%% BioMed_Central_Tex_Template_v1.06
%%                                      %
%  bmc_article.tex            ver: 1.06 %
%                                       %

%%IMPORTANT: do not delete the first line of this template
%%It must be present to enable the BMC Submission system to
%%recognise this template!!

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                     %%
%%  LaTeX template for BioMed Central  %%
%%     journal article submissions     %%
%%                                     %%
%%          <8 June 2012>              %%
%%                                     %%
%%                                     %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                                                 %%
%% For instructions on how to fill out this Tex template           %%
%% document please refer to Readme.html and the instructions for   %%
%% authors page on the biomed central website                      %%
%% http://www.biomedcentral.com/info/authors/                      %%
%%                                                                 %%
%% Please do not use \input{...} to include other tex files.       %%
%% Submit your LaTeX manuscript as one .tex document.              %%
%%                                                                 %%
%% All additional figures and files should be attached             %%
%% separately and not embedded in the \TeX\ document itself.       %%
%%                                                                 %%
%% BioMed Central currently use the MikTex distribution of         %%
%% TeX for Windows) of TeX and LaTeX.  This is available from      %%
%% http://www.miktex.org                                           %%
%%                                                                 %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% additional documentclass options:
%  [doublespacing]
%  [linenumbers]   - put the line numbers on margins

%%% loading packages, author definitions

%\documentclass[twocolumn]{bmcart}% uncomment this for twocolumn layout and comment line below
\documentclass{bmcart}

\usepackage{xcolor}

%%% Load packages
%\usepackage{amsthm,amsmath}
%\RequirePackage{natbib}
%\RequirePackage[authoryear]{natbib}% uncomment this for author-year bibliography
%\RequirePackage{hyperref}
\usepackage[utf8]{inputenc} %unicode support
%\usepackage[applemac]{inputenc} %applemac support if unicode package fails
%\usepackage[latin1]{inputenc} %UNIX support if unicode package fails


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                             %%
%%  If you wish to display your graphics for   %%
%%  your own use using includegraphic or       %%
%%  includegraphics, then comment out the      %%
%%  following two lines of code.               %%
%%  NB: These line *must* be included when     %%
%%  submitting to BMC.                         %%
%%  All figure files must be submitted as      %%
%%  separate graphics through the BMC          %%
%%  submission process, not included in the    %%
%%  submitted article.                         %%
%%                                             %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%\def\includegraphic{}
%\def\includegraphics{}
\usepackage{epsfig}
\usepackage{graphicx}



\usepackage{changepage}

% color can be used to apply background shading to table cells only
%\usepackage[table]{xcolor}
\usepackage{multirow}

% array package and thick rules for tables
\usepackage{array}

% create "+" rule type for thick vertical lines
\newcolumntype{+}{!{\vrule width 2pt}}


