Choice Of Time Scale Research Articles

LONGITUDINAL METHODS FOR ASSESSING PROGRESSION OF MULTIMORBIDITY AND RELATED HEALTH OUTCOMES

Abstract The growing body of longitudinal research on multimorbidity (≥ 2 chronic conditions) has identified that multimorbidity progression in mid and late life is associated with change in other health domains (e.g., mobility limitations) and can have far-reaching effects on person-centered outcomes such as health-related quality of life. Several increasingly accessible quantitative methods can be applied to the longitudinal study of multimorbidity and related health outcomes, but there has been relatively little work describing and synthesizing the merits and limitations of methods available for this purpose. We will discuss the application and limitations of popular longitudinal methods that can be applied to the study of change in multimorbidity and associated health outcomes. We will consider overarching issues in the longitudinal study of multimorbidity including operationalizing multimorbidity, data-related concerns such as measurement invariance, and choice of time scale (i.e., change in age or calendar time). We will then cover methods aligned to four specific research objectives: 1) examining individual change in multimorbidity, 2) identifying population sub-groups that follow similar trajectories of multimorbidity progression, 3) understanding when, how, and why individuals/groups shift to more advanced stages of multimorbidity, and 4) examining the co-progression of multimorbidity with key health domains over time. This work will help establish a common language for assessing longitudinal changes in multimorbidity, inform research that can fill gaps in our knowledge regarding multimorbidity progression and critical periods of change, and support the identification of groups that experience divergent rates and etiological pathways of disease progression.

Investigating the impact of calibration timescales on streamflow simulation, parameter sensitivity and model performance for Indian catchments

ABSTRACT Hydrological model calibration is a quintessential step in model development, and the time scale of calibration depends on the application. However, the implications of choice of time scale of calibration have not been explored extensively. Here, we evaluate the effect of the time scale of calibration on model sensitivity, best parameter ranges, and predictive uncertainty for three river basins using the Soil and Water Assessment Tool (SWAT) model. Multiple models were set up for three different catchments from southern India. Our results showed that the sensitivity of the parameters, best parameter ranges, and model performance are conditioned on the time scale of calibration. The models calibrated at coarser time scales marginally outperformed the models calibrated at fine time scale in terms of Nash-Sutcliffe efficiency and percentage bias. Transfer of parameters across scales (both from coarse to fine and from fine to coarse) have a general tendency to worsen the model performance in all three catchments, with few exceptions.

Choice of time-scale in time-to-event analysis: evaluating age-dependent associations

PurposeTo compare hazard ratios obtained by using time on study (conventional) versus biological age as the time-scale in survival analyses for a known age-dependent association between an exposure and outcome. MethodsWe conducted a retrospective cohort study of 9 million people in Ontario, Canada who were followed from 2003 to 2018 to identify incident ischemic stroke using linked administrative health data. Using cause-specific hazards models, we calculated hazard ratios (HR) of ischemic stroke in women compared to men using the two different time scales. By using piecewise estimates and interaction terms, we evaluate the effect of sex on stroke incidence across age groups. ResultsIn unadjusted analyses, the reduction in the hazard of ischemic stroke in women compared to men was greater with age as time-scale (HR 0.77; 0.76–0.78) compared to conventional time-scale (HR 0.93; 0.92–0.93); however, the estimates were similar (HR 0.78 with age vs. 0.77 with conventional) in multivariable adjusted analyses. The estimates obtained by two methods across different age groups varied modestly, except in those under 30 years (HR 1.47; 1.19–1.83 with age vs. 1.08; 0.99–1.17 with conventional). ConclusionsWhen evaluating age-dependent association between an exposure and outcome, estimates of association vary based on the time-scale used in survival analysis, requiring thoughtful consideration.

Age Bias in Time From Diagnosis Comparisons of Prostate Cancer Treatment.

Observational studies of prostate cancer treatment have demonstrated a major survival benefit with prostatectomy; randomized trials have been less certain in this regard. This discrepancy is hypothesized to be due to the use survival calculations based on time from diagnosis (TFD), which can bias toward better survival for younger cohorts. Attained age is an alternative timescale that can mitigate this effect. A Surveillance, Epidemiology and End Results comparison of prostatectomy, radiotherapy (XRT), and conservative management for localized prostatic cancer was conducted to compare these 2 timescales. Kaplan-Meier analysis was used to contrast overall survival based on TFD and attained age from 279,064 prostate cancer cases. Proportional hazards models were constructed and baseline hazard functions estimated. The prostatectomy cohort averaged 9 to 12 years younger than the radiotherapy or conservative management cohorts, and the baseline hazard depended more strongly upon age than TFD. Survival calculations based on TFD demonstrated a major benefit with prostatectomy compared with XRT and conservative management, consistent with prior observational studies. Calculations based on attained age, however, demonstrated lesser differences between treatment cohorts and were more consistent with published randomized trials. The survival benefit apparent to prostatectomy in conventional observational cohort studies could reflect an age-related bias attributable to their use of TFD analysis. Care is warranted in the choice of timescale in observational analysis if large age differences exist between treatment cohorts. Randomized controlled trials remain the most reliable means to compare prostate cancer treatments.

Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics.

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

A reference relative time-scale as an alternative to chronological age for cohorts with long follow-up.

BackgroundEpidemiologists have debated the appropriate time-scale for cohort survival studies; chronological age or time-on-study being two such time-scales. Importantly, assessment of risk factors may depend on the choice of time-scale. Recently, chronological or attained age has gained support but a case can be made for a ‘reference relative time-scale’ as an alternative which circumvents difficulties that arise with this and other scales. The reference relative time of an individual participant is the integral of a reference population hazard function between time of entry and time of exit of the individual. The objective here is to describe the reference relative time-scale, illustrate its use, make comparison with attained age by simulation and explain its relationship to modern and traditional epidemiologic methods.ResultsA comparison was made between two models; a stratified Cox model with age as the time-scale versus an un-stratified Cox model using the reference relative time-scale. The illustrative comparison used a UK cohort of cotton workers, with differing ages at entry to the study, with accrual over a time period and with long follow-up. Additionally, exponential and Weibull models were fitted since the reference relative time-scale analysis need not be restricted to the Cox model. A simulation study showed that analysis using the reference relative time-scale and analysis using chronological age had very similar power to detect a significant risk factor and both were equally unbiased. Further, the analysis using the reference relative time-scale supported fully-parametric survival modelling and allowed percentile predictions and mortality curves to be constructed.ConclusionsThe reference relative time-scale was a viable alternative to chronological age, led to simplification of the modelling process and possessed the defined features of a good time-scale as defined in reliability theory. The reference relative time-scale has several interpretations and provides a unifying concept that links contemporary approaches in survival and reliability analysis to the traditional epidemiologic methods of Poisson regression and standardised mortality ratios. The community of practitioners has not previously made this connection.

Time Scale in Follow-up Studies

To the Editor: Colonge et al.’s manuscript on the choice of primary time scale for epidemiologic follow-up studies makes an important contribution to methods for longitudinal data analysis.1 We agree with their assessment that the choice of time scale should be based on “the goals of the study and the need for confounder adjustment.” As the authors say, in most studies of disease incidence, age will be the appropriate time scale (especially when compared to time on study), but there may be other relevant time scales for different applications. For example, in studies of disease prognosis, time since onset or diagnosis is commonly used.2, 3 In a study examining the association between the use of a particular medication and breast cancer recurrence, time since initial breast cancer diagnosis may be an important confounder and one that should be accounted for flexibly. Risk of breast cancer recurrence depends on time since diagnosis in a complex way (Figure 1, unpublished data). And, time since diagnosis might also be associated with the exposure of interest, making it a confounder. If time since diagnosis is chosen as the time scale, age should be adjusted for as a covariate in multivariable regression models as it, too, is related to the recurrence risk. The choice of age as a timescale (with adjustment for time since diagnosis) is not incorrect for this application as age is also associated with recurrence risk and, in some cases, exposure; however, we think using time since diagnosis may adjust more completely for confounding in some studies of disease prognosis. If both elements of time are potential confounders, both should be accounted for – one as the timescale and one as a covariate in the model. The interpretation of the hazard ratios is essentially the same regardless of which is selected as time scale and which is modeled; however, the choice may affect the ability to control for confounding. Whether it is better to use age or time since diagnosis as the time scale in studies of prognosis may depend on the specific application; in some cases, it may not affect the results.4 With the growing interest in follow-up studies of disease outcomes, additional research on how to select among multiple biologically relevant time scales is necessary. Figure 1 Kernel-smoothed estimate of hazard of second breast cancer event over years since diagnosis by age at diagnosis, in a cohort of early stage breast cancer patients diagnosed in 1990–2008.

Improved Computation of Balancing Transformations for Aeroservoelastic Models via Time Scale Conversion

Design of modern control laws motivates the creation of state-space models from aeroservoelastic models. Balanced truncation is often used to create reduced-order models. In the present work, a reduced-order model that employs a change in time scale in computing the balancing transformation is developed. The transformation matrix necessary to transform the original aeroservoelastic model is found from the aeroservoelastic model employing the recast time scale. Results from an aeroservoelastic wing and a supersonic transport model are shown, and it is demonstrated that, with an appropriate choice of time scale, the methodology results in greatly improved conditioning for the Lyapunov equations used to find the Gramians employed in the balancing transformation.

