The authors would like to thank Ivan Hanigan for his support in extracting and interpreting the ultraviolet radiation satellite data. The work was supported by the NHMRC Career Development Award (Clinical) to HB [ID628856], NHMRC Project Grant [1032484], NHMRC Center for Research Excellence [Grant ID 1001216] and the MSBase Foundation. The MSBase Foundation is a not-for-profit organization that receives support from Merck Serono, Biogen Idec, Novartis Pharma, Bayer-Schering, Sanofi-Aventis and BioCSL. RL is supported by a NHMRC Career Development Award [ID 1004898].

NOTE: Each step described corresponds to a section of Stata code with the same number in the code file provided. Stata command names have been italicised in the following protocol.
1. Prepare and Plot the Observed Relapse Onset Data
<ol>
	<li>Open a do file by clicking on the &#34;New Do-file Editor&#34; button and use the generate command to calculate the number of relapse onsets dated to each of the twelve calendar months for each of the three geographic levels to be model...

Tim Spelman received honoraria for consultancy and funding for travel from Biogen Idec Inc; Orla Gray received travel support from Biogen Idec, Merck Serono and Novartis; compensation for serving on scientific advisory boards from Biogen Idec, Genzyme, Novartis and Merck Serono; Robyn Lucas did not disclose any competing interests and Helmut Butzkueven received compensation for serving on scientific advisory boards and as a consultant for Biogen Idec and Novartis; speaker honoraria from Biogen Idec Australia, Merck Serono Australia, and Novartis Australia; travel support from Biogen Idec Australia and Merck Serono Australia; research support from CASS Foundation (Australia), Merck Serono Australia, the Royal Melbourne Hospital Friends of the Neurosciences Foundation, and the University of Melbourne.

The protocol described herein details a systematic regression based technique, guided by visual plot analysis, of global MS relapse onset data. It takes as a starting point a relatively simple descriptive analysis of relapse data from 20 countries across both hemispheres, allowing the user to explore theories regarding the temporality of relapse onset timing in MS and testing these theories formally through the use of trigonometric models. Through a step-wise process of first plotting global relapse onset data and then s...

