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Biomedical subjects

P Royston

Publications and source records attributed to P Royston.

At least 19 recordsLinked to original sources

The use of cusums and other techniques in modelling continuous covariates in logistic regression.

The assessment of continuous covariates singly as possible predictors in a multivariable logistic regression model is an important first step in the analysis. An approach to plotting which uses a cusum (cumulative sum) of the binary response variable is described. Extreme-deviation statistics associated with the cusum may be used to detect monotonic and non-monotonic trends. Probability plots of the covariate in the two groups defined by the response variable may help to determine the appropriate scale (transformation) of the covariate and to anticipate possible problems with the logistic fit. The ratio of the variances in the response/non-response groups is informative about the need for a quadratic term in the logistic model. Smoothed scatterplots of the response are valuable in displaying the observed and fitted values. The techniques are illustrated with two data sets.

Binomial Distribution

Cumulative conception and livebirth rates after in-vitro fertilisation.

Cumulative conception and livebirth rates related to age and cause of infertility provide the most useful estimate of success after in-vitro fertilisation (IVF), but limited data are available. It is also uncertain whether the probability of pregnancy, livebirth, and pregnancy failure changes with repeated treatment cycles. To assess the effects of patients' age and cause of infertility on these outcomes, we studied the results of 5055 consecutive IVF cycles (773 clinical pregnancies, 518 livebirths) undertaken on 2735 patients in a single IVF unit. Cumulative conception and livebirth rates were analysed by the life-table approach and differences in rates between age-groups and between causes of infertility were measured by the log-rank test and logistic regression modelling. Both conception and livebirth rates per cycle declined with age (p less than 0.001), and cumulative conception and livebirth rates after five treatment cycles were about 54% and 45%, respectively, at 20-34 years, compared with 38.7% and 28.9% at 35-39 years and 20.2% and 14.4% at greater than or equal to 40 years. The two rates were significantly different between causal groups (p less than 0.001 and p = 0.02, respectively) and were lowest in patients with male infertility or multiple infertility factors. The pregnancy failure rate was higher (p = 0.006) in women over the age of 34 years and there was a significant decline in the chances of pregnancy and livebirth per cycle with successive treatment cycles.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult

Which measures of skewness and kurtosis are best?

Indices of distributional shape based on linear combinations of order statistics have recently been described by Hosking. Their usefulness as tools for practical data analysis is examined. They are found to have several advantages over the conventional indices of skewness and kurtosis (square root of b1 and b2) and no serious drawbacks. It is proposed, therefore, that they should replace square root of b1 and b2 in routine data analysis. To implement this suggestion, action by the developers of standard statistical software is needed.

Bias

Model-based screening by risk with application to Down's syndrome.

Screening for a disorder may be carried out by assessing the risk that an individual is affected given the values of variables whose distributions alter when the disorder is present. An optimal screening policy is obtained by identifying those individuals whose risk is greater than some cut-off value. This paper summarizes the way in which risk is derived from the likelihood ratio of being affected by the disorder, and compares three different methods of estimating the likelihood ratio, namely direct estimation, logistic regression and distribution modelling. For continuous variables that have a multivariate normal distribution, screening by risk is equivalent to the use of quadratic discrimination. The paper shows how estimates of the risk and associated detection and false positive rates can be derived for a screening policy which uses specified risk cut-offs. Screening by risk has the counter-intuitive property that as the separation in the distribution of screening variables between affected and unaffected individuals increases, the detection and false positive rates may both increase. The approach is explored using data on antenatal screening for Down's syndrome. The method of choice is model-based; the model is described and tested for goodness of fit. Complications arising from outliers and non-normality must be overcome before an appropriate assessment of risk can be made. The concept of shrinkage is used to estimate the detection of false positive rates that may be expected in a new data set.

Confidence Intervals

Estimation, reference ranges and goodness of fit for the three-parameter log-normal distribution.

The three-parameter log-normal distribution (3PL) is an appropriate model for many of the continuous variables encountered in medicine. It is shown how to obtain different types of estimate and approximate (sometimes conservative) confidence intervals for the parameters of the 3PL and for certain functions of them, particularly in the calculation of reference ranges of clinical measurements. A simple non-iterative estimate of the shift parameter is described. The Shapiro-Wilk test of non-normality is modified to allow it to be used for testing for departure from the 3PL. Its power is compared with that of other well-known tests. The methods are illustrated using several data sets.

