial (local, regional, widespread) aspects of deep somatic pain influence the sensory and affective dimensions of pain. Acute pain consisted of a short bout of pain, lasting about 100 s. Tonic pain was the experience of experimentally maintained pain for 18 min. Both acute and tonic pain were induced by infusion of an algesic or control substance into muscle with the subject blinded with respect to the type of infusion and randomization of the application sequence. Comparing the response of experimental subjects to a group of matched cases with persistent masticatory myalgia alone or in combination with widespread musculoskeletal pain, we examine whether the experimental state is different from the matched clinical condition, and whether there is a difference between the condition being restricted to the face or not. The McGill pain questionnaire was used to assess the sensory and affective correlates of pain. The normalized sensory score for acute/unilateral face pain was different from that established for tonic/unilateral face pain (P = 0.055, borderline s.), and so was the normalized affective score (P = 0.009, s.). When comparing tonic/unilateral versus tonic/bilateral face pain, the affective scores increased with increased pain involvement (P = 0.009, s.) while the sensory sores were unaffected by the additional pain induced in the contralateral masseter muscle (P = 0.357, n.s). Notably, sensory and affective scores for tonic/bilateral and persistent/bilateral face pain were not statistically different (sensory: P = 0.169, n.s.; affective: P = 0.643, n.s). On the other hand, when contrasting persistent/bilateral face pain with persistent/ widespread musculoskeletal pain, both scores were significantly different (sensory: P < 0.001, s.; affective: P = 0.041, s.). Time in and spread of pain influenced the perceptual correlates of pain to a significant degree. The major increase in the sensory dimension occurred from 'no pain' to 'acute pain'. Affective scores showed the most significant increases from acute to tonic pain, particularly with greater spatial involvement. The significant increases in sensory scores observed when contrasting persistent facial pain alone and in combination with widespread musculoskeletal pain was attributed to the broader body experience. Because the perceptual correlates of tonic and matched persistent (chronic) pain states were similar, we concluded that it does not require months for the development of the sensory and affective meaning of persistent pain as assumed.

Pain descriptors characteristic of persistent facial pain

The McGill Pain Questionnaire is an instrument that is widely used to assess the multidimensional experience of pain. Although it was introduced more than 20 years ago, limited information is available about its use in patients suffering from persistent facial pain. The aim of this study was to investigate the response patterns of persistent facial pain patients to the McGill Pain Questionnaire, to correlate these patterns with patients' beliefs about the seriousness of the condition, and to compare the findings with data reported from other painful conditions. The study sample consisted of 200 consecutive female patients referred to a tertiary care facial pain clinic. The Pain Rating Index scores of the McGill Pain Questionnaire subscales and the total number of words chosen by these patients closely matched the summary scores reported by Wilkie et al, who pooled data from seven pain conditions (cancer, chronic back, mixed chronic, acute/postoperative, labor/gynecological, dental, and experimentally induced) in their meta-analysis. On the other hand, when the data collected in this study were compared with those from specific clinical subsets, such as cancer patients, chronic back pain patients, or dental patients, differences in McGill Pain Questionnaire scores could be identified. Differences were also found in the choice of specific pain descriptors. More than 20% of the facial pain patients selected "radiating" and "pressing"; this was not the case for those suffering from other pain conditions. Facial pain patients who felt that their condition was more serious or different from what the treatment providers had told them had a greater likelihood of choosing specific word categories of the McGill Pain Questionnaire.

Treatment-seeking patterns of facial pain patients: many possibilities, limited satisfaction