The most common form of multiple sclerosis (MS) is Relapsing Remitting Multiple Sclerosis (RRMS). RRMS is characterized by episodic deteriorations in neurological function, followed by partial or complete recovery. Globally, the incidence and prevalence of MS increase with increasing distance away from the equator in both hemispheres.1-3 Whether the frequency of relapse events that occur specifically in RRMS also vary with latitude, and whether there is any underlying seasonal variation in any such association, remains unclear. To date studies exploring seasonality in relapse timing have been limited to single clinical centers, limiting any inferences regarding seasonal trends in relapse timing to solitary geographical locations and thus unable to explore broader latitudinal influences. 4-14 These studies have been further limited by small sample sizes and sparse relapse data. A 2000 meta-analysis of ten studies from clinical centres in Europe, the United States and Canada, where each study included a minimum of thirty cases reporting the season-of-onset of relapses, described a clear seasonal trend in the timing of relapse onset, with relapses peaking in spring and with a winter trough4. Similar cyclical annual trends in onset have been observed in subsequent, albeit smaller, studies in both Japan15 and Spain16. However, a comparable United States study failed to corroborate this pattern17. To date, these studies and observations have been limited to the northern hemisphere. The MSBase study group recently analyzed a large global dataset of MS relapses across both northern and southern hemispheres to explore seasonal trends in the timing of relapse onset in addition to latitudinal influences on the relationship between peak relapse probability and seasonal ultraviolet radiation (UVR) trough18. Central to these methods was the application of trigonometric regression to visualize and evaluate trends in the timing of relapse onset and UVR distributions.
The overall goal of this study was to test the hypothesis that temporal variation in the timing of relapse onset in MS varied predictably with season in both the northern and southern hemispheres and this seasonality was influenced by latitude. The rationale for the use of trigonometric modelling to investigate these questions was its flexibility for characterizing two- or three-dimensional phenomena that are known or suspected to describe discrete, predictable and consistent shapes or patterns, such as the annual cycle of peaks and troughs commonly observed in biological or epidemiological phenomena possessing seasonality.19-22 A disadvantage of conventional time-series analyses, including Fourier analysis, is the presumption that time series are often characterized by stochastic processes.21,23,24 By contrast, incorporating trigonometric functions into a regression type model has the advantage of both facilitating exploration of regular and systematic structures in periodic data whilst exploiting the regression model structure to explore other correlates or adjust for confounders of seasonality.
Trigonometric regression has previously been used widely in the medical epidemiological literature to explore temporality in topics as diverse infectious disease outbreak detection, the role of circadian rhythms in everything from autonomic nervous system dysfunction to preterm placental abruption through to seasonal correlates of congenital malformations and the timing of presentations of accident and emergency.25-32 Such modelling typically demands larger sample sizes than more conventional time-series analyses and as such this is the first time it has been applied to a global dataset of MS relapse onset. Trigonometric regression as described here is suitable tool for investigators exploring any phenomena which is known to or suspected of cycling systematically over time. Not only can such modelling help characterise and visualize these patterns, it further permits the user to explore potential drivers and correlates of these trends.
Regarding the specific example of MS relapse onset presented here, the use of scatter and residual plots to visualize and assess how closely a hypothesized trigonometric model form fits the data constitutes the critical step in determining: 1) whether the observed data provide sufficient evidence to support a hypothesis of seasonality or other temporal trends in the timing of relapse onset; and 2) whether the frequency and arrangement of sine and cosine functions which define a particular trigonometric model is adequate to permit use of this model for subsequent inference and prediction. Regression modelling also permits control for important confounders of any observed seasonal or latitudinal effect such as patient-level propensities for relapse, particularly factors which in themselves are time-varying such as the duration of pre-relapse exposure to disease-modifying drug (DMD) treatment. Isolating independent geographic and temporal predictors and correlates of relapse onset timing in MS has the potential to guide biological investigation into the mechanisms of relapse events which in turn may inform the development of future treatment interventions aimed at preventing or delaying disease exacerbation.
The MSBase Registry
MS patients contributing relapse data to this analysis were sourced from the international MSBase registry. Established in 2004, the registry longitudinally collates demographic, disease activity, clinical examination and investigation characteristics and metrics from consenting patients attending MS clinic using an internet-based, physician-owned and operated system.33 Member centers follow a common protocol that defines the minimum dataset required to be uploaded at agreed regular intervals to ensure outcome data such as relapse events are consistently and prospectively compiled. The date of relapse onset is included as a mandatory minimum dataset variable. In addition relevant clinical data associated with these relapse events is commonly collected including corticosteroid treatment and functional system affected. The use of the common iMed data entry system further ensures a unified approach across centers to data collection and reporting. This project holds Human Research Ethics Committee approval or exemption at each contributing center. Informed consent according to local laws from all patients included in the analysis is mandatory.
Inclusion criteria
A total of 9811 patients contributing 32,762 relapse events were included in the analysis. Clinical MS centres with a minimum of 20 registered patients consented, uploaded and tracked in the registry as of the 1st December 2013 (date of data compilation) were eligible for inclusion in the analysis. To ensure all relapse events included in the analysis were prospectively observed, only relapse onsets dated subsequent to the first recorded patient disability assessment (using the Kurtzke Expanded Disability Status Score (EDSS)) were included in the analysis. All patients contributing relapse data to the analysis satisfied formal diagnostic criteria for MS.34,35
Outcome measures
This study considered two primary outcomes: 1) whether there was temporal variation in the probability of relapse onset at the level of the geographic location, the hemisphere and/or globally; and 2) whether there was a relationship between latitude and the lag, in months, between the timing of seasonal UVR trough and the subsequent peak relapse probability date. The MSBase Study group hypothesized that as absolute vitamin D levels are lower in regions further away from the equator and location-specific seasonal population level vitamin D nadirs are likely reached earlier following the winter solstice in such distal locations, then the effect of low vitamin D levels on increased MS relapse probability would similarly describe such temporal and latitudinal patterns.
Relapse definition and dates
A relapse was defined as occurrence of new symptoms or exacerbation of existing symptoms persisting for at least 24 hours, in the absence of concurrent illness or fever, and occurring at least 30 days after a previous attack. This definition has previously been applied in an MSBase relapse phenotype analysis. 36 The follow-up period for each eligible patient across which relapse events could be observed was defined as the period spanning the date of first EDSS assessment through to the date of the most recent EDSS assessment recorded in the registry prior to the data of data extract and compilation. In instances where the exact day of relapse onset was unavailable or unable to be determined for a particular month, clinics used either the 1st or 15th day of the month as default dates. Of the 32,762 relapses analysed in this report, 7913 (24.2%) and 4594 (14.0%) were recorded on the 1st and 15th day of the month respectively, significantly higher than the proportions recorded on any other day of the month which ranged from 0.8% through 5.6%. To correct for this, relapses recorded on either the 1st of 15th day of the month were randomized to a day within a 15 day interval either side of both these default dates. The internal validity of this approach was confirmed via sensitivity analyses which demonstrated that the modelled estimate of peak relapse date under default date randomization was not significantly different from a model using either the original reported dates or excluding default dates entirely.

