Comparison of profile-likelihood-based confidence intervals with other rank-based methods for the two-sample problem in ordered categorical data.

For ordered categorical data from randomized clinical trials, the relative effect, the probability that observations in one group tend to be larger, has been considered appropriate for a measure of an effect size. Although the Wilcoxon-Mann-Whitney test is widely used to compare two groups, the null hypothesis is not just the relative effect of 50%, but the identical distribution between groups. The null hypothesis of the Brunner-Munzel test, another rank-based method used for arbitrary types of data, is just the relative effect of 50%. In this study, we compared actual type I error rates (or 1 - coverage probability) of the profile-likelihood-based confidence intervals for the relative effect and other rank-based methods in simulation studies at the relative effect of 50%. The profile-likelihood method, as with the Brunner- Munzel test, does not require any assumptions on distributions. Actual type I error rates of the profile-likelihood method and the Brunner-Munzel test were close to the nominal level in large or medium samples, even under unequal distributions. Those of the Wilcoxon-Mann-Whitney test largely differed from the nominal level under unequal distributions, especially under unequal sample sizes. In small samples, the actual type I error rates of Brunner-Munzel test were slightly larger than the nominal level and those of the profile-likelihood method were even larger. We provide a paradoxical numerical example: only the Wilcoxon-Mann-Whitney test was significant under equal sample sizes, but by changing only the allocation ratio, it was not significant but the profile-likelihood method and the Brunner-Munzel test were significant. This phenomenon might reflect the nature of the Wilcoxon-Mann-Whitney test in the simulation study, that is, the actual type I error rates become over and under the nominal level depending on the allocation ratio.

Longitudinal analysis of pre- and post-treatment measurements with equal baseline assumptions in randomized trials.

For continuous variables of randomized controlled trials, recently, longitudinal analysis of pre- and posttreatment measurements as bivariate responses is one of analytical methods to compare two treatment groups. Under random allocation, means and variances of pretreatment measurements are expected to be equal between groups, but covariances and posttreatment variances are not. Under random allocation with unequal covariances and posttreatment variances, we compared asymptotic variances of the treatment effect estimators in three longitudinal models. The data-generating model has equal baseline means and variances, and unequal covariances and posttreatment variances. The model with equal baseline means and unequal variance-covariance matrices has a redundant parameter. In large sample sizes, these two models keep a nominal type I error rate and have high efficiency. The model with equal baseline means and equal variance-covariance matrices wrongly assumes equal covariances and posttreatment variances. Only under equal sample sizes, this model keeps a nominal type I error rate. This model has the same high efficiency with the data-generating model under equal sample sizes. In conclusion, longitudinal analysis with equal baseline means performed well in large sample sizes. We also compared asymptotic properties of longitudinal models with those of the analysis of covariance (ANCOVA) and t-test.

Trends in smoking and lung cancer mortality in Japan, by birth cohort, 1949-2010.

OBJECTIVE: To determine smoking trends in Japan in comparison with lung cancer mortality. METHODS: Age-specific smoking prevalence among cohorts born between 1897 and 1985 were determined for the period 1949-2010. The percentages of the cohorts born between 1893 and 1979 who initiated smoking early (e.g. before the age of 20 years) were determined. The results were compared against lung cancer mortality rates in people aged 40-84 years belonging to cohorts born between 1868 and 1968. FINDINGS: In males, smoking prevalence was generally high, particularly among those born before the late 1950s, and early initiation was fairly uncommon. Early initiation was most common among recent birth cohorts of males, who showed relatively low prevalences of smoking. In females, the prevalence of smoking was generally low and early initiation was very uncommon, particularly among those born in the late 1930s and before the late 1940s, respectively. Recent cohorts of females showed relatively high prevalences of smoking and relatively high percentages of early initiation. In both sexes, lung cancer mortality was generally low but increased over the study period. CONCLUSION: Lung cancer mortality in Japanese males was relatively low given the high prevalence of smoking, perhaps because early initiation was fairly uncommon. Over the last four decades, however, early initiation of smoking has become more common in both sexes. The adverse effect this is likely to have on lung cancer mortality rates has probably not been observed because of the long time lag between smoking initiation and death from lung cancer.