Knowledge about the different kinds of treatment provided to patients with nonmalignant musculoskeletal facial pain is limited. The present study was based on 206 consecutive patients who were referred to a university-based tertiary care clinic for the diagnosis and management of persistent facial pain. Its purpose was to get information about the number and specialty of providers consulted by patients prior to their referral, and to follow the underlying treatment-seeking patterns. The results showed that on average 4.88 providers from 44 different categories were consulted. A general dentist or a dental specialist was seen by about 70% of patients. For patients whose first provider was a dentist, the most likely subsequent provider was another dentist. Conversely, if the first provider was a physician, chances were greater that the subsequent provider was a physician rather than a dentist. Among the nondental therapies patients received, physical therapy was chosen most frequently (42.2%). More than 60% of patients had at least one nondental treatment; however, the majority of these patients experienced two or more different types of such therapy (e.g., chiropractic, osteopathic, relaxation training). Patients' satisfaction with care and treatment was moderate, since only 18.5% of the patients were very satisfied, while 27.7% were dissatisfied or very dissatisfied. The present findings, which corroborate a recent study from the Kansas City, Missouri, region, indicate that patients with persistent facial pain see a large number of different providers, and that nonmedical/nondental treatment approaches are common. The moderate satisfaction experienced with any of the therapies points out that much needs to be done before this patient population is served satisfactorily.

Pain maps from facial pain patients indicate a broad pain geography

Two hundred consecutive female patients, who were referred to a university-based facial pain clinic, were asked to mark all painful sites on sketches showing the contours of a human body in the frontal and rear views. The drawings were analyzed with transparent templates containing 1875 (frontal view) and 1929 (rear view) square cells of equal size. The average patient scored 71.8 cells in the frontal and 99.7 cells in the rear view (corresponding to 3.8% and 5.2% of the maximum possible scores). In individual patient drawings, however, up to 42.7% and 44.9% of all cells were marked. Only 37 cases (18.5%) exhibited pain that was limited to the trigeminal system. An analysis of the pain distribution according to the arrangements of dermatomes revealed three distinct clusters of patients: (1) pain restricted to the region innervated by the trigeminal nerves (n = 37); (2) pain in the trigeminal dermatomes and any combination involving the spinal dermatomes C2, C3, and C4, but no other dermatomes (n = 32); and (3) pain sites involving dermatomes in addition to the ones listed above (n = 131). Mean ages in the three clusters were 38.7, 35.5, and 37.5 years, respectively (p = 0.62, n.s.). Widespread pain existed for longer durations (median, 48 months) than conditions involving local and regional pain (median, 24 months) (p = 0.02, s.). Our findings showed that among a great percentage of persistent facial pain patients the pain distribution is more widespread than commonly assumed, and that the persistence of pain in the regional and widespread pain presentations is significantly greater than in cases with pain limited to the trigeminal system.

Temporomandibular disorders--pain outside the head and face is rarely acknowledged in the chief complaint

STATEMENT OF PROBLEM

With diagnostic and therapeutic procedures being heavily influenced by the patient's chief complaint, the question arises whether this information alone represents a solid basis for clinical action.

PURPOSE

The aim of this investigation was to assess the agreement between pain complaints and patient generated paper-and-pencil drawings of the distribution of pain in patients suffering from temporomandibular disorders.

METHODS

The study included 140 adult female patients with temporomandibular disorders. Pain drawings served as a standard, against which the oral reports were compared. In 40 (29%) of the patients, pain was limited to the head and face; in the remaining subjects, it exceeded the boundaries of these regions. Nine potential pain sites were distinguished (head, face, neck, shoulders, arms, chest, abdomen, back, and legs). Whenever one of these regions was part of the drawing or the pain complaint, it was counted. Sensitivity, specificity, and kappa indices were computed for each site.

RESULTS

Patients with pain limited to the head and face showed a close correspondence between pain report and drawing. On the other hand, patients with temporomandibular disorders with concomitant pain sites outside the head and face frequently did not mention these additional pain locations. This was reflected in low sensitivities (minimum: 0.00; maximum: 0.48) and low kappa values (minimum: -0.02; maximum: 0.19).

CONCLUSIONS

This study showed that the chief complaint frequently underestimates the real extent of pain involvement.