<table border="0" cellpadding="0" cellspacing="0" width="816">
	<tbody>
		<tr height="42">
			<td height="42" style="height:42px;width:216px;">Stata SE Version 13</td>
			<td style="width:136px;">StataCorp, College Station, Texas</td>
			<td style="width:119px;">Version 13</td>
			<td style="width:345px;">Statistical analysis software used for analysis</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Microsoft Excel 2010</td>
			<td style="width:136px;">Microsoft</td>
			<td style="width:119px;">2010</td>
			<td>Spreadsheet program for calendar date look-up</td>
		</tr>
	</tbody>
</table>

a method of trigonometric modelling of seasonal variation demonstrated with multiple sclerosis relapse data

This report describes a novel Stata-based application of trigonometric regression modelling to 55 years of multiple sclerosis relapse data from 46 clinical centers across 20 countries located in both hemispheres. Central to the success of this method was the strategic use of plot analysis to guide and corroborate the statistical regression modelling. Initial plot analysis was necessary for establishing realistic hypotheses regarding the presence and structural form of seasonal and latitudinal influences on relapse probability and then testing the performance of the resultant models. Trigonometric regression was then necessary to quantify these relationships, adjust for important confounders and provide a measure of certainty as to how plausible these associations were. Synchronization of graphing techniques with regression modelling permitted a systematic refinement of models until best-fit convergence was achieved, enabling novel inferences to be made regarding the independent influence of both season and latitude in predicting relapse onset timing in MS. These methods have the potential for application across other complex disease and epidemiological phenomena suspected or known to vary systematically with season and/or geographic location.

The application of trigonometric regression to 32,762 relapse events sourced from 46 clinical centers across 20 countries was the basis for providing a defensible statistical argument for the observation that the timing of relapse onset in MS is cyclic and seasonal across both hemispheres and that the duration between seasonal UVR trough and subsequent relapse peak correlates with latitude. Critical to this was the reliance upon plot analysis to guide the necessarily iterative process of model development, evaluation and...

Watch this Scientific Journal Video about A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data at JoVE.com

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Combining plot analysis with trigonometric regression is a robust method for exploring complex, cyclical phenomena such as relapse onset timing in multiple sclerosis (MS). This method enabled unbiased characterisation of seasonal trends in relapse onset permitting novel inferences around the influence of seasonal variation, ultraviolet radiation (UVR) and latitude.

This report describes a novel Stata-based application of trigonometric regression modelling to  55 years of multiple sclerosis relapse data from 46 ...

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10.6K ビュー.  Royal Melbourne Hospital. Combining plot analysis with trigonometric regression is a robust method for exploring complex, cyclical phenomena such as relapse onset timing in multiple sclerosis (MS). This method enabled unbiased characterisation of seasonal trends in relapse onset permitting novel inferences around the influence of seasonal variation, ultraviolet radiation (UVR) and latitude. 