Time Scale and Adjusted Survival Curves for Marginal Structural Cox Models

Typical applications of marginal structural time-to-event (e.g., Cox) models have used time on study as the time scale. Here, the authors illustrate use of time on treatment as an alternative time scale. In addition, a method is provided for estimating Kaplan-Meier-type survival curves for marginal structural models. For illustration, the authors estimate the total effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome (AIDS) or death in 1,498 US men and women infected with human immunodeficiency virus and followed for 6,556 person-years between 1995 and 2002; 323 incident cases of clinical AIDS and 59 deaths occurred. Of the remaining 1,116 participants, 77% were still under observation at the end of follow-up. By using time on study, the hazard ratio for AIDS or death comparing always with never using highly active antiretroviral therapy from the marginal structural model was 0.52 (95% confidence interval: 0.35, 0.76). By using time on treatment, the analogous hazard ratio was 0.44 (95% confidence interval: 0.32, 0.60). In time-to-event analyses, the choice of time scale may have a meaningful impact on estimates of association and precision. In the present example, use of time on treatment yielded a hazard ratio further from the null and more precise than use of time on study as the time scale.

Mid-Cretaceous seafloor spreading pulse: Fact or fiction?

Research Article| August 01, 2009 Mid-Cretaceous seafloor spreading pulse: Fact or fiction? M. Seton; M. Seton * 1EarthByte Group, School of Geosciences, Madsen Building F09, University of Sydney, Sydney, NSW 2006, Australia *E-mail: maria.seton@usyd.edu.au. Search for other works by this author on: GSW Google Scholar C. Gaina; C. Gaina 2Center for Geodynamics, Geological Survey of Norway, Leiv Eirikssons vei 39, N-7491 Trondheim, Norway Search for other works by this author on: GSW Google Scholar R.D. Müller; R.D. Müller 1EarthByte Group, School of Geosciences, Madsen Building F09, University of Sydney, Sydney, NSW 2006, Australia Search for other works by this author on: GSW Google Scholar C. Heine C. Heine 1EarthByte Group, School of Geosciences, Madsen Building F09, University of Sydney, Sydney, NSW 2006, Australia †Current address: StatoilHydro Global Exploration Technology, Drammensveien 264, N-0246 Oslo, Norway Search for other works by this author on: GSW Google Scholar Geology (2009) 37 (8): 687–690. https://doi.org/10.1130/G25624A.1 Article history received: 23 Oct 2008 rev-recd: 18 Mar 2009 accepted: 22 Mar 2009 first online: 03 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation M. Seton, C. Gaina, R.D. Müller, C. Heine; Mid-Cretaceous seafloor spreading pulse: Fact or fiction?. Geology 2009;; 37 (8): 687–690. doi: https://doi.org/10.1130/G25624A.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Two main hypotheses compete to explain the mid-Cretaceous global sea-level highstand: a massive pulse of oceanic crustal production that occurred during the Cretaceous Normal Superchron (CNS) and the “supercontinent breakup effect,” which resulted in the creation of the mid-Atlantic and Indian ocean ridges at the expense of subducting old ocean floor in the Tethys and the Pacific. We have used global oceanic paleo-age grids, including now subducted ocean floor and two alternative time scales, to test these hypotheses. Our models show that a high average seafloor spreading rate of 92 mm/a in the Early Cretaceous that decreased to 60 mm/a during the Tertiary, with peaks of 86 mm/a and 70 mm/a at 105 Ma and 75 Ma ago, respectively, correspond to the two observed sea-level highstands in the Cretaceous. Calculations using GTS2004 produce lower seafloor spreading rates during the same period and diminish the mid-Cretaceous spreading pulse. Global ridge lengths increased in the earliest Cretaceous but stayed relatively constant through time. However, we find that the average age of the ocean basins through time is only weakly dependent on the choice of time scale. The expansive mid- and Late Cretaceous epicontinental seas, coupled with warm climates and oxygen-poor water masses, were ultimately driven by the younger average age of the Cretaceous seafloor and faster seafloor spreading rather than a vast increase in mid-ocean ridge length due to the breakup of Pangea or solely by higher seafloor spreading rates, as suggested previously. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Comments on ‘Choice of time scale and its effect on significance of predictors in longitudinal studies’ by Michael J. Pencina, Martin G. Larson and Ralph B. D'Agostino, Statistics in Medicine 2007; 26:1343–1359