Analysis of cohort effects in mixed longitudinal data sets

Mixed longitudinal designs are among the most efficient for the study of growth and developmental processes. In this approach, one studies several (birth) cohorts, each for a relatively short length of time, and then links the growth curves for the individual cohorts together to obtain the growth curve for the entire length of time spanned by the ages of the subjects in all cohorts. Thus, e.g., in the Nijmegen Growth Study, three cohorts were each studied for 5 years, the intent being to join the three curves together to form a single curve covering the entire period from 4 to 14 years of age. In order for this approach to be valid, there either should be no cohort effects (secular trends) or the fitted curve must be adjusted in some way to correct for such effects if they exist. The question thus arises as to how one should test for the presence of cohort effects and what one should do about them if found. The problems which may arise using height and weight data from the Nijmegen Growth Study are illustrated. In particular for girls, height and weight both show cohort effects (at 9.25 years of age) when the raw data are used. If, however, the observed data are used to estimate the values at the target age, and these values are used in the comparison, differences between the cohorts are no longer significant. The problems are further illustrated using data from a mixed longitudinal data set of cleft lip and palate patients and data from the National Dutch Growth Study 1980.

PC program for assessing the effect of a treatment when subjects are growing: comparative studies

We describe, illustrate, and make available a menu-driven PC program which can be used to assess the effect of a treatment on growth when random allocation of subjects to the treatment and control groups is not feasible. Three different estimators of, and confidence intervals for, this effect are computed, namely, the simple gains, standardized gains, and covariance adjusted estimators. It is shown by means of several examples that these estimators can differ substantially, and some guidelines for choosing between them in specific circumstances are provided.

PC program for simultaneously testing equality of means and variances for paired bivariate normal data

A menu-driven PC program for simultaneously testing the equality of means and variances for paired bivariate normal data is described, illustrated and made available. While the corresponding tests for independent samples are well-known and widely implemented, in the paired situation only the test for no change in mean values (the paired t-test) has been similarly covered. Tests for no change in variability, while important, are less well-known and not implemented in most commercial statistical computing programs.

PC program for comparing two regression lines over a specified finite interval

A method due to Tsutakawa and Hewett (Biometrics 34 (1978) 391-398) for comparing two regression lines over a specified, finite interval has been implemented. We describe and illustrate the procedure and program, and make the latter available to interested readers.

PC program extending the Potthoff-Roy longitudinal data analysis model to allow missing data: Kleinbaum's method

Potthoff and Roy (Biometrika, 51 (1964) 313-326) generalized the multivariate analysis of variance model into a form that is especially useful for the study of longitudinal growth curve data. Applications of this method have, however, been limited by the requirement that each case in the sample be measured at the same set of time points, i.e. there can be no missing data. In this paper we describe, illustrate, and make available a user-friendly, interactive PC program implementing Kleinbaum's (J Mult Anal, 3 (1973) 117-124) extension of the Potthoff-Roy model to allow incomplete measurement sequences. These missing data are permitted to arise either randomly or by design as in mixed longitudinal studies.

PC program for determining the dose necessary to produce a given amount of change

Given a simple linear regression equation of the form D = alpha + beta Z, it is well-known how to predict, and construct confidence intervals for, the value of D corresponding to a given Z. In this paper we describe, illustrate and make available a menu-driven PC program which can be used to solve the inverse problem, namely, to estimate and construct confidence intervals for the value of Z corresponding to a given value of D. We describe the procedure in the context of a dose-response relationship, where it is desired to estimate the dose (Z) to effect a given amount of change (D), but the method is more general than this. In particular, it may be usefully applied in calibration problems where one may wish to estimate the true value of a measurement given the value as read from a measuring device.

PC program for assessing the relationship between rate of change and initial value

A menu-driven PC program implementing Blomqvist's [J. Am. Stat. Assn. 72, 746-749, 1977] method for assessing the relationship between rate of change and initial value is described, illustrated and made available. It is shown that the naive approach to this problem--computing the correlation between the initial value and either the amount or rate of change--results in a negatively biased estimator. The extent of this bias can be dramatic and may lead investigators to conclude that a negative correlation is present when none exists; or that there is no correlation when in fact the correlation is positive. Blomqvist's (maximum likelihood) estimator avoids this bias, and is obtained by a transformation of the naive estimator.

