The place of crossover designs in infertility trials

Many people regard infertility as an unsuitable condition in which to run cross-over designs. Because if treatments are successful, then some women will become pregnant in the first period of treatment and if they become pregnant in the first period they are very unlikely to be treated in the second period. If data from only one period are available, then it will not be possible to perform the within-patient comparison. Hence, it could be argued, such designs are inherently unsuitable since they have a built-in tendency to produce missing data. To sum up this point of view, cross-over designs in infertility are likely to produce fewer data than one would wish and should be avoided. We see things differently, however. Suppose a parallel design is employed. If a couple is entered onto a parallel group design in infertility, they will have been allocated to one or the other treatment only. If the woman fails to achieve pregnancy, having been given that treatment, what could then be more natural than to offer the couple the chance of trying another? If another treatment is tried, then will it not be appropriate to record the outcome? Hence, in the worst case one will have all the data one would have from a parallel group trial but in practice one is likely to have more. How can more data be worse than less?Thus, to sum up our point of view, a cross-over trial is likely to produce more data than one would otherwise have had and should be encouraged. A debate along these lines has been running for some years now, with some promoting and occasionally running cross-over trials and others criticising them for doing so. In this thesis we use the logistic random effects model to illustrate that the message that the crossover design should be avoided is not the correct one. Rather, when using the crossover design one should be sure to analyze it correctly. The study has found that treatment estimates obtained by allowing women to get pregnant twice has lower standard errors than treatment estimates obtained by conducting the realistic infertility trials. In the scenario involving no period effects the two treatment estimates are not biased. In the scenario involving period effect, the standard errors of the treatment estimate obtained in the realistic data increases rapidly, while the standard errors of treatment estimate obtained by allowing women to get pregnant twice are not dissimilar from the standard errors obtained in the scenario involving no period effect. There is nothing wrong in conducting crossover designs in infertility provided appropriate statistical methods are employed. With the infertility crossover data set we can obtain not only conditional treatment estimates but also marginal estimates. Whereas in the parallel design we can only obtain marginal estimates. The study has found that if the treatment estimate say theta, can be obtained using parallel design data set, then surely, theta can be obtained using the crossover design data set, but not vice versa. Moreover the treatment estimate theta obtained using the crossover data set will be more consistent than the treatment estimate obtained using the parallel design. We recommend that crossover designs be used in infertility trials because it will surely benefit couples as couples will be have the opportunity to try both treatments

Word Problem for Groups and Monoids

Chapter 1 defines basic ideas such as definition of monoids, homomorphisms of monoids, congruences, factor monoids, free monoids, monoid presentations (rewriting systems), homomorphisms of monoids defined by presentations into known monoids, equivalent rewriting system, Tietze transformation and noetherian induction. In chapter 2 we give definitions of some properties of rewriting systems, eg noetherian, confluency, locally confluency and completeness. We also mention some well known reduction orderings. Some important theorems and lemmas are proved, which will later be used in the thesis. We define what is meant by a monoid to be left (right) FPinfinity. In chapter 3 we constuct free groups, free product of two monoids, monoids with amalgamated submonoids, HNN-extension in monoids and finally monoids with commutative submonoids using the concept of monoid presentations (rewriting system). The irreducibles of each presentation is discussed. And in each presentation, we emphasize that the irreducibles are unique, using theorems and lemmas proved in chapter 2. The word problem for monoids and groups is discussed in chapter 4. Examples of groups and monoids with solvable (unsolvable) word problem are given. We discuss residual properties of a monoid (group) and prove that residually finite monoids have solvable word problem

A New Class of Generalized Power Lindley Distribution with Applications to Lifetime Data

In this paper, a new class of generalized distribution called the Kumaraswamy Power Lindley (KPL) distribution is proposed and studied. This class of distributions contains the Kumaraswamy Lindley (KL), exponentiated power Lindley (EPL), power Lindley (PL), generalized or exponentiated Lindley (GL), and Lindley (L) distributions as special cases. Series expansion of the density is obtained. Statistical properties of this class of distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, quantile function, mean deviations, Bonferroni and Lorenz curves, entropy and Fisher information are derived. Method of maximum likelihood is used to estimate the parameters of this new class of distributions. Finally, a real data example is discussed to illustrate the applicability of this class of distribution