Algorithms

Atrial natriuretic peptide, cyclic guanosine monophosphate and sodium excretion during postnatal adaptation in male infants below 34 weeks gestation with severe respiratory distress syndrome.

The role of atrial natriuretic peptide (ANP), in the perinatal period, is at present unclear. In adults urinary cyclic guanosine monophosphate (cGMP) is considered an index of the biological activity of plasma ANP. The aim of this study was to determine the relationship between plasma ANP, cGMP excretion (cGMPex) and sodium excretion (Naex) in preterm infants in the first days after birth. Sequential, 4 hourly, measurements of plasma ANP, cGMPex and Naex were made in 12 male neonates of median gestational age 27 weeks (range 25-33) and median birth weight 0.981 kg (range 0.635-2.029) over a median period of 5.2 days (range 2.3-10). The ratios of cGMPex to ANP and of Naex to cGMPex were each plotted against postnatal age. The ratio of cGMPex to ANP increased ten fold in the first 3-4 days after birth but then remained relatively constant; the ratio of Naex to cGMPex showed a steady increase from birth. We conclude that, in extremely immature infants, renal sodium loss in response to cGMP increases rapidly during the first 10 days after birth. In addition, after 3-4 days from birth, plasma ANP ia associated with a constant proportionate rate of cGMP excretion though, as the plateau ratio of cGMPex to ANP varied widely between babies, cGMPex cannot be used to predict plasma ANP in cross sectional studies. These changes may reflect postnatal adaptation and/or maturation of both ANP receptors and cGMP mediated cascades. In the immediate postnatal period, plasma ANP may also have a non-renal role.

Age Factors

The effect of pethidine on the neonatal EEG.

Thirty-two preterm infants were monitored with an on-line cotside EEG system for periods of up to nine days. Changes in the normal pattern of discontinuity of the EEG were seen in association with pethidine administration. The duration of the EEG suppression after pethidine administration was greatest after the first dose and progressively less with subsequent doses. It was not related to the gestational maturity or postnatal age at which the dose was given. This system of EEG analysis allowed recognition of this previously undescribed effect of pethidine on the neonatal EEG, and should have application to monitoring the effects of brain function of other drugs in routine neonatal practice.

Brain

Identifying the fertile phase of the human menstrual cycle.

The identification of the human fertile phase as the time during which a woman or a couple may conceive is elusive. The fertile time depends on many factors in each individual menstrual cycle and may be said to be more of a statistical than a physiological entity. This paper reviews the application of statistical methods to three areas related to conception and the fertile phase. The first is the prediction and detection of ovulation from serial measurements, such as hormones, basal body temperature and cervical mucus, throughout the menstrual cycle. Typically, such variables increase from some baseline level to a peak around ovulation (the most fertile time), then subside to low levels in the postovulatory phase. The statistical challenge is to detect the rise (signalling the onset of potential fertility) and subsequent fall. Analytic methods considered include thresholds, Bayesian change-point models and particularly the cumulative sum (cusum) technique which is both simple to apply and understand, and effective. The second area comprises appropriate methods of analysing and interpreting data from clinical studies of the fertile phase, especially in so-called natural family planning (NFP) where it is usual for women to observe several indices of potential fertility. Such studies usually try to establish the temporal relationships between markers of the fertile phase and examine the success of different combinations of markers in delineating the fertile time in comparison with a standard 'defined' phase, for example, the interval from three days before to two days after the peak of luteinizing hormone. The third area is the assessment of the probability of conception on certain days of the cycle, which is vital to the understanding of the fertile phase and its application to NFP. Direct estimation of such probabilities is impractical; instead, resort must be made to estimation by maximum likelihood of the parameters of specially constructed models. Suitable models are described. Finally, the need for a new prospective study of the probability of conception in relation to the markers of the fertile phase used in the symptothermal method of NFP is discussed.

Female

Constructing time-specific reference ranges.