ANCOVA for nonparallel slopes: the Johnson-Neyman technique

The Johnson-Neyman (JN) procedure, as originally formulated (Stat Res Mem, 1 (1936) 57-93), applies to a situation in which measurements on 1 dependent (response) variable, X, and 2 independent (predictor) variables, Z1 and Z2, are available for the members of 2 groups. The expected value of X is assumed to be a linear function of Z1 and Z2, but not necessarily the same function for both groups. The JN technique is used to obtain a set of values for the Z variables for which one would reject, at a specified level of significance alpha (e.g., alpha = 0.05), the hypothesis that the 2 groups have the same expected X values. This set of values, or 'region of significance,' may then be plotted to obtain a convenient description of those values of Z1 and Z2 for which the 2 groups differ. The technique can thus be described as a generalization of the analysis of covariance (ANCOVA) which does not make the assumption that the regression coefficients for the regression of X on the covariates, Z1 and Z2, are equal in the groups being compared. In this paper we describe, illustrate and make available a menu-driven PC program (TXJN2) implementing the JN procedure.

PC program implementing an alternative to the paired t-test which adjusts for regression to the mean

In many biomedical research contexts, treatment effects are estimated from studies based on subjects who have been recruited because of high (low) measurements of a response variable, e.g., high blood pressure or low scores on a stress test. In this situation, simple change scores will overestimate the treatment effect; and the use of the paired t-test may find significant change due not to the treatment per se but, rather, due to regression towards the mean. A PC program implementing a procedure for adjusting the observed change for the regression effect in simple pre-test-post-test experiments is described, illustrated, and made available to interested readers. The method is due to Mee and Chua (Am Stat, 45 (1991) 39-42) and may be considered as an alternative to the paired t-test which separates the effect of the treatment from the so-called regression effect.

Extension of the Carter-Yang polynomial growth curve model to allow unique times of measurement for subjects

A PC program extending the procedure due to Carter and Yang (Commun Stat: Theory Methods, 8 (1986) 2507-2526) to allow unique times of measurement for subjects is described, illustrated and made available. Given longitudinal observations on each of N subjects comprising a single group, this program determines the lowest degree polynomial in time adequate to fit the average growth curve (AGC); estimates this curve and provides confidence bands for the AGC, and confidence intervals for the corresponding polynomial regression coefficients; and so-called prediction intervals which, with a given level of confidence, will contain the growth curve of a 'new' subject from the same population of which the N subjects constitute a random sample. Two kinds of missing data are accommodated. First, in the context of studies planned so that subjects will be measured at identical times and, second, in unstructured studies where subjects may present with their own, unique times of measurement.

PC program for assessing the effect of a treatment when subjects are growing: the randomized parallel groups design

A method for separating the effects of a treatment from those of normal development in the case of a randomized parallel groups design with pre- and post-treatment measures is described and implemented. The program allows the user to enter either summary statistics (published data are often in this form), or the pre- and post-treatment measurements for each individual. The program is illustrated using data reflecting the extent to which a treatment can be expected to impede normal growth, but the method and program are more general than this. All that is required is that the measurement be one that normally increases over time.

Assessing the effect of a treatment when subjects are growing at different rates

The analysis of covariance is often used in the context of premeasure/postmeasure designs to compare treatment and control groups in both randomized [1] and nonrandomized [2] studies. The intent is to adjust the difference between the changes in the 2 groups for any difference which might exist at baseline, i.e., for any difference between the premeasures in the 2 groups. An important assumption underlying the use of the analysis of covariance is that the slopes of the lines for the regression of the postmeasure on the premeasure in the 2 groups are equal. In this paper we describe a program which can be used to test the hypothesis of equal slopes; and performs an alternative analysis which does not depend on this assumption. This is done in the context of comparing treatment and control groups with respect to a measurement subject to natural maturation as in [3]. Equal slopes in this context means equal growth rates; unequal slopes implies that the 2 groups are growing at different rates. The method, known as the Johnson-Neyman procedure [4] is, however, more general than this, and can be used in any two-sample comparison where an alternative to the usual analysis of covariance is deemed appropriate. The procedure identifies a 'region of significance' which is especially useful in practice. This region consists of a set of values of the premeasure for which the treatment and the control groups are significantly different with respect to the postmeasure.

