Time-stamp: <2007-07-08 20:41:24 chl>

The following briefly describes the motivating studies used throughout the textbook of Molenberghs and Verbeke, Models for discrete longitudinal data (Springer, 2005).

All materials related to the two textbooks published by these authors can be found on the website : http://www.censtat.uhasselt.be/software/.

I have translated the datasets from SAS format (sas7bdat) into csv files as this the best choice for dealing with data into R. For those who want to analyse the data using the SAS System, the original datasets are also provided. All analyses were done with R version 2.5.0 (2007-04-23).

The analgesic trial

The data come from a single-arm clinical trial in 395 patients who are given analgesic treatment for pain caused by chronic nonmalignant disease. Treatment was to be administered for 12 months and assessed by means of a 'Global Satisfaction Assessment' (GSA) scale, rated on a five-point scale: (1) = very good; (2) = good; (3) = indifferent; (4) = bad; (5) = very bad.

Apart from the outcome of interest, number of covariates are available, such as age, sex, weight, duration of pain in years prior to the start of the study, type of pain, physical functioning, psychiatric condition, respiratory probelms, etc. GSA was rated by each person four times during the trial, at months 3, 6, 9 and 12. It should be noted that there are numerous missing values. Not only monotone or dropout occurs, there are also subjects with intermittent values.

The toenail data

The data were obtained from a randomized, double-blind, parallel group, multicenter study for the comparison of two oral treatments (in what follows coded as A and B) for toenail dermatophyte onychomycosis (TDO), described in full detail by De Backer et al. (1996). TDO is a common toenail infection, difficult to treat, affectinf more than 2 out of 100 persons. Antifungal compounds, classically used for treatment of TDO, need to be taken until the whole nail has grown out healthy. The development of new compounds, however, has reduced the treatment duration to 3 months. The aim at the present study was to compare the efficacy and safety of 12 weeks of continuous therapy with treatment A or with treatment B.

In total, 2 x 189 patients were randomized, distributed over 36 centers. Subjects were followed during 12 weeks (3 months) of treatment and followed further, up to a total of 48 weeks (12 months). Measurements were taken at baseline, every month during treatment, and every 3 months afterwards, resulting in a maximum of 7 measurements per subject. At the firts occasion, the treating physician indicates one of the affected toenails as the target nail, the nail which will be followed over time. The analysis will be restricted to only those patients for which the target nail was one of the two big toenails. This reduces the sample under consideration to 146 and 148 subjects, in group A and group B, respectively.

One of the responses of interest was the unaffected nail length, measured from the nail bed to the infected part of the nail, which is always at the free end of the nail, expressed in mm. This outcome has been extensively studied in the other textbook dealing with continuous measurements data (Verbeke and Molenberghs, 2000). Another important outcome in this study was the severity of the infection, coded as 0 (not severe) or 1 (severe). The question of interest was whether the percentage of severe infection decreased over time, and whether that evolution was different for the two treatment groups.

Due to a variety of reasons, the outcome has been measured at all 7 scheduled time points, for only 224 (76%) out of the 298 participants. It should be noted thta the occurence of missingness is similar in both treatment groups.

References:

De Backer, M., De Keyser, P., De Vroey, C. and Lesaffre, E. (1996). A 12-week treatment for dermatophyte toe onychomycosis: terbinafine 250mg/day vs. itraconazole 200mg/day--a double-blind comparative trial. British Journal of Dermatology, 134, 16-17.

The fluvoxamine trial

Accumulated experience with fluvoxamine, a serotonin reuptake inhibitor, in controlled clinical trials has show it to be as effective as conventional antidepressant drugs and more effective than placebo in the treatment of depression (Burton, 1991). However, many patients who suffer from depression have concomitant morbidity with conditions such as obsessive-compulsive disorder, anxiety disorders and, to some extent, panic disorders. In most trials, patients with comorbidity are excluded, and therefore, it is of interest to gather evidence as to the importance of such factors, with a view on improved diagnosis and treatment. The general aim of this study was to determine the profile of fluvoxamine in ambulatory clinical psychiatric practice.