\newcolumntype{M}[1]{>{\centering\arraybackslash}m{#1}}

%%% Put your definitions there:
\startlocaldefs
\endlocaldefs


%%% Begin ...
\begin{document}

%%% Start of article front matter
\begin{frontmatter}

\begin{fmbox}
\dochead{Supplementary Information}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                          %%
%% Enter the title of your article here     %%
%%                                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\title{Supplementary Information: Impact of population based indoor residual
spraying with and without mass drug administration with
dihydroartemisinin-piperaquine on malaria prevalence in a high transmission
setting: a controlled trial in northeastern Uganda}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                          %%
%% Enter the authors here                   %%
%%                                          %%
%% Specify information, if available,       %%
%% in the form:                             %%
%%   <key>={<id1>,<id2>}                    %%
%%   <key>=                                 %%
%% Comment or delete the keys which are     %%
%% not used. Repeat \author command as much %%
%% as required.                             %%
%%                                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\author[
%   addressref={aff1},
%   corref={aff1},                    % id of corresponding address, if any
%   email={dorothy@pilgrimafrica.org}
%]{\inits{DE}\fnm{Dorothy} \snm{Echodu}}
%\author[
%   addressref={aff2},
%   email={yadoke@yahoo.com}
%]{\inits{AY}\fnm{Adoke} \snm{Yeka}}
%\author[
%   addressref={aff3},
%   email={thomas@pilgrimafrica.org}
%]{\inits{TE}\fnm{Thomas} \snm{Eganyu}}
%\author[
%   addressref={aff3},
%   email={wycliff.odude@pilgrimafrica.org}
%]{\inits{WO}\fnm{Wycliff} \snm{Odude}}
%\author[
%   addressref={aff3},
%   email={fred.bukenya@pilgrimafrica.org}
%]{\inits{FB}\fnm{Fred} \snm{Bukenya}}
%\author[
%   addressref={aff4},
%   email={b.amoah@lancaster.ac.uk}
%]{\inits{BA}\fnm{Benjamin} \snm{Amoah}}
%\author[
%   addressref={aff3},
%   email={humphrey@pilgrimafrica.org}
%]{\inits{HW}\fnm{Humphrey} \snm{Wanzira}}
%\author[
%   addressref={aff5},
%   email={KATHRYN.COLBORN@cuanschutz.edu}
%]{\inits{KC}\fnm{Kathryn} \snm{Colborn}}
%%\author[
%   addressref={aff1,aff6},               % id's of addresses, e.g. %{aff1,aff2}
%   %noteref={n1},                        % id's of article notes, if any
%   email={richardelliott@boisestate.edu}   % email address
%]{\inits{RCE}\fnm{Richard C.} \snm{Elliott}}
%\author[
%   addressref={aff1},
%   email={suzanne@pilgrimafrica.org}
%]{\inits{SP}\fnm{Suzanne E.} \snm{Powell}}
%\author[
%   addressref={aff3},
%   email={kilamam@gmail.com}
%]{\inits{MK}\fnm{Maxwell} \snm{Kilama}}
%\author[
%   addressref={aff2},
%   email={mulebeker@gmail.com}
%]{\inits{RM}\fnm{Ronald} \snm{Mulebeke}}
%\author[
%   addressref={aff7},
%   email={jnankabirwa@yahoo.co.uk}
%]{\inits{JN}\fnm{Joan} \snm{Nankabirwa}}
%\author[
%   addressref={aff4},
%   email={b.amoah@lancaster.ac.uk}
%]{\inits{EG}\fnm{Emanuele} \snm{Giorgi}}
%\author[
%   addressref={aff1},
%   email={mellisa@pilgrimafrica.org}
%]{\inits{MR}\fnm{Mellisa} \snm{Roskosky}}
%\author[
%   addressref={aff3},
%   email={osborn.omoding@pilgrimafrica.org}
%]{\inits{OO}\fnm{Osborn} \snm{Omoding}}
%\author[
%   addressref={aff7},
%   email={sgonahasa1983@gmail.com}
%]{\inits{SG}\fnm{Samuel} \snm{Gonahasa}}
%\author[
%   addressref={aff7},
%   email={opigojimmy@gmail.com}
%]{\inits{JO}\fnm{Jimmy} \snm{Opigo}}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                          %%
%% Enter the authors' addresses here        %%
%%                                          %%
%% Repeat \address commands as much as      %%
%% required.                                %%
%%                                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\address[id=aff1]{%
%  \orgname{Pilgrim Africa},
%  \street{8001 14th Avenue NE, Suite A},
%  \postcode{98115}
%  \city{Seattle, WA},
%  \cny{USA}
%}

%\address[id=aff2]{%
%  \orgname{Makerere University College of Health Sciences, School of %Public
%Health}
%  \street{P.O. Box 7072},
%  \city{Kampala}
%  \cny{Uganda}
%}

%\address[id=aff3]{%
%  \orgname{Pilgrim Africa},
%  \street{Plot 8 Engwau Road, PO Box 577},
%  \city{Soroti}
%  \cny{Uganda}
%}