Analysis of longitudinal data in craniofacial research: some strategies

Although it is generally acknowledged that longitudinal data provide the most information on growth and development and other time-dependent phenomena, such data are often analyzed by conventional (cross-sectional) statistical methods. This widespread practice ignores the distinctive characteristics (e.g., covariance structure) of longitudinal data and may yield misleading results. The purpose of this article is to present some strategies and make available computer programs for the appropriate analysis of longitudinal data. User-friendly PC programs for the estimation of average growth curves, computation of tracking indices, prediction of future values, diagnosis, classification, clustering, estimation of missing values, and testing hypotheses concerning individual and group differences are presented. Benefits of these methods over the usual techniques are illustrated with the example of maxillary growth in the rhesus monkey.

GTRACK: a PC program for computing Goldstein's growth constancy index and an alternative measure of tracking

This paper reviews Goldstein's 'growth constancy index,' Xi, a measure of tracking which can be used to determine whether or not individuals maintain their relative positions in the distribution of a given measurement as that distribution changes over time. We suggest that Xi is an appropriate measure of tracking when the (standardized) measurements arise in the context of a Model I ANOVA, but that the intraclass correlation coefficient, rI, may be preferred when a Model II ANOVA is applicable. We also describe--and make available--a PC program which allows the user to choose between Model I and Model II, and computes the appropriate tracking index and confidence intervals for the corresponding parameter.

A PC program for classification into one of several groups on the basis of longitudinal data

A stand-alone, menu-driven PC program, ZCLASS, written in GAUSS386i, for classifying subjects into one of several distinct, existing groups on the basis of longitudinal data is described, illustrated, and made available to interested readers. The program accepts data from studies where common times of measurement are planned, but missing data are accommodated in that one or more measurement sequences may be incomplete.

Implementation of exact and approximate randomization tests for polynomial growth curves

Two stand-alone, menu-driven PC programs, written in GAUSS386i, which compare groups of growth curves in a completely randomized design using either (a) exact or (b) approximate randomization tests, are described, illustrated, and made available to interested readers. The programs accommodate missing data in the context of studies planned to have common times of measurement, but where some of the measurement sequences are incomplete. The measurement whose growth is being monitored need not have a Gaussian distribution. We consider the hypothesis that the mean growth curves in G groups are the same; and either compute the exact P value (exact test), or estimate, and provide a confidence interval for, the P value (approximate test).

A PC program for computing McMahan's tracking indices from one-sample longitudinal data sets

Tracking refers to regular, predictable growth behavior. Most definitions of the term are related to the idea that tracking occurs to the extent that individuals' repeated measurements maintain their relative positions in the distribution of the measurement whose growth is being monitored as that distribution changes over time. In this paper we describe four indices of tracking, all due to McMahan (Biometrics, 37 (1981) 447-455), which may be used to measure the extent to which a given longitudinal sample exhibits this 'regular behavior,' and we provide a program, written in GAUSS386i, for performing the associated computations. An example is given, and the values of McMahan's indices are compared to several alternative measures of tracking.

A PC program for diagnosing abnormal growth, growth velocity and acceleration from longitudinal observations

A PC program, written in GAUSS386i, implementing Zerbe's (Growth, 43 (1979) 263-272) procedure for diagnosis on the basis of longitudinal data is described, illustrated and made available to interested readers. Given longitudinal observations on N normal individuals, this technique can be used to characterize normal growth, velocity and acceleration, and to determine whether or not a new individual can be considered normal with respect to any or all of these parameters. Missing data are allowed, and there is no requirement that the variable whose growth is being monitored has a normal distribution. The method and program are illustrated using a data set with a substantial amount of missing data. Information on obtaining a copy of the program and hardware requirements are given in the Appendix.

A PC program for computing confidence bands for average and individual growth curves

Dawson et al. (Am. J. Med. Genet. 7, 529-536, 1980) developed a procedure for constructing confidence bands for both average and individual growth curves which may be of considerable value in the study of growth and development. This paper describes their method for constructing, and provides a menu-driven GAUSS386i program for computing these confidence bands. It is demonstrated how these bands are useful for both the diagnosis and prognostication of growth patterns with known levels of confidence. It is assumed that the study is planned so that individuals will be measured at the same times, but missing data are allowed.