A total of 315 patients were enrolled with one or more of the following diagnoses: depression, obsessive, compulsive disorder, and panic disorder. Several covariates were recorded, such as gender and initial severity on a 5-point ordinal scale, where severity increases with category. After recruitment of the patient in the study, he or she was investigated at four visits (weeks 2, 4, 8, and 12). On the basis of about twenty psychiatric symptoms, the therapeutic effect and the side-effects were scored at each visit in an ordinal manner. Side-effect is coded as (1) = no; (2) = not interfering with functionality of patient; (3) = interfering significantly with functionality of patient; (4) = the side-effect surpasses the therapeutic effect. Similarly, the effect of therapy is recorded on a four-point ordinal scale: (1) = no improvement over baseline or worsening; (2) = minimal improvement (not changing functionality); (3) = moderate improvement (partial disappearance of symptoms); and (4) = important improvement (almost disappearance of symptoms). Thus a side effect occurs if new symptoms occur while there is therapeutic effect if old symptoms disappear.

There is also a lot a non negligeable amount of missing data but a much larger fraction is fully observed than in the analgesic trial. Among the incomplete sequences, dropout is much more common than intermittent missingness, the latter type confined to two sequences only. It should also be noted that there are subjects, 14 in total without any follow-up measurements. This group of subjects is still an integral part of the trial, as they contain baseline information, includinf covariate information and baseline assessement of severity of the mental illness.

References:

Burton, S. W. (1991). A review of fluvoxamine and its uses in depression. International Clinical Psychopharmacology, 6 (Suppl. 3), 1-17.

The epilepsy data

The data are obtained from a randomized double-blind, parallel group multicenter study for the comparison of placebo with a new anti-epileptic drug (AED), in combination with one or two other AED's. The study is described in full detail in Faught et al. (1996). The randomization of epilepsy patients took place after a 12-week baseline period that served as a stabilization period for the use of AED's, and during wich the number of seizures were counted. After that period, 45 patients were assigned to the placebo group, 44 to the active (new) treatment group. Patients were then measured seekly. Patients were followed (double-blind) during 16 weeks, after which they were entered into a long-term open-extension study. Some patients were followed for up to 27 weeks. The outcome of interest is the number of epileptic seizures experienced during the last week, i.e., since the last time the outcome was measured. The key research question is whether or not the additional new treatment reduces the number of epileptic seizures.

There is an unstable behavior that could be applained by the presence of extreme values, but it is also accounted by the fact that very little obervations are available. There is also a serious drop in the the number of measurements past the end of the actual double-blinde period, i.e., past week 16.

References:

Faught, E., Wilder, B. J., Ramsay, R. E., Reife, R. A., Kramer, L. D., Pledger, G. W. and Karim, R. M. (1996). Topiramate placebo-controlled dose-ranging trial in refractory partial epilepsy using 200-, 400-, and 600-mg daily dosages. Neurology, 46, 1684-1690.

The POPS study

The Project on Preterm and Small-for-gestational age infants (POPS) collected information on 1338 infants born in The Netherlands in 1983 and having gestational age less than 32 weeks and/or birthweight less than 1500g (Verloove et al., 1988). In total, 133 clinics were involved. The study population represents 94% of the births in that year with similar gestational age and birthweight characteristics. Prenatal, perinatal, and postnatal information as well as two year follow-up data were collected. Furthermore, the data base contains information on the delivery and specific details of the infant. After two years the child was reexamined.

Three ability scores were measured at the age of two, and risks factors were measured at delivery. All ability scores were recorded in a dichotomous manner. They were available for 799 children. The first score (ABIL1) checks whether the child can pile three bricks, ABILS1 = 1 corresponds to 'no', whereas ABIL1 = 2 to 'yes'. The second score (ABIL2) measures whether the physical movements of the child are natural, ABIL2 = 1 (no) and ABIL2 = 2 (yes). Although ABIL2 is a purely physical ability score, ABIL1 is a combination of physical and mental qualities. The third ability score, ABIL3, expressess whether or not the child is able to put a ball in a box if he or she is asked to do so. The problem is to determine the risk factors for low performance at the three tests. Further it is of interest to compare the predicted probabilities taking into account the relationship between the responses to those calculated under the assumption of independent responses.

On the 1338 subjects, 818 (61.1%) have all three ability scores observed, and 471 (35.2%) have none of them. Only 49 (3.7%) have partial information. The latter is not unexpected, since two years lapsed between enrollment and the assessment of the ability scores.