%\address[id=aff4]{%
%  \orgname{Lancaster University}
%  \street{Furness College, B73}
%  \city{Lancaster, United Kingdom}
%  \postcode{LA1 4YG}
%  \cny{UK}
%}

%\address[id=aff5]{%
%  \orgname{University of Colorado Anschutz Medical Campus}
%  \street{12631 East 17th Avenue}
%  \city{Aurora, CO}
%  \postcode{80045}
%  \cny{USA}
%}

%\address[id=aff6]{%                           % unique id
%  \orgname{Micron School of Materials Science and Engineering, Boise %State University}, % university, etc
%  \street{Engineering Building, Suite 338},                     %
%  %\postcode{}                                % post or zip code
%  \city{Boise, ID},                              % city
%  \postcode{83725}
%  \cny{USA}                                    % country
%}


%\address[id=aff7]{%
%  \orgname{National Malaria Control Division}
%  \street{Ministry of Health Uganda}
%  \city{Kampala, Uganda}
%  \cny{UG}
%}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                          %%
%% Enter short notes here                   %%
%%                                          %%
%% Short notes will be after addresses      %%
%% on first page.                           %%
%%                                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{artnotes}
%\printaddress{aff1}
%\printaddress{aff2}
%\printaddress{aff3}
%\printaddress{aff4}
%\printaddress{aff5}
%\printaddress{aff6}
%\printaddress{aff7}
%\note{Sample of title note}     % note to the article
%\note[id=n1]{Equal contributor} % note, connected to author
\end{artnotes}

\end{fmbox}% comment this for two column layout



\end{frontmatter}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                          %%
%% The Main Body begins here                %%
%%                                          %%
%% Please refer to the instructions for     %%
%% authors on:                              %%
%% http://www.biomedcentral.com/info/authors%%
%% and include the section headings         %%
%% accordingly for your article type.       %%
%%                                          %%
%% See the Results and Discussion section   %%
%% for details on how to create sub-sections%%
%%                                          %%
%% use \cite{...} to cite references        %%
%%  \cite{koon} and                         %%
%%  \cite{oreg,khar,zvai,xjon,schn,pond}    %%
%%  \nocite{smith,marg,hunn,advi,koha,mouse}%%
%%                                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%% start of article main body
% <put your article body there>

%%%%%%%%%%%%%%%%
%% Background %%
%%

\section*{Supporting Information}
  \subsection*{Appendix I. Spatiotemporal geostatistical model}

Let $p_j(x_i, t_i)$ denote the probability of a positive qPCR result from the
$j$-th individual sampled at $i$-th location $x_i$ and month $t_i$, where $t_i
\in \{1, \dots, 31 \}$, with $t_i=1$ representing November 2016. Conditionally
on a spatio-temporal Gaussian process $S(x_{i}, t_i)$ and unstructured random
effects $Z(x_{i}, t_i)$, we modeled the probability of positive qPCR test
$p_j(x_i, t_i)$ as logit-linear regression given by,
\begin{eqnarray}
\label{eqn:pr1}
\log \left\{ \frac{p_j(x_{i}, t_i)}{1 - p_j(x_{i}, t_i)}\right\}
 &=& \beta_0 + s(a_{ij}) + \beta_4 t_i + \beta_5 I(t_i \in {HTS})   + \nonumber \\
 & & \beta_6I(t_i \in {Baseline}) + \beta_7I(t_i \in Kap_{base}) + \beta_8I(t_i \in Tor_{base})  +  \nonumber \\
 & & \alpha_1 I(x_i \in Tor) +  \alpha_2 I(x_i \in Kap) +   S(x_{i}, t_i) + Z(x_{i}, t_i),
\end{eqnarray}
where $s(a_{ij})$ is a linear spline expressed by,
\begin{eqnarray}
\label{eqn:pr2}
s(a_{ij}) &=& \beta_1 \textrm{min}({a_{ij}, a_0}) +  \beta_2 I(a_{ij}>a_1)\textrm{min}({a_{ij}-a_1, a_1-a_0})  + \nonumber\\
& & \beta_3 \textrm{max}(a_{ij} - a_1, 0).  
\end{eqnarray}
In this expression, $a_{ij}$ denotes the age of person $j$ at location $x_i$,
and $a_0=10$ and  $a_1=29$ are ages where a change in the slope of the linear
spline is imposed. The values of 10 and 29 years were chosen based on a
deviance profile of all possible combinations for $a_0$ and $a_1$ using a
standard generalized linear model. In the above equation,  $\beta_1$, $\beta_2$
and $\beta_3$ are the slopes of age in different age groups, that is the
effects of age on the log-odds of prevalence in the age groups $0-10$, $10-29$,
and $30+$ respectively.