The Gamma log-logistic Weibull distribution: model, properties and application

In this paper, a new generalized distribution called the gamma log-logistic Weibull (GLLoGW) distribution is proposed and studied. The GLLoGW distribution include the gamma log-logistic, gamma log-logistic Rayleigh, gamma log logistic exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic as well as other special cases as sub-models. Some mathematical properties of the new distribution including moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and R\'enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A Monte Carlo simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and an application to real dataset to illustrate the usefulness of the model is given

The Gamma-Generalized Inverse Weibull Distribution with Applications to Pricing and Lifetime Data

A new distribution called the gamma-generalized inverse Weibull distribution which includes inverse exponential, inverse Rayleigh, inverse Weibull, Frechet, generalized inverse Weibull, gamma-exponentiated inverse exponential, exponentiated inverse exponential, Zografos and Balakrishnan-generalized inverse Weibull, Zografos and Balakrishnan-inverse Weibull, Zografos and Balakrishnan-generalized inverse exponential, Zografos and Balakrishnan-inverse exponential, Zografos and Balakrishnan-generalized inverse Rayleigh, Zografos and Balakrishnan-inverse Rayleigh, and Zografos and Balakrishnan-Fr\u27echet distributions as special cases is proposed and studied in detail. Some structural properties of this new distribution including density expansion, moments, Renyi entropy, distribution of the order statistics, moments of the order statistics and L-moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrate its usefulness are presented

Bilateral breast reconstruction with abdominal free flaps:a single centre, single surgeon retrospective review of 55 consecutive patients

Breast reconstruction using free tissue transfer is an increasingly utilised oncoplastic procedure. The aim was to review all bilateral breast reconstructions using abdominal free flaps by a single surgeon over an 11-year period (2003–2014). A retrospective review was performed on all patients who underwent bilateral breast reconstruction using abdominal free flaps between 2003 and 2014 by the senior author (DAM). Data analysed included patient demographics, indication for reconstruction, surgical details, and complications. Fifty-five female patients (mean 48.6 years [24–71 years]) had bilateral breast reconstruction. The majority (41, 74.5%) underwent immediate reconstruction and DIEP flaps were utilised on 41 (74.5%) occasions. Major surgical complications occurred in 6 (10.9%) patients, all of which were postoperative vascular compromise of the flap. Failure to salvage the reconstruction occurred on 3 (5.5%) occasions resulting in a total flap failure rate of 2.7%. Obesity (>30 kg/m2) and age > 60 years were shown to have a statistically increased risk of developing postoperative complications (P<0.05). Our experience demonstrates that abdominal free flaps for bilateral breast reconstruction fares well, with a flap failure rate of 2.7%. Increased body mass index and patient age (>60 years) were associated with higher complication rates

A New Generalized Log-Logistic Erlang Truncated Exponential Distribution with Applications

We introduce a new distribution via the Marshall-Olkin generator calledthe Marshall-Olkin Log-logistic Erlang-Truncated Exponential (MOLLoGETE) distribution.  Some structural properties of the distribution including series expansion of the density function, sub-models, hazard function, moments, conditional moments, mean deviations, distribution of order statistics, R´enyi entropy and maximum likelihood estimates are presented.  The new density function is an infinite linear combinations of Burr XII-Erlang-Truncated Exponential distributions.  The new generalization is applied to real data sets to evaluate the model performance

Prevalence of asthma among school children in Gaborone, Botswana.