References:

Verloove, S. P. and Verwey, R. Y. (1988). Project on preterm and small-for-gestational age infants in the Netherlands, 1983 (Thesis, University of Leiden). University Microfilms International, Ann Arbor, Michigan, USA, no. 8807276.

National toxicology program data

The developmental toxicity studies introduced in this section are conducted at the Research Triangle Institute, which is under contract to the National Toxicology Program of the United States (NTP data). These studies investigate the effects in mice of five chemicals: ethylene glycol (Price et al., 1985), diethylene glycol dimethyl ether (Price et al., 1987), and di(2-ethylhexyl)phthalate (Tyl et al., 1988).

  1. Ethylene Glycol

Ethylene glycol (EG) is also called 1,2-ethanediol and can be represented by the chemical formula HOCH2CH2OH. It is a high-volume industrial chemical with many applications. EG is used as an antifreeze in cooling and heating systems, as one of the components of hydraulic brake fluids, as an ingredient of electrolytic condensers, and as a solvent in the paint and plastics industries. Furthermore, EG is employed in the formulation of several types of inks, as a softening agent for cellophane, and as a stabilizer for soybean foam used to extinguish oil and gasoline fires. Also, one uses EG in the synthesis of various chemical products, such as plasticizers, synthetic fibers, and waxes.

EG may represent little hazard to human health in normal industrial handling, except possibly when used as an aerosol or at elevated temperatures. EG at ambient temperatures has a low vapor pressure and is not very irritating to the eyes or skin. However, accidental or intentional ingestion of antifreeze products, of which approximately 95% is EG, is toxic and may result in death.

Price et al. (1985) describe a study in which timed-pregnant CD-1 mice were dosed by gavage with EG in distilled water. Dosing occurred during the period of organogenesis and structural development of the foetuses (gestational days 8 through 15). The doses selected for the study were 0, 750, 1500, or 3000 mg/kg/day. Available data are: the number of dams containing at least one implant, the number of dams having at least one viable fetus, the number of live foetuses, the mean litter size, and the percentage of malformation for three different classes: external malformations, visceral malformations, and skeletal malformations. While for EG, skeletal malformations are substantial in the highest dose group, external and visceral malformations show only slight dose effects.

  1. Di(2-ethylhexyl)Phthalate

Di(2-ethylhexyl)phthalate (DEHP) is also called octoil, dicotyl phthalate, or 1,2-benzenedicarboxylic acid bis(2-ethylhexyl) ester. It can be represented by C24H38O4. DEHP is used in vacuum pumps. Furthermore, this ester as well as other phthalic acid esters are used extensively as plasticizers for numerous plastic devices made of polyvinyl chloride. DEHP provides the finished plastic products with desirable flexibility and clarity.

It has been well documented that small quantities of phthalic acid esters may leak out of polyvinyl chloride plastic containers in the presence of food, milk, blood, or various solvents. Due to their ubiquitous distribution and presence in human and animal tissues, considerable concern has developed as to the possible toxic effects of the phthalic acid esters.

In particular, the developmental toxicity study described by Tyl et al. (1988) has attracted much interest in the toxicity of DEHP. The doses selected for the study were 0, 0.025, 0.05, 0.1, and 0.15%, corresponding to a DEHP consumption of 0, 44, 91, 191, and 292 mg/kg/day, respectively. Females were observed daily during treatment, but no maternal deaths or distinctive clinical signs were observed. The dams were sacrificed, slightly prior to normal delivery, and the status of uterine implantation sites recorded. A total of 1082 live foetuses were dissected from the uterus, anesthetized, and examined for external, visceral, and skeletal malformations.

There is a clear dose-related trends in the malformation rates. The average litter size (number of viable animals) decreases with increased levels of exposure to DEHP, a finding that is attributable to the dose-related increase in fetal deaths.

  1. Diethylene Glycol Dimethyl Ether

Other names for diethylene glycol dimethyl ether (DYME) are diglyme and bis(2-methoxyethyl) ether. DYME has as its chemical formula: CH3O(CH2)2O(CH2)2OCH3. It is a component of industrial solvents. These are widely used in the manufacture of protective coatings such as lacquers, metal cotings, baking enamels, etc. Although to date, several attempts have proven inadequate to evaluate the potential of glycol ethers to produce human reproductive tocicity, structurally related compounds have been identified as reproductive toxicants in several mammalian species, producing (1) testicular toxicity and (2) embryotoxicity.