We used linear functions of time (corresponding to $\beta_4$) to account for
long-term trends. Seasonality was included by classifying the year into a high
transmission season (June-August), with prefactor $\beta_5$ and low
transmission season otherwise.

We accounted for differences in prevalence between different trial arms at
baseline by including indicator variables of whether or not a data point was
sampled at baseline in ($Baseline$), Kapujan during baseline ($Kap_{base}$)
and Toroma during baseline ($Tor_{base}$) corresponding to $\beta_6 \, \beta_7,
\beta_8$, respectively.

To account for the different intervention strategies, $Tor$ represents Toroma,
Arm B, which received IRS only while $Kap$ represents Arm A, Kapujan, which received
both IRS and MDA. The main regression parameters of interest are therefore
$\alpha_1, \alpha_2$, respectively, which when lesser, represents a greater
impact of the corresponding intervention. Arm C, Magoro, the SOC
arm, is the reference category.
\begin{table}[!ht]
  \begin{center}
%\begin{adjustwidth}{-1.25in}{0in}
    \caption{Estimates of the geostatistical parameters.}
\label{tab:reg}
\begin{tabular}{lccccc}
\hline \hline
Variable & Parameter       & Point estimate   & 95\% CI    \\
\hline
\textit{ Other covariates effects} & & & \\
Intercept (Control, low trans.) & $\exp(\beta_0)$ & 0.4234 & (0.3405, 0.5264) \\
Age trend in $0-10$ y/o & $\exp(\beta_1)$ & 1.2006 & (1.1806, 1.2210) \\        
Age trend in $10-29$ y/o & $\exp(\beta_2)$ & 0.9368 & (0.9288, 0.9448) \\        
Age trend in $\geq 29$ y/o & $\exp(\beta_3)$ & 0.9913 & (0.9862, 0.9965) \\      
Time trend & $\exp(\beta_4)$ & 1.0107 & (1.0029, 1.0187) \\                      
Seasonal effect (High trans. season) & $\exp(\beta_5)$ & 1.7408 & (1.4697, 2.0619) \\

Baseline main effect & $\exp(\beta_6)$ & 1.6108 & (1.2547, 2.0680) \\            
Baseline effect in the arm with IRS Only & $\exp(\beta_7)$ & 2.5774 & (1.9520, 3.4033) \\
Baseline effect in the arm with MDA + IRS & $\exp(\beta_8)$ & 5.4293 & (4.0901, 7.2069) \\
\hline
\textit{Interventions effects} & & & \\
IRS Only & $\exp(\alpha_1)$ & 0.3533 & (0.3150, 0.3963) \\                      
MDA + IRS & $\exp(\alpha_2)$ & 0.1987 & (0.1768, 0.2233) \\                      
\hline
\textit{Residual spatiotemporal effects} & & & \\
Signal variance & $\sigma^2$ & 5.4445 & (4.8036, 6.1710) \\                      
Range parameter & $\phi$ & 1.0260 & (0.8526, 1.2347) \\                          
Nugget effect & $\tau^2$ & 0.4559 & (0.3611, 0.5757) \\                          
Temporal effect & $\psi$ & 2.3645 & (1.5550, 3.5954) \\
\hline
\end{tabular}
\end{center}
\end{table}