Reference ranges which take time (such as age) into account are often required in medicine, but simple, systematic and efficient statistical methods for constructing them are lacking. A method is described which is based on low order polynomial curves (linear, quadratic or occasionally cubic), together with guidelines for when and how to apply a logarithmic transformation to the variable analysed, testing for departures from normality, and assessment of the adequacy of the reference range which is constructed from the regression line plus or minus a multiple of the standard deviation. Standard statistical packages may be used to carry out the calculations. The question of comparing two or more groups of patients is addressed. Three examples are discussed in detail.

Adolescent

Estimation of reference ranges from normal samples.

Reference ranges are very widely used in medicine, and are typically computed as mean plus or minus two standard deviations. However, their precise statistical basis is rarely discussed, and is open to different interpretations. They are sometimes calculated using the Student t distribution and satisfy the condition that the expected coverage of the reference population is some nominal value such as 95 percent or 99 per cent. A case is made for using reference ranges which are based on estimating symmetric centiles of the underlying normal distribution, and appropriate formulae are given. The simplest such estimator, the sample mean plus or minus the normal-based number of sample standard deviations, is shown to have both theoretical and practical advantages.

Normal Distribution

Estimating departure from normality.

Departure of a sample from a normal distribution should be assessed by a quantity that is meaningful in terms of the data, rather than merely by the P-value from a test statistic. Indices of departure based on the Shapiro-Francia W' and the Shapiro-Wilk W statistics are derived, and shown to have a natural interpretation in relation to the normal probability plot. A new diagnostic plot is proposed. An example is given which shows the relationship between one of the new indices and errors in calculated reference ranges due to non-normality of the data.

Adult

An evaluation of the Bioself 110 electronic fertility indicator as a contraceptive aid.

The Bioself 110 is a hand-held electronic device that combines the BBT and calendar methods of fertility regulation for planning or preventing pregnancy. A pilot study was undertaken in three centers in the United Kingdom to evaluate the Bioself 110 as a contraceptive aid. This paper deals with 1238 cycles from 131 women. Only one unplanned pregnancy occurred where a volunteer correctly used the Bioself 110 and had intercourse on a supposedly "safe" day. A second pregnancy was experienced by a volunteer who incorrectly used the device and had intercourse on what she though was a "safe" day. Another 11 unplanned pregnancies occurred due to barrier method failures, as well as 11 pregnancies where the volunteers knowingly had unprotected intercourse during the fertile phase. There were five planned pregnancies. The Bioself 110 was correctly used in 71% of the cycles studied. Eighty-four percent of the volunteers indicated that they were satisfied with the Bioself 110 after six to twelve cycles of use. It was concluded that the Bioself 110 can serve as an effective family planning aid and should be added to the menu of contraceptive methods available to women today.

Adolescent

Detection of endometrial cancer by transvaginal ultrasonography with color flow imaging and blood flow analysis: a preliminary report.

A prospective study was undertaken to assess whether changes in uterine blood flow could be used to detect endometrial cancer in 138 selected postmenopausal women (34 had uterine bleeding, 17 with endometrial cancer; 104 did not have uterine bleeding; 1 had endometrial cancer). Thirty-five of the asymptomatic women were receiving estrogen replacement therapy (ERT). The endpoints were endometrial (including tumoral) thickness and a pulsatility index (PI) derived from flow velocity waveforms recorded from both uterine arteries and from within a tumor. We found an overlap in endometrial thickness between those women with endometrial cancer and those without. The mean arterial PI value was invariably lower in women with postmenopausal bleeding and endometrial cancer (mean 0.91, range 0.31-1.49) than in those with other reasons for the blood loss (mean 3.83, range 1.95-6.40). The index was 1.10 in the woman with endometrial cancer but no sign of postmenopausal bleeding. Blood flow impedance was inversely related to stage of cancer. PI values in healthy women tended to increase slightly with age, but decrease during ERT. The detection rate was 100% within the limitations of the study design, and the false-positive rate was 1% for all women not receiving ERT and 11% for patients receiving ERT. Malignant tumors show signs of altered vascularization and a low PI (mean 0.49, range 0.29-0.92). We conclude that transvaginal ultrasonography, with or without color flow imaging, and blood flow analysis can be used to detect endometrial cancer in women with postmenopausal bleeding. A screening procedure for asymptomatic women must allow for changes in uterine blood flow during ERT.