Impacts of early smoking initiation: long-term trends of lung cancer mortality and smoking initiation from repeated cross-sectional surveys in Great Britain.

OBJECTIVE: To show long-term trends of smoking initiation in Great Britain including unanalysed data and assess the impact of early smoking initiation on the lung cancer mortality in later ages focusing on birth cohorts. DESIGN: Reanalysis of repeated cross-sectional surveys conducted 13 times during 1965-1987. SETTING: Great Britain. PARTICIPANTS: Men and women aged 16 years and over in each survey. PRIMARY OUTCOME MEASURES: Smoking initiation for 1898-1969 birth cohorts and lung cancer mortality in 1950-2009. RESULTS: In men, 1900-1925 birth cohorts showed high smoking initiation (>32%, >50% and >80% at 15, 17 and 29 years old, respectively). Correspondingly, the lung cancer mortality in these cohorts exceeded 1 per 1000 at a young age (50-54 years old). In women, smoking initiation increased clearly from the 1898 cohort to the 1925 cohort (2% to 12%, 4% to 24%, and 13% to 54% at 15, 17 and 29 years old, respectively). Correspondingly, the age at which the mortality exceeded 1 per 1000 became younger (75-79 to 60-64 years old). In both men and women, short-term decreases in initiation were seen from the late-1920s cohorts. Correspondingly, lung cancer mortality decreased. In women, initiation increased again after the mid-1930s cohorts, and mortality increased after they became 60-64 years old. CONCLUSIONS: Clear relationships between smoking initiation and lung cancer mortality across birth cohorts were observed. Countries with rapid increases in initiation in teens should not underestimate the risk in the distant future. Because of the long time lags within cohorts compared with rapid changes in smoking habits across cohorts, age-specific measures focusing on birth cohorts should be monitored.

Dose-response relationship from longitudinal data with response-dependent dose modification using likelihood methods.

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose-response relationship. In this study, we consider the dose-response relationship under these situations. We show that maximum-likelihood estimates are consistent without modeling the dose-modification mechanisms when the selection of the dose as a time-dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose-modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose-response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum-likelihood estimates of the dose-response relationship are consistent under the dose modification based only on observed responses.

An autoregressive linear mixed effects model for the analysis of unequally spaced longitudinal data with dose-modification.

The assessment of the dose-response relationship is important but not straightforward when the therapeutic agent is administered repeatedly with dose-modification in each patient and a continuous response is measured repeatedly. We recently proposed an autoregressive linear mixed effects model for such data in which the current response is regressed on the previous response, fixed effects, and random effects. The model represents profiles approaching each patient's asymptote, takes into account the past dose history, and provides a dose-response relationship of the asymptote as a summary measure. In an autoregressive model, intermittent missing data mean the missing values in previous responses as covariates. We previously provided the marginal (unconditional on the previous response) form of the proposed model to deal with intermittent missing data. Irregular timings of dose-modification or measurement can also be treated as equally spaced data with intermittent missing values by selecting an adequately small unit of time. The likelihood is, however, expressed by matrices whose sizes depend on the number of observations for a patient, and the computational burden is large. In this study, we propose a state space form of the autoregressive linear mixed effects model to calculate the marginal likelihood without using large matrices. The regression coefficients of the fixed effects can be concentrated out of the likelihood in this model by the same way of a linear mixed effects model. As an illustration of the approach, we analyzed immunologic data from a clinical trial for multiple sclerosis patients and estimated the dose-response curves for each patient and the population mean.

An estimation method of the clearance for a one-compartment model of a single bolus intravenous injection by a single sampling.

In clinical trials, sometimes only a single drug concentration can be measured from a patient, because of the burden on the patient. From a single concentration, we cannot generally obtain point estimates of each pharmacokinetic parameter in a patient. In this article, we propose a method to estimate the clearance using a one-compartment model of a single-bolus intravenous injection from a single concentration at a sampling point between 1.5 and 2.5 half-lives. This method requires an assumed value for the volume of distribution but is robust to misspecification. This approach is illustrated by simulated concentration data and cadralazine concentration data.

Analysis of covariance with pre-treatment measurements in randomized trials: comparison of equal and unequal slopes.

