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Florence Nightingale: statistician and consultant epidemiologist.

Florence Nightingale became a legend in her own lifetime and the image of the lady with the lamp still influences public thinking about the practice of nursing and its practitioners. Like many legends, her story has been adapted to suit changing circumstances and purposes. One could speculate why it is that particular aspects have come into greater prominence at particular times in history. This article explores a less-known aspect of her work, her expertise and use of statistics and epidemiology. And it illustrates how that expertise was called upon to address a major health problem in New Zealand in 1860.

Data Collection↗
PubMed1986

Examination of the generalized age distribution.

The formula for the age distribution and other relationships that follow from it for any (non-stable) population presented by Preston and Coale are significant contributions to demography. The formulas summarize the relationships among various demographic measures precisely, and are formally analogous to the relationships that hold for stable populations. The significance of these formulas cannot be overstated; they allow us to understand clearly the relationships among demographic measures in any arbitrary population. However, when it comes to using them for estimating demographic measures when census data are defective, the method of estimation is still affected by defective data. The reason is that the series of age-specific growth rates reflects the observed census age distributions exactly so that any defects in the census data are summarized in the growth rates. This paper begins with the formulation of the discrete version of the "new synthesis" developed by Preston and Coale. With the discrete formulation, the three kinds of errors introduced when the continuous time formulas are applied to real data can be avoided. Then it is pointed out that when two accurate census data are available, the Preston-Coale procedure of "estimating" the age distribution at the second census is equivalent to checking the identity of the age distribution formula. Also "estimating" mortality by the procedure of Preston-Coale is shown to be equivalent to obtaining mortality directly from intercensal survival rates. That the procedure which involves the age-specific growth rates is equivalent to those that involve the intercensal survival rates may have escaped notice because there are no a priori constraints for patterns of age-specific growth rates to follow. The irregularity in growth rates due to defective data are not distinguishable from true irregularity that exists in the population, contrary to the well-known regularity in the pattern of survival rates in human populations.

Actuarial Analysis↗
PubMed1984

The analysis of linkages in demographic theory.

Many seemingly different questions that arise in the analysis of population change can be phrased as the same technical question: How, within a given demographic model, would variable y change if the age- or time-specific function f were to change arbitrarily in shape and intensity? At present demography lacks the machinery to answer this question in analytical and general form. This paper suggests a method based on modern functional calculus for deriving closed-form expressions for the sensitivity of demographic variables to changes in input functions or schedules. It uses this "linkage method" to obtain closed-form expressions for the response of the intrinsic growth rate, birth rate, and age composition of a stable population to arbitrary marginal changes in its age patterns of fertility and mortality. It uses it also to obtain expressions for the transient response of the age composition of a nonstable population to time-varying changes in the birth sequence, and to age-specific fertility and mortality patterns that change over time. The problem of "bias" in period vital rates is also looked at.

Adult↗
PubMed1984

Population redistribution and changes in the size-density slope.

As regional population density increases territorial units tend to subdivide. For maximum societal time-efficiency the slope relating the logarithms of unit areas to those of unit densities should be -2/3. When boundaries become fixed, however, observed slopes tend to drift toward a value of zero. It was earlier hypothesized that such slope-erosion was due to increasing concentration of the population. Historical data for the primary political divisions of ten nations shows general support for the hypothesis.

Europe↗
PubMed1981

Some further observations on the index of residential differentiation.

The relationship between the index of residential differentiation (RDI), a recently introduced measure of residential segregation which is designed to summarize the distribution of c social groups in a single index, and the indices of dissimilarity (D) and segregation (SI) is examined. It is demonstrated that RDI is a natural extension of D, and that when c = 2, RDI = D; when c greater than 2, it is possible to stipulate RDI in terms of SI, but it is not possible to stipulate RDI in a straightforward manner in terms of D. An adjusted RDI is then suggested in which random segregation rather than complete desegregation is used as the baseline.

Demography↗
PubMed1977

Community satisfaction, expectations of moving and migration.

A previous residential mobility model (Speare, 1974) assumes an additive relationship between residential satisfaction, desire to move, and mobility. This paper elaborates the model and applies it to intercounty migration. An interaction between community satisfaction and expectations to migrate is hypothesized which distinguishes four groups of decision makers. A survey in Durham, North Carolina and a unique mobility follow-up over eight years provide the data to test the model and the interaction. Furthermore, using various time periods for identifying migrants offers some methodological insights. Results support Speare's general formulation but only after the interaction is taken into account. A three-year migration interval is found to be appropriate.

Attitude↗
PubMed1991

[Population effects of fluctuation in fecundity and mortality in Triatoma infestans: simulation using Leslie matrices].

The population effects of known fluctuations in fecundity and mortality of T. infestans was studied through simulation using Leslie matrices. The effect of mortality and fecundity cycles was a stepped cycling through the growing phase, with no significant population decreases. Density dependent regulation stabilizes changes during the steady phase. The main effect is on population composition with the establishment of a regular annual cycle in the proportion of different age groups. Cycles with high number of larvae may be misinterpreted as an adult plague.

Animals↗
PubMed1995

Looking for chaos in brain slices.