Aged

Ultrasound screening for familial ovarian cancer.

We have used transvaginal ultrasonography to screen 776 asymptomatic women for familial ovarian cancer. Every woman had at least one first- or second-degree relative develop the disease (677, 87%; and 98, 13%, respectively). The mean age of the study population was 51 years (range, 24 to 78 years); 52% were premenopausal, 36% were naturally postmenopausal, and 12% had undergone a hysterectomy. Overall, 43 women (5.5%) were referred for surgical investigation and 39 had a laparatomy. Nineteen/thirty-nine (48%) had bilateral ovarian masses, and 15% of abnormal ovaries had more than one type of histopathology. Twenty-three tumors and thirty-two tumor-like conditions were detected. There were 3 cases of primary ovarian cancer (prevalence, 3.9/1000), all FIGO stage Ia. None of the women has developed ovarian cancer within the first year of the scan (giving a provisional detection rate of 100%). The false positive rate was 40/773 (5.2%), the predictive value of a positive screen result was 7.7%, and the odds in favor of finding any mass at laparotomy were about 19 to 1 or for any tumor, 1 to 1. At surgery the odds against finding primary ovarian cancer were 12 to 1. The positive predictive value of the screening procedure and the prevalence of the disease were significantly higher than the corresponding values from a previous population-based screening program.

Adult

Symptothermal and hormonal markers of potential fertility in climacteric women.

One hundred seventy-seven menstrual cycles in 36 women between 45 and 53 years of age were studied prospectively. All the women were experienced in the symptothermal method of natural family planning. The objective was to determine the symptothermal and hormonal indices of potential fertility by measuring urinary estrone glucuronide and pregnanediol glucuronide. Thirty-three percent had regular cycles consistent with potential fertility, 19% had cycles consistent with infertility, and 47% had a mixture of both types of cycle.

Biomarkers

Analysis of serial measurements in medical research.

In medical research data are often collected serially on subjects. The statistical analysis of such data is often inadequate in two ways: it may fail to settle clinically relevant questions and it may be statistically invalid. A commonly used method which compares groups at a series of time points, possibly with t tests, is flawed on both counts. There may, however, be a remedy, which takes the form of a two stage method that uses summary measures. In the first stage a suitable summary of the response in an individual, such as a rate of change or an area under a curve, is identified and calculated for each subject. In the second stage these summary measures are analysed by simple statistical techniques as though they were raw data. The method is statistically valid and likely to be more relevant to the study questions. If this method is borne in mind when the experiment is being planned it should promote studies with enough subjects and sufficient observations at critical times to enable useful conclusions to be drawn. Use of summary measures to analyse serial measurements, though not new, is potentially a useful and simple tool in medical research.

Animals

Maternal smoking habits and Down's syndrome.

Two series of pregnancies were studied to investigate the relationship between maternal smoking and the risk of fetal Down's syndrome. In the first series, ascertained in the 1960s, in which smoking habits were determined after the outcome of pregnancy was known, the proportion of smokers (47 per cent) among the 461 women whose pregnancies ended in the birth of an infant with Down's syndrome was similar to that in the 461 controls (46 per cent) who had pregnancies affected by other congenital disorders. In the second series, ascertained between 1973 and 1984, smoking habits were determined by measurement of cotinine in antenatal serum samples that were routinely collected and stored or, if a serum sample was not available, from information in the antenatal notes. In this series, the proportion of smokers (14 per cent) among the 91 women who had pregnancies associated with Down's syndrome was lower than that among 413 controls (19 per cent), though this was not statistically significant. Collectively, our results provide no evidence for an association between fetal Down's syndrome and smoking. Other published studies found a deficit of smokers among women who had pregnancies associated with Down's syndrome. This may be partly due to some studies not taking adequate account of maternal age (older women are more likely to have had a Down's syndrome pregnancy but are less likely to be smokers) and partly due to the greater tendency for positive findings to be published than negative ones.

Adult