In randomized trials, an analysis of covariance (ANCOVA) is often used to analyze post-treatment measurements with pre-treatment measurements as a covariate to compare two treatment groups. Random allocation guarantees only equal variances of pre-treatment measurements. We hence consider data with unequal covariances and variances of post-treatment measurements without assuming normality. Recently, we showed that the actual type I error rate of the usual ANCOVA assuming equal slopes and equal residual variances is asymptotically at a nominal level under equal sample sizes, and that of the ANCOVA with unequal variances is asymptotically at a nominal level, even under unequal sample sizes. In this paper, we investigated the asymptotic properties of the ANCOVA with unequal slopes for such data. The estimators of the treatment effect at the observed mean are identical between equal and unequal variance assumptions, and these are asymptotically normal estimators for the treatment effect at the true mean. However, the variances of these estimators based on standard formulas are biased, and the actual type I error rates are not at a nominal level, irrespective of variance assumptions. In equal sample sizes, the efficiency of the usual ANCOVA assuming equal slopes and equal variances is asymptotically the same as those of the ANCOVA with unequal slopes and higher than that of the ANCOVA with equal slopes and unequal variances. Therefore, the use of the usual ANCOVA is appropriate in equal sample sizes.

Analysis of covariance with pre-treatment measurements in randomized trials under the cases that covariances and post-treatment variances differ between groups.

When primary endpoints of randomized trials are continuous variables, the analysis of covariance (ANCOVA) with pre-treatment measurements as a covariate is often used to compare two treatment groups. In the ANCOVA, equal slopes (coefficients of pre-treatment measurements) and equal residual variances are commonly assumed. However, random allocation guarantees only equal variances of pre-treatment measurements. Unequal covariances and variances of post-treatment measurements indicate unequal slopes and, usually, unequal residual variances. For non-normal data with unequal covariances and variances of post-treatment measurements, it is known that the ANCOVA with equal slopes and equal variances using an ordinary least-squares method provides an asymptotically normal estimator for the treatment effect. However, the asymptotic variance of the estimator differs from the variance estimated from a standard formula, and its property is unclear. Furthermore, the asymptotic properties of the ANCOVA with equal slopes and unequal variances using a generalized least-squares method are unclear. In this paper, we consider non-normal data with unequal covariances and variances of post-treatment measurements, and examine the asymptotic properties of the ANCOVA with equal slopes using the variance estimated from a standard formula. Analytically, we show that the actual type I error rate, thus the coverage, of the ANCOVA with equal variances is asymptotically at a nominal level under equal sample sizes. That of the ANCOVA with unequal variances using a generalized least-squares method is asymptotically at a nominal level, even under unequal sample sizes. In conclusion, the ANCOVA with equal slopes can be asymptotically justified under random allocation.

Association between autism and variants in the wingless-type MMTV integration site family member 2 ( WNT2) gene.

Autism is a severe neurodevelopmental disorder with a complex genetic aetiology. The wingless-type MMTV integration site family member 2 (WNT2) gene has been considered as a candidate gene for autism. We conducted a case-control study and followed up with a transmission disequilibrium test (TDT) analysis to confirm replication of the significant results for the first time. We conducted a case-control study of nine single nucleotide polymorphisms (SNPs) within the WNT2 gene in 170 patients with autism and 214 normal controls in a Japanese population. We then conducted a TDT analysis in 98 autistic families (trios) to replicate the results of the case-control study. In the case-control study, three SNPs (rs3779547, rs4727847 and rs3729629), two major individual haplotypes (A-T-C and G-G-G, consisting of rs3779547, rs4727847, and rs3729629), and global probability values of the haplotype distributions in the same region (global p=0.0091) showed significant associations with autism. Furthermore, all of these significant associations were also observed in the TDT analysis. Our findings provide evidence for a significant association between WNT2 and autism. Considering the important role of the WNT2 gene in brain development, our results therefore indicate that the WNT2 gene is one of the strong candidate genes for autism.

Screening method for severe sleep-disordered breathing in hypertensive patients without daytime sleepiness.