Many signals measured from the nervous system exhibit apparently random variability that is usually considered to be noise. The development of chaos theory has revealed that such random appearing variability may not, in fact, be random, but rather may be deterministic behavior that can reveal important information about the system's underlying mechanisms. We present some new methods for distinguishing determinism from randomness in experimental data, and we apply these methods to population neural responses recorded from hippocampal tissue slices.

Brain↗
PubMed2003

Prediction of frequency-dependent ultrasonic backscatter in cancellous bone using statistical weak scattering model.

The goal of this study was to propose a model for the ultrasonic frequency-dependent backscatter coefficient in cancellous bone. This model allows us to address the inverse problem and to predict the mean trabecular thickness. A weak scattering model is used and the backscatter coefficient is expressed in terms of an autocorrelation function of the medium. Different autocorrelation functions (Gaussian, exponential and densely populated media) were used to compute the backscatter coefficient and comparison is made with experimental data for 19 specimens and for frequency ranging from 0.4 to 1.2 MHz. For each specimen, a nonlinear regression was performed and the mean trabecular thickness is estimated. Experimental data and theoretical predictions were averaged over the 19 specimens. A good agreement between experimental data and predictions was found for both the magnitude and the frequency-dependence of the backscatter coefficient. We also found a good agreement between the experimental mean trabecular thickness (Tb. Th = 130 +/- 6.5 micro m) derived from the analysis of bone 3-D microarchitecture using high-resolution microtomography and theoretical predictions (d(Gauss) = 140 +/- 10 micro m, d(exponential) = 153 +/- 12.5 micro m and d(dense) = 138 +/- 6.5 micro m). These results open interesting prospects for the estimation of the mean trabecular thickness from in vivo measurements.

Acoustics↗
PubMed2004

Synchronous cultures from the baby machine. A model for animal cells.

A baby-machine system that produces newborn Escherichia coli cells from cultures immobilised on a membrane was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth, and a model designed to characterise the nature and quality of the synchrony of such cells in a quantitative manner has been published. The baby machine has now been adapted for animal cells, and the present article is an attempt to modify the model to include these cells as well. The model consists of five elements, giving rise to five adjustable parameters (and a proportionality constant): a major, essentially synchronous group of cells with ages distributed normally about zero; a minor, random component from a steady-state population on the membrane that had undergone only very little age selection during the elution process; a fixed background count, to allow for the signals recorded by the electronic particle counter produced by debris and electronic noise; a time-shift, to account for differences between time of cell division and end of sample collection; and the coefficient of variation of the interdivision-time distribution, taken to be reciprocal-normal. It is this last feature, a reciprocal-normal rather than a Pearson type III interdivision-time distribution, that distinguishes this version of the model from its predecessor. The model is fitted by unconstrained non-linear least-squares to data from three different leukemia cell lines. The standard errors of the parameters are quite small in all cases, making their estimates highly significant; the quality of the fit is striking. The five parameters of the model can be divided into two nuisance parameters, two that are associated with the methodology and one that describes an inherent property of the cell itself; it turns out that both methodology parameters are zero in all three data sets studied. We also discuss the partition of the transition-time dispersion between the age distribution of the newborn cells and the age distribution of dividing cells and show that a reliable estimate of the corresponding parameters requires an experiment that extends over at least two and a half doubling times.

Animals↗
PubMed2001

Comparison of nonlinear mixed-effect and non-parametric expectation maximisation modelling for Bayesian estimation of carboplatin clearance in children.

OBJECTIVE: The pharmacodynamic-pharmacokinetic relationships for carboplatin involve the area under the curve of ultrafiltrable plasma concentrations versus time (AUC). The objective of the study was to compare two specific population pharmacokinetic methodologies, nonlinear mixed-effect model (NONMEM) and non-parametric expectation maximisation (NPEM), when they are applied to sparse carboplatin pharmacokinetic data in order to obtain an individual value for carboplatin clearance by Bayesian estimation. METHODS: The data from 117 patients (from 1 month to 18 years old) were available. For 20 patients randomly selected, the carboplatin clearance obtained by Bayesian estimation using two plasma ultrafiltrable concentrations was compared with that obtained by individual analysis using all concentrations. RESULTS: Both methodologies were unbiased with mean relative percentage errors (95%CI) of -1.9% ( 7.8; +4.1%) and +6.4% (-2.1; +14.9%) for NONMEM and NPEM, respectively. A comparison of precision between the two methods showed that they were not significantly different (12.5% for NONMEM, and 18.9% for NPEM), but the percentage error ranged between -21% and + 19% for NONMEM, and -35% and + 42% for NPEM. A NONMEM analysis was also performed with all the data available (117 children) in order to update an equation describing the relationship between carboplatin clearance and the patients' covariates. The best relationship corresponded to the equation: clearance (ml/min) = [4.47 x body weight x (1 -0.22 x Np)/(l + 0.0156 x Scr)] +6.4, with body weight in kilograms and where Scr is serum creatinine in micromoles per litre and Np= 1 or 0 for unilateral nephrectomy or not, respectively. CONCLUSION: These methodologies may be useful for dose individualisation and drug monitoring of carboplatin in paediatric patients. Since the mode of administration of carboplatin in paediatric practice in some protocols is daily 1-h i.v. infusion repeated up to five times, dose individualisation may be performed from the clearance observed after the first administration, given an overall target AUC.

Adolescent↗