Statistics in MedicineVolume 28, Issue 8 p. 1315-1317 Letter to the Editor Comments on ‘Choice of time scale and its effect on significance of predictors in longitudinal studies’ by Michael J. Pencina, Martin G. Larson and Ralph B. D'Agostino, Statistics in Medicine 2007; 26:1343–1359 Mitchell H. Gail, Mitchell H. Gail Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorBarry Graubard, Barry Graubard Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorDavid F. Williamson, David F. Williamson Rollins School of Public Health, Emory University, Atlanta, GA, U.S.A.Search for more papers by this authorKatherine M. Flegal, Katherine M. Flegal National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, U.S.A.Search for more papers by this author Mitchell H. Gail, Mitchell H. Gail Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorBarry Graubard, Barry Graubard Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, U.S.A.Search for more papers by this authorDavid F. Williamson, David F. Williamson Rollins School of Public Health, Emory University, Atlanta, GA, U.S.A.Search for more papers by this authorKatherine M. Flegal, Katherine M. Flegal National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, U.S.A.Search for more papers by this author First published: 13 March 2009 https://doi.org/10.1002/sim.3473Citations: 19AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume28, Issue815 April 2009Pages 1315-1317 RelatedInformation

Choice of time scale and its effect on significance of predictors in longitudinal studies

Time-to-event regression is a frequent tool in biomedical research. In clinical trials this time is usually measured from the beginning of the study. The same approach is often adopted in the analysis of longitudinal observational studies. However, in recent years there has appeared literature making a case for the use of the date of birth as a starting point, and thus utilize age as the time-to-event. In this paper, we explore different types of age-scale models and compare them with time-on-study models in terms of the estimated regression coefficients they produce. We consider six proportional hazards regression models that differ in the choice of time scale and in the method of adjusting for the years before the study. By considering the estimating equations of these models as well as numerical simulations we conclude that correct adjustment for the age at entry is crucial in reducing bias of the estimated coefficients. The unadjusted age-scale model is inferior to any of the five other models considered, regardless of their choice of time scale. Additionally, if adjustment for age at entry is made, our analyses show very little to suggest that there exists any practically meaningful difference in the estimated regression coefficients depending on the choice of time scale. These findings are supported by four practical examples from the Framingham Heart Study.

Choice of time‐scale in Cox's model analysis of epidemiologic cohort data: a simulation study

Cox's regression model is widely used for assessing associations between potential risk factors and disease occurrence in epidemiologic cohort studies. Although age is often a strong determinant of disease risk, authors have frequently used time-on-study instead of age as the time-scale, as for clinical trials. Unless the baseline hazard is an exponential function of age, this approach can yield different estimates of relative hazards than using age as the time-scale, even when age is adjusted for. We performed a simulation study in order to investigate the existence and magnitude of bias for different degrees of association between age and the covariate of interest. Age to disease onset was generated from exponential, Weibull or piecewise Weibull distributions, and both fixed and time-dependent dichotomous covariates were considered. We observed no bias upon using age as the time-scale. Upon using time-on-study, we verified the absence of bias for exponentially distributed age to disease onset. For non-exponential distributions, we found that bias could occur even when the covariate of interest was independent from age. It could be severe in case of substantial association with age, especially with time-dependent covariates. These findings were illustrated on data from a cohort of 84,329 French women followed prospectively for breast cancer occurrence. In view of our results, we strongly recommend not using time-on-study as the time-scale for analysing epidemiologic cohort data.

Effects of an introduced polychaete, Sabella spallanzanii, on the development of epifaunal assemblages

Increasing awareness of the ecological and economic problems caused by marine intro- ductions has brought calls for the development of predictive models of their impacts on other species. We examined the effects of an introduced marine polychaete, Sabella spallanzanii (Gmelin, 1791), on the development of subtidal marine epifaunal assemblages. As an invader of hard subtidal substrata, S. spallanzanii alters the structure of the habitat by forming a canopy of filamentous feeding struc- tures suspended above the substratum on long, slender tubes. As resident species (including S. spal- lanzanii) can strongly affect the recruitment of sessile taxa into these assemblages, we predicted that one of the effects of this introduction would be to change the relative abundances of understorey spe- cies and hence the assemblage structure. In this study we aimed to determine whether the effects of S. spallanzanii on sessile assemblages would be apparent after periods of 2 or 6 mo, and to evaluate the mechanisms underlying any of such observed effects. Further experiments on individual taxa were done to assess the influence of this exotic species on growth rate and mortality of sessile inver- tebrates as possible reasons for observed effects. The abundances of 9 taxa were affected by the pres- ence of S. spallanzanii after 10 wk of assemblage development on cleared and canopy-covered areas. Multivariate analyses showed that assemblages beneath canopies were significantly different from those outside canopies. After 6 mo, however, there were few differences between canopy-covered and cleared areas, and assemblages did not differ. We found little evidence that S. spallanzanii canopies could affect already established assemblages. There were significant effects of the S. spal- lanzanii canopy on survival and growth rates of epifaunal taxa, although the results were not consis- tent among experiments, suggesting temporal variability in the processes that cause such changes. There are several implications of these results for the assessment of the impacts of exotic species, including the appropriate choice of timescale over which to conduct experiments and the generality of such experiments.