Price et al. (1987) describe a study in which timed-pregnant mice were dosed with DYME throughout major organogenesis (gestational days 8 through 15). The doses selected for the study were 0, 62.5, 125, 250 and 500 mg/kg/day.

References:

Price, C. J., Kimmel, C. A., Tyl, R. W. and Marr, M. C. (1985). The developmental toxicity of ethylene glycol in mice. Toxicology and Applied Pharmacology, 81, 113-127.

Price, C. J., Kimmel, C. A., George, J. D. and Marr, M. C. (1987). The developmental toxicity of diethylene glycol dimethyl ether in mice. Fundamental and Applied Toxicology, 8, 115-126.

Tyl, R. W., Price, C. J., Marr, M. C. and Kimmel, C. A. (1988). Developmental toxicity evaluation of dietary di(2-ethylhexyl)phthalate in Fischer 344 rats and CD-1 mice. Fundamental and Applied Toxicology, 10, 395-412.

The sports injuries trial

These data come from a randomized, parallel group, double-blind trial in men comparing the effect of an active treatment to placebo on post-operative shivering and per-operative hemodynamics. The primary responses of interest were severity of post-operative shivering measured from the end of anesthesia every 5 minutes during 30 minutes as none (0), mild (1), moderate (2), or severe (3), and effect of treatment on overall consciousness assessed from the end of anesthesia at 10, 20, 30, 45, 60, 90 and 120 minutes as impossible to awake (0), difficult to awake (1), easy to awake (2), and awake, eyes open (3). One hundred forty patients were assigned to each treatment group.

Since this trial occurred in a very short time period, there is very little missing data. There was one patient who had no response information for either variable, so this patient is excluded from all analyses. There were also 3 patients with some missing information on shivering or overall consciousness, leaving 138 patients with complete information.

One interesting feature of these data is that there are structural zeros in the awake variables. A patient could never become less awake over time, thus the cross-tabulation of the score over time contains zeros in the lower left corner.

Age related macular degeneration trial

These data arise from a randomized multi-centric clinical trial comparing an experimental treatment (interferon-alpha) to a corresponding placebo in the treatment of patients with age-related macular degeneration. Throughout the analyses done, we focus on the comparison between placebo and the highest dose (6 million units daily) of interferon-alpha (Z), but the full results of this trial have been reported elsewhere (Pharmacological Therapy for Macular Degeneration Study Group 1997). Patients with macular degeneration progessively lose vision. In the trial, the patients' visual acuity was assessed at different time points (4 weeks, 12 weeks, 24 weeks, and 52 weeks) through their ability to read lines of letters on standardized vision charts. These charts display lines of 5 letters of decreasing size, which the patient must read from top (largest letters) to bottom (smallest letters). Each line with at least 4 letters correctly read is called one 'line of vision'. The patient's visual acuity is the total number of letters correctly read. The primary endpoint of the trial was the loss of at least 3 lines of vision at 1 year, compared to their baseline performance (a binary endpoint). The secondary endpoint of the trial was the visual acuity at 1 year (treated as a continuous endpoint). Buyse and Molenberghs (1998) examined whether the patient's performance at 6 months could be used as a surrogate for their performance at 1 year with respect to the effect of interferon-alpha. They looked at whether the loss of 2 lines of vision at 6 months could be used as a surrogate for the loss of at least 3 lines of vision at 1 year. They also looked at whether visual acuity at 6 months could be used as a surrogate for visual acuity at 1 year.

Visual acuity can be measured in several ways. First, one can record the number of letters read. Alternatively, dichotomized versions (at most 3 lines of vision lost, or at least 3 lines of vision lost) can be used as well. Therefore, these data will be useful to illustrate methods for the joint modeling of continuous and binary outcomes, with or without taking the longitudinal nature into account. In addition, though there are 190 subjects with both month 6 and month 12 measurements available, the total number of longitudinal profiles is 240, but only for 188 of these have the four follow-up measurements been made.

References:

Buyse, M. and Molenberghs, G. (1998). The validation of surrogate end-points in randomized experiments. Biometrics, 54, 1014-1029.