Background: Asthma prevalence is high (&gt;10%) in developed countries and although data is still missing for most of Africa, rates are increasing in developing regions as they become more westernized. We investigated the prevalence of asthma in school children in Gaborone, Botswana. Methods: This was a cross sectional descriptive study. ISAAC methodology was used. A representative proportionate size random sample of two age groups of children (13-14 year olds and 6-7 year olds) was consecutively enrolled from 10 schools. The schools were selected using a table of random numbers. A minimum sample size of 924 individuals (462 from each group) was adequate to achieve a precision of 3 % around our estimated prevalence of asthma of 10% with 95% confidence assuming a non-response rate of 20%. Data was collected using the validated International study of Asthma and Allergies in children (ISAAC) questionnaire. In accordance with the ISAAC criteria, Asthma was defined as wheezing in the previous 12 months. Data was captured in microsoft excel and analysed using SPSS version 23. Results: The prevalence of asthma (wheezing in the previous 12 months) was 16.5% (194/1175). Among the 6-7 year olds, the prevalence of asthma (wheezing in the previous 12 months) was 15.9%, while among the 13-14 years olds it was 16.8 %. The prevalence school type was 22.3 % in private schools versus 14.5 % in public schools. More severe asthma was associated with older children, 13 -14 years. The older children reported more limited speech due to wheezing (OR= 2.0, 95% CI =1.034, 3.9, p-value=0.043), ever had asthma (OR= 1.5, 95% CI=1.031, 2.3, p-value=0.034) and wheezing during exercise (OR=3.4, 95% CI= 2.5, 4.9, p-value= &lt;0.001) compared to the younger children 6-7 years. Children from private schools had more wheezing symptoms. They were more likely to have ever wheezed (OR=2.2, .95% CI=1.7,2.9, p-value &lt; 0.0001), wheezed in the previous twelve months (have asthma) (OR=1.7,95%CI=1.2,2.4, p-value = 0.001), ever had asthma (OR=2.4, 95% CI=1.7,3.5, pvalue&lt; 0.0001), and wheezed during exercise (OR=1.8, 95% CI=1.4,2.4, p-value &lt; 0.0001). Conclusion: The prevalence of asthma amongst school children in Gaborone, Botswana is high with older children experiencing more severe symptoms of asthma

The rising tide of polypharmacy and drug-drug interactions:population database analysis 1995-2010

Background: The escalating use of prescribed drugs has increasingly raised concerns about polypharmacy. This study aims to examine changes in rates of polypharmacy and potentially serious drug-drug interactions in a stable geographical population between 1995 and 2010. Methods: This is a repeated cross-sectional analysis of community-dispensed prescribing data for all 310,000 adults resident in the Tayside region of Scotland in 1995 and 2010. The number of drug classes dispensed and the number of potentially serious drug-drug interactions (DDIs) in the previous 84 days were calculated, and age-sex standardised rates in 1995 and 2010 compared. Patient characteristics associated with receipt of ≥10 drugs and with the presence of one or more DDIs were examined using multilevel logistic regression to account for clustering of patients within primary care practices. Results: Between 1995 and 2010, the proportion of adults dispensed ≥5 drugs doubled to 20.8%, and the proportion dispensed ≥10 tripled to 5.8%. Receipt of ≥10 drugs was strongly associated with increasing age (20-29 years, 0.3%; ≥80 years, 24.0%; adjusted OR, 118.3; 95% CI, 99.5-140.7) but was also independently more common in people living in more deprived areas (adjusted OR most vs. least deprived quintile, 2.36; 95% CI, 2.22-2.51), and in people resident in a care home (adjusted OR, 2.88; 95% CI, 2.65-3.13). The proportion with potentially serious drug-drug interactions more than doubled to 13% of adults in 2010, and the number of drugs dispensed was the characteristic most strongly associated with this (10.9% if dispensed 2-4 drugs vs. 80.8% if dispensed ≥15 drugs; adjusted OR, 26.8; 95% CI 24.5-29.3). Conclusions: Drug regimens are increasingly complex and potentially harmful, and people with polypharmacy need regular review and prescribing optimisation. Research is needed to better understand the impact of multiple interacting drugs as used in real-world practice and to evaluate the effect of medicine optimisation interventions on quality of life and mortality.Publisher PDFPeer reviewe