PC program for growth prediction in the two-stage polynomial growth curve model

We consider the problem of growth prediction in the context of the two-stage (or random coefficients) one-sample polynomial growth curve model and provide a PC program, written in GAUSS386i, to perform the associated computations. The problem considered is that of estimating the value of the measurement under consideration for a 'new' individual at the Tth time point given measurements on that individual at T-1 previous points in time and the values of the measurement on N 'similar' individuals at all T time points. The times of measurement t1, t2, ..., tT need not be equally spaced, but we assume that each of the N individuals comprising the normative sample were measured at these times. The method and the program are illustrated using the data set previously considered (Schneiderman and Kowalski, Am J Phys Anthrop, 67 (1985) 323-333) consisting of mandibular ramus height measurements (in mm) for 12 male rhesus monkeys at T = 5 yearly intervals (coded 1, 2, 3, 4, and 5). Results are compared with those obtained under a less restrictive set of assumptions concerning the covariance matrix of the observations than is made in the context of the two-stage model. It is seen that the accuracies of prediction of the two methods, for this and other data sets, are quite close, suggesting that the less restrictive model may be preferred in many situations.

Dose related remineralization using intraoral fluoride-releasing devices in situ

Dose-related remineralization of enamel lesions was studied in situ. Enamel specimens with subsurface lesions were mounted on lower molars bilaterally and exposed to five regimens: (A) control with a F-free dentifrice three times daily; (B) NaF dentifrice brushed three times daily; (C) fluoride-releasing device (FRD; 0.07 mg F/day release rate) plus F-free dentifrice; (D) FRD (0.232 mg F/day) plus F-free dentifrice, F/day and (E) FRD (0.232 mg/F/day) plus NaF dentifrice. Resting and stimulated saliva samples were obtained for salivary flow and F content determinations. Twenty-eight subjects participated in this double-blind, random-assignment crossover study. After 50 days the enamel specimens were recovered, sectioned, microradiographed, and scanned with image analysis. Regimens D and E demonstrated approximately 30% additional remineralization as compared with to controls, and regimens B and C showed 13.7 and 10.5% increased remineralization as compared with to controls. The increased remineralization of the regimens generally paralleled the increase in salivary F and clearly demonstrated a dose-related response which was some threefold in relation to release rate, salivary F, and percent remineralization.

PC program for estimating polynomial growth, velocity and acceleration curves when subjects may have missing data

A stand-alone, menu-driven PC program, written in GAUSS386i, for estimating polynomial growth, velocity, and acceleration curves from longitudinal data is described, illustrated and made available to interested readers. Missing data are accommodated: we assume that the study is planned so that individuals will have common times of measurement, but allow some of the sequences to be incomplete. The degrees, Di, adequate to fit the growth profiles of the N individuals are determined and the corresponding polynomial regression coefficients are calculated and can be saved in ASCII files which may then be imported into a statistical computing package for further analysis. Examples of the use of the program are provided.

PC program extending the two-stage polynomial growth curve model to allow missing data

A stand-alone, menu-driven PC program, written in GAUSS386i, extending the analysis of one-sample longitudinal data sets satisfying the two-stage polynomial growth curve model (Ten Have et al., Am J Hum Biol, 3 (1991) 269-279) to allow missing data is described, illustrated and made available to interested readers. The method and the program are illustrated using data previously analyzed by the authors (Schneiderman and Kowalski, Am J Phys Anthropol, 67 (1985) 323-333) but with several randomly chosen data points discarded and treated as missing.

Clustering on the basis of longitudinal data

A menu-drive PC program, ZDIST, for computing the distances between the estimated polynomial growth curves of subjects who have been followed longitudinally is described, illustrated, and made available to interested readers. These distances can be computed on the basis of the individual growth curves themselves and/or from estimates of individuals' growth velocity and acceleration curves. The resulting distance matrices can be saved in ASCII format and subsequently imported into any clustering program which accepts this type of input, e.g. SYSTAT.