The high prevalence of sleep-disordered breathing (SDB) in hypertensive patients has been well studied. However, regular screening of SDB in these patients is not performed routinely as the diagnostic procedures are both time-consuming and labour-intensive. Overnight portable device screening is useful, but is sometimes not acceptable for asymptomatic SDB patients. We evaluated the usefulness of daytime 30-min recording with a portable recording device during pulse wave velocity (PWV) measurement sessions as a screening method for detection of asymptomatic SDB in hypertensive patients. Eighty-one hypertensive patients underwent 30-min daytime screening session using a Type III portable recording device during PWV measurement. Each screening session was followed by full overnight Level I polysomnography (PSG). The screening session included recordings of airflow (mouth-nose), chest movement, oximetry, and electrocardiography. The correlation coefficient between respiratory disturbance index (RDI) by screening session and apnea-hypopnea index (AHI) by PSG was 0.64. Using AHI ≥ 30 as diagnostic of severe SDB, 47 of 80 patients had the disorder based on PSG results. Using an RDI cut-off value of 22, the sensitivity and specificity for detection of severe SDB were 86.1% and 64.5%, respectively. Daytime 30-min recording with a portable device for apnea detection during PWV recording is useful for screening of asymptomatic severe SDB in hypertensive patients.

Changes in body mass index by birth cohort in Japanese adults: results from the National Nutrition Survey of Japan 1956-2005.

BACKGROUND: The National Nutrition Survey, Japan (NNS-J) provides annual anthropometric information for a whole nation over 50 years. Based on this survey, the mean body mass index (BMI) of Japanese men and elderly women has increased in recent decades, but that of young women has decreased. We examined the effect of birth cohort on this phenomenon. METHODS: We analysed data from the NNS-J for subjects aged 20-69 years. BMI during 1956-2005 and the prevalence of overweight and obesity (BMI >/= 25 kg/m(2)) during 1976-2005 were estimated. RESULTS: The BMI increased with age in every birth cohort, with similar increments, and did not peak until 60-69 years of age. However, with cross-sectional age, the BMI usually peaked before 60-69 years of age. The differences among cohorts already existed at 20-29 years of age, and slightly increased in men between 20-29 and 30-39 years of age. The BMI in all male age groups increased from the 1891-1900 through 1971-80 cohorts. However, in women, the figure increased until the 1931-40 cohorts, but later decreased. Changes in prevalence were generally consistent with changes in BMI. The recent increase (decrease in young women) in the mean BMI is attributable to birth cohort, indicating that thinner (fatter) and less recent birth cohorts have been replaced by fatter (thinner) ones. CONCLUSIONS: A cohort effect was quantitatively demonstrated based on a repeated annual survey. In Japan, the differences in BMI among cohorts were already established by young adulthood.

Association of the neuronal cell adhesion molecule (NRCAM) gene variants with autism.

Autism is a severe neurodevelopmental disorder of early childhood. Genetic factors play an important role in the aetiology of the disorder. In this study, we considered the NRCAM gene as a candidate gene of autism. This gene is expressed in the central nervous system and located in the 7q region, a susceptibility locus of autism. We conducted a case-control study of 18 single nucleotide polymorphisms (SNPs) within the NRCAM gene for possible association with autism in 170 autistic patients and 214 normal controls in a Japanese population. Seven SNPs in the NRCAM gene were significantly associated with autism, among which rs2300045 indicated the most prominent result (p=0.0009 uncorrected, p=0.017 corrected). In haplotype analyses, several individual haplotypes, including a common NRCAM haplotype C-T-T-C-T-T-G-C for rs3763463, rs1859767, rs1034825, rs2300045, rs2300043, rs2300039, rs722519, and rs2216259, showed a significant association after Bonferroni correction (p=0.0035 uncorrected, p=0.028 corrected). These haplotypes were located in the 5' intron-2 region of the gene. In addition, we also assessed the above mentioned SNPs and haplotypes using the transmission disequilibrium test with 148 trios of autistic families. Haplotype G-T-T-T-T-C-G-C in the same eight SNPs was also associated with autism. In summary, our findings provide evidence for a significant association of NRCAM with autism. Considering the important role of the NRCAM gene in brain development, our results therefore indicated that the NRCAM gene is one of the strong candidate genes for autism.

A bivariate autoregressive linear mixed effects model for the analysis of longitudinal data.