Time Scales and Organizational Theory

A critical specification lacking from much theory and research on organizations is that of time scale. Specification of the relevant time scale is as critical as the specification of the appropriate level or unit of analysis, a concept to which it is related. We define and explore five types of time scales and consider their implications for both the social constructionist and positivist approaches. Using examples from strategy and organizational theory, we show how the choice of time scale has important implications for the development of theory.

On the choice of timescale in glacial rebound modelling: mantle viscosity estimates and the radiocarbon timescale

SUMMARY Most glacial rebound studies have been carried out with respect to the radiocarbon timescale, whose departures from the calendar timescale are becoming increasingly well established. In consequence, it has sometimes been argued that the choice of the radiocarbon timescale may invalidate some of the conclusions drawn from rebound and sea-level analyses. The purpose of this note is to compare rebound model results based on both timescales, using the British Isles data for the test. The results indicate that the choice of timescale is unimportant provided that the time dimension of viscosity is appropriately defined. The results confirm that the radiocarbon viscosities are about 15 per cent less than the corresponding calendar-time viscosities. Also, provided that consistency of timescales is maintained in the analysis, and that the timeaccuracy estimates of the radiocarbon data reflect the departures from a linear timescale, the use of the radiocarbon timescale does not impinge on inferences drawn about the timing of melting of ice sheets or eustatic sea-level change.

Fastest known spreading on the Miocene Cocos‐Pacific Plate Boundary

New magnetic anomaly identifications for the central part of the Cocos plate and the corresponding part of the Pacific plate indicate a pulse of extremely rapid seafloor spreading in the middle Miocene, about 11–18 Ma, possibly beginning as early as 25 Ma. The spacing of anomalies 5A–5D indicates a full spreading rate for the southern Cocos‐Pacific boundary of 180–210 mm/yr, depending on the choice of time scale. Relative to the maximum 0–3 Ma spreading rate of 152 mm/yr, this result significantly expands the upper limit of well documented rates.

Diagnostic plots for departures from proportional hazards in cohort study data

The assumption of proportional hazards is routinely made in the analysis of cohort studies, whether a simple SMR calculation or a full survival analysis is used. In this paper, we introduce simple plots for checking the validity of the assumption. The plots are of two kinds. The first, which has been used previously for survival data, makes use of the fact that the individual integrated hazards are distributed as unit exponential varieties under proportional hazards, and involves plotting their estimates against expected exponential order statistics. The second displays the evolution of relative risk as a function of time, and in this case, a choice of time scale must be made for the plots. A score test for proportional hazards is also derived, and the methods are illustrated by data on cancer mortality among the employees of a South Wales nickel refinery.

On a heat transport model for a turbulent plane jet

Distributions of the temperature-pressure gradient correlations are obtained from measured budgets of the longitudinal and lateral heat fluxes in the self-preserving region of a slightly heated turbulent plane jet into still air. These correlations are consistent with a model which includes only the turbulence interaction contribution to the pressure fluctuations. The comparison between model and experiment is not affected by the choice of time scale in the model. Terms whose gradients form the major contribution to diffusion in the budgets for heat fluxes and the temperature variance are only qualitatively consistent with gradient-type models.

Dynamic operation of an a.c. network analyser

Methods are described for representing synchronous machines, by means of which an a.c. network analyser can be constructed to solve both steady-state and transient power-system problems automatically, without the need for tedious step-by-step processes. An existing a.c. network analyser may readily be converted to dynamic operation by modification of the generator units only, as herein lies the only radical alteration in representation proposed. Choice of time scale for the study of electro-mechanical transients is arbitrary. However, advantages are indicated for a time scale of the order of 1 min on the analyser corresponding to 1 sec on the actual power system. Results of tests (employing a.c. network analyser units) are included, and possible improvements are discussed.