A PC program to aid in the choice of the design matrix in multiple linear regression

A PC program, DESIGN, which can be used to evaluate and compare alternative choices of the design matrix, X, in the general linear model y = X beta + epsilon is described, illustrated and made available to interested readers. Given X, the program (1) computes various measures of the 'stability' of X and X'X and (2) determines the precisions of estimates of the model parameters, beta, and of predicted values, ŷ, at the given design points. Examples focusing on polynomial regression are given.

Longer-term growth prediction using GAUSS

In several areas of biomedicine, one needs to predict future measurements for a growing individual on the basis of longitudinal data. Here we consider the problem of estimating the values of a given measurement for a particular individual at T-T* points in time, given T* observations on that individual, and all T values for a sample of N "similar" individuals. This extends our previous discussion [Schneiderman et al., Comput. Biol. Med. 22, 181-188 (1992)], which was limited to the case T* = T-1, to longer-term predictions. We again make a user-friendly GAUSS program available to perform the associated computations. Examples illustrating the use of the program and the accuracy of the predictions it provides are included.

Data analysis in craniofacial biology with special emphasis on longitudinal studies

Recommendations are made for strengthening data description and analysis in craniofacial biology. Special emphasis is placed on longitudinal data, and PC programs for accomplishing appropriate analyses in this context are described and made available to interested readers. Some more general recommendations are treated in less detail. These include the effective description of data using stem-and-leaf displays and/or boxplots, the use of decision-analytic methods in the management of patients with dentofacial deformities, and the valid application of certain statistical methods in single-subject studies. Finally, it is conjectured that computer-intensive methods such as randomization tests and jackknifing will play an increasingly prominent role in craniofacial research.

Regression imputation of missing values in longitudinal data sets

A stand-alone, menu-driven PC program, written in GAUSS, which can be used to estimate missing observations in longitudinal data sets is described and male available to interested readers. The program is limited to the situation in which we have complete data on N cases at each of the planned times of measurement t1, t2,..., tT; and we wish to use this information, together with the non-missing values for n additional cases, to estimate the missing values for those cases. The augmented data matrix may be saved in an ASCII file and subsequently imported into programs requiring complete data. The use of the program is illustrated. Ten percent of the observations in a data set consisting of mandibular ramus height measurements for N = 12 young male rhesus monkeys measured at T = 5 time points are randomly discarded. The augmented data matrix is used to determine the lowest degree polynomial adequate to fit the average growth curve (AGC); the regression coefficients are estimated and confidence intervals for them are determined; and confidence bands for the AGC are constructed. The results are compared with those obtained when the original complete data set is used.

In situ remineralization of enamel lesions using continuous versus intermittent fluoride application

Remineralization of early enamel lesions was studied in situ using a F chewing gum or a F-releasing device (FRD). Enamel specimens with subsurface lesions were mounted in removable lower appliances in 6 adults. A F-free dentifrice was used for all regimens. Test groups chewed five sticks/day (0.1 mg F/stick), or one FRD (0.5 mg F/day) was mounted in the midline of the appliance. The microhardness was measured after the 21-day intraoral exposure, and in vitro acid resistance testing was performed. Separate specimens were used to measure F content or changes in mineral density. Comparable values for both F gum and FRDs were higher (p > 0.05) than controls for acid resistance testing and percent remineralization. The F content for FRDs exceeded that of both F gum and controls.

In situ remineralization of subsurface enamel lesion after the use of a fluoride chewing gum

In situ remineralization of early enamel lesions by a fluoride chewing gum was studied. Human enamel specimens with subsurface lesions were mounted in removable lower appliances for 6 adults. Subjects used a F-free dentifrice 3x/day and chewed five sticks/day for the F gum group (0.1 mg F/stick) or five sticks of sugarless gum. No gum was chewed for controls. Surface microhardness was performed on: (1) sound enamel; (2) lesions; (3) after intraoral exposure, and (4) after acid-resistance testing (ART). Separate specimens were etched and measured for F uptake and image analyses on microradiographs were performed for all regimens. delta Z values were calculated and converted to percent of mineralization. Values for F gum were significantly higher (p > 0.05) than non-F gum and controls for ART, percent remineralization, and F uptake up to 70 microns depth.