In clinical studies, dependent bivariate continuous responses may approach equilibrium over time. We propose an autoregressive linear mixed effects model for bivariate longitudinal data in which the current responses are regressed on the previous responses of both variables, fixed effects, and random effects. The equilibria are modeled using fixed and random effects. This model is a bivariate extension of the model for univariate longitudinal data given by Funatogawa et al. (Statist. Med. 2007; 26:2113-2130). As an illustration of the approach we analyze parathyroid hormone and serum calcium measurements in the treatment of secondary hyperparathyroidism in chronic hemodialysis patients.

An autoregressive linear mixed effects model for the analysis of longitudinal data which include dropouts and show profiles approaching asymptotes.

We are interested in longitudinal data of a continuous response that show profiles with an initial sharp change and approaching asymptotes for each patient, and many patients drop out with a reason related to the response. In this paper, we focus on a model that assumes a dropout process is missing at random (MAR). In this dropout process, we can obtain consistent maximum likelihood estimators as long as both the mean and covariance structures are correctly specified. However, parsimonious covariance structures for the profiles approaching asymptotes are unclear. An autoregressive linear mixed effects model can express the profile with random individual asymptotes. We show that this model provides a new parsimonious covariance structure. The covariance structure at steady state is compound symmetry and the other elements of the covariance depend on the measurement points. In simulation studies, the estimate of the asymptote is unbiased in MAR dropouts, but biased in non-ignorable dropouts. We also applied this model to actual schizophrenia trial data.

Do overweight children necessarily make overweight adults? Repeated cross sectional annual nationwide survey of Japanese girls and women over nearly six decades.

OBJECTIVE: To compare growth curves of body mass index from children to adolescents, and then to young adults, in Japanese girls and women in birth cohorts born from 1930 to 1999. DESIGN: Retrospective repeated cross sectional annual nationwide surveys (national nutrition survey, Japan) carried out from 1948 to 2005. SETTING: Japan. PARTICIPANTS: 76,635 females from 1 to 25 years of age. MAIN OUTCOME MEASURE: Body mass index. RESULTS: Generally, body mass index decreased in preschool children (2-5 years), increased in children (6-12 years) and adolescents (13-18 years), and slightly decreased in young adults (19-25 years) in these Japanese females. However, the curves differed among birth cohorts. More recent cohorts were more overweight as children but thinner as young women. The increments in body mass index in early childhood were larger in more recent cohorts than in older cohorts. However, the increments in body mass index in adolescents were smaller and the decrease in body mass index in young adults started earlier, with lower peak values in more recent cohorts than in older cohorts. The decrements in body mass index in young adults were similar in all birth cohorts. CONCLUSIONS: An overweight birth cohort in childhood does not necessarily continue to be overweight in young adulthood. Not only secular trends in body mass index at fixed ages but also growth curves for wide age ranges by birth cohorts should be considered to study obesity and thinness. Growth curves by birth cohorts were produced by a repeated cross sectional annual survey over nearly six decades.

An estimation method of the half-life for a one-compartment model of a single bolus intravenous injection by a single sampling.

In clinical trials, sometimes only a single drug concentration can be measured from a patient because of the patient's burden. In this case, the sampling point is usually identical for all patients. From a single concentration, we cannot generally obtain point-estimates of each pharmacokinetic parameter. In this paper, we propose a method to estimate the half-life of a one-compartment model of a single bolus intravenous injection from a single concentration at a sampling point of or after three half-lives. We analytically show that the later the sampling point is the better estimate of the half-life we can get. This approach is illustrated by simulated concentration-data and nicorandil concentration-data. Therefore, we compared the performance of the proposed method with that of the Bayesian approach.

The bayesian bias correction method of the first-order approximation of nonlinear mixed-effects models for population pharmacokinetics.

Population pharmacokinetic analysis usually employs nonlinear mixed-effects models. To estimate the parameters, Beal and Sheiner (1982) proposed the first-order method that employs a first-order Taylor series expansion around the means of random individual parameters. Because of the small computational burden and the high convergence proportion of maximization of the log likelihood function, this method is often used in practice. However, it is known that the estimates are biased. This paper proposes a simple procedure to reduce the bias. The proposed method maximizes the nonapproximated log likelihood functions of each individual given estimates of the population parameters derived from the first-order method, and the derived Bayes estimates of the random individual parameters are utilized to improve the estimates of the population mean parameters. We confirmed that the proposed method reduced the bias using simulated data and actual erythropoietin concentration data.