A GAUSS program for computing the Foulkes-Davis tracking index for polynomial growth curves

We have previously published a GAUSS program for computing the Foulkes-Davis tracking index, gamma, from a one-sample longitudinal data set when no assumptions were made concerning the structure of the individual growth curves (Schneiderman et al., Am J Hum Biol, 4 (1992) 417-420). In this paper we consider the computation of the Foulkes-Davis index assuming that each individual growth curve may be adequately represented by a polynomial function in time and a GAUSS program performing these computations is made available. As with the two other tracking indices we have described, gamma and kappa (Schneiderman et al., Am J Hum Biol, 2 (1990) 475-490), this one can be used to evaluate regularity in patterns of growth or adaptation. An example is presented where statural growth in the same three groups considered in the earlier papers are analyzed. The small disparities between these and the earlier results are discussed in view of the different assumptions of the models and the differences in how they operationalize the concept of tracking.

A PC program for growth prediction in the context of Rao's polynomial growth curve model

We consider the problem of growth prediction in the context of Rao's [1] one-sample polynomial growth curve model and provide a PC program, written in GAUSS, to perform the associated computations. Specifically, the problem considered is that of estimating the value of the measurement under consideration for a "new" individual at the Tth time point given measurements on that individual at T-1 previous points in time and the values of the measurement on N "similar" individuals at all T time points. The times of measurement t1, t2, . . ., tT need not be equally spaced, but we assume that each of the N individuals comprising the normative sample were measured at these times. The method and the program are illustrated using the leave-one-out method on a sample of N = 12 male rhesus monkeys whose mandibular ramus height was measured five times at yearly intervals.

A PC program for performing multigroup longitudinal comparisons using the Potthoff-Roy analysis and orthogonal polynomials

A PC-program performing the Potthoff-Roy (PR) multigroup (G-sample) analysis of longtidinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is important) for which serial data are available. Specifically, this method fits polynomials to the average growth curves in the samples, and tests hypotheses concerning the curves themselves and the individual coefficients of the polynomials. The program features the utilization of orthogonal polynomial regression coefficients (OPRCs) and is written in GAUSS, a relatively inexpensive yet comprehensive matrix programming language. It is documented that using OPRCs to comprise the within-individual or time design matrix has several advantages over the more usual choice of the successive-powers-of-t form of this matrix and an example of one important such advantage is provided. GAUSS was employed to make the program readily-accessible (i.e., executable code) to biomedical investigators. The GAUSS compiler is not required to run this program. Information regarding the availability of the program is provided in the Appendix.

Rao's polynomial growth curve model for unequal-time intervals: a menu-driven GAUSS program

For lack of alternatives, longitudinal data are often analyzed with cross-sectional statistical methods, for instance, t-tests, ANOVA and ordinary least-squares regression. Appropriate statistical software has been generally unavailable to investigators using serial records to study growth and development or treatment effects. In an earlier paper (Schneiderman and Kowalski, Am. J. Phys. Anthropol., 67 (1985) 323-333.) we described a suitable method, Rao's polynomial growth curve model (Rao, Biometrika, 46 (1959) 49-58), and provided an SAS computer program for the analysis of a single sample of complete longitudinal data. This method included the computation of an average polynomial growth curve, its 95% confidence band, its coefficients and corresponding confidence intervals. The present paper extends this method to accommodate a sample with observations made at unequal time-intervals. Significant improvements in the accessibility, operation and user-friendliness of the program have been made, facilitated by recent advances in microcomputer technology. This stand-alone GAUSS program (no compiler necessary) runs on PC-compatibles and is available at a nominal cost. In this report we provide an overview of the statistical model, the general structure of the program, and give an example in which a developmental variable (human upper incisor angulation) is analyzed. Ease of installation and use, speed of execution and color graphic displays of growth curves and confidence bands, and most importantly, suitability to longitudinal data, make this method/program a potentially valuable tool for those interested in growth, development, and treatment effects in humans and other species. Some areas in which this method will have immediate applications are orthodontics, maxillofacial surgery and pediatrics.