We modelled the spatially and temporally correlated random variations $S(x_{i},
t_i)$ as a stationary and isotropic Gaussian process with the separable
correlation function,
\begin{eqnarray}
\rho(u, v; (\sigma^2, \phi, \psi)) =
\rho_1(u; (\sigma^2, \phi)) \rho_2(v; \psi),
\end{eqnarray}
where the spatial component of the correlation function is modelled as
$\rho_1(u; (\sigma^2, \phi)) = \exp(-u/\phi)$, where $\phi$ regulates the pace
at which the spatial correlation decays for increasing distance $u$ between any
two locations, and the temporal correlation function as $\rho_2(v; \psi) = 1/(1
+ v/\psi)$ with $v$ being the difference between any two time points. We
modelled the spatially unstructured random effects $Z(x_{i}, t_i)$ as
independent and identically distributed Gaussian random variables with variance
$\tau^2$.

The final data consisted of 15925  qPCR tests for \textit{P. falciparum}, of
which 6730 (42.3\%) were positive. Table \ref{tab:reg} shows parameter
estimates of the geostatistical model of equations \ref{eqn:pr1}-\ref{eqn:pr2}. As
expected, the odds ratio increases sharply in the early years of life until age
10, and it decreases moderately thereafter until around the age of 30, after
which there is very slow decrease in later years (Fig. \ref{fig:age_effect}).
The estimate range of the spatial correlation is about 1.0km, beyond which the
spatial correlation takes values smaller than 0.05. The estimated range of the
temporal correlation is about one month. As indicated by the larger estimate of
$\sigma^2$ than $\tau^2$, the spatial variation dominates substantially the
unexplained variation on a scale smaller than the minimum observed distance.
\begin{figure}[!ht]
\includegraphics[width=0.85\textwidth]{age_effect.pdf}
\caption{The effect of age on odds ratio. The solid line indicates the odds
ratio at different ages, and the shaded grey area is the associated 95\%
confidence interval.}
\label{fig:age_effect}
\end{figure}

\subsection*{Appendix II. Additional DiD Analyses}

The DiD design is a quasi-experimental method that relies on the assumption
that in the absence of any intervention, the study arms receiving the enhanced
malaria interventions have identical trends in outcomes as the SOC
(control) arm.

Using SAS 9.4, the model used a binomial logistic regression with the
proportion of positive malaria cases by diagnostic tool (qPCR, microscopy and
RDT) and age as the dependable variables. Indicator variables for survey timing
(baseline/post-intervention surveys) and study arms were used, with co-variates
determined through backwards stepwise procedure, and an interaction term
between survey timing and study arms. Statistical significance threshold was
set at alpha = .05 using two tailed tests. Log odds were converted to odds
ratios by calculating the exponentiated regression coefficient of the
interaction terms in the model. DiD analyses were not done
for positive malaria cases in the `all ages' group by RDT, since malaria
prevalence at baseline was significantly higher in the SoC (Arm C)
compared to Arms A and B by this metric.

After adjusting for age, ITN use and gender, Fig. \ref{mdaVSsoc} (upper left)
shows the odds of qPCR confirmed malaria in residents receiving MDA+IRS were
significantly lower compared to residents receiving SOC, at all
survey time points.  The aOR of qPCR malaria confirmation was 90\% lower in
residents who received 1 round of MDA+IRS compared to the SoC arm (DiD aOR =
.10 [95\% CI: .08 –.14], p$<.001$); adjusted odds remained consistent 6 months
following rounds 2 and 3 (DiD aOR = .18 [95\% CI: .07 – .15], p$<.001$) and
(DiD aOR = .17 [95\% CI: .13 – .31], p$<.001$), respectively. The odds of
malaria 6 months following 4 full rounds of MDA+IRS was 70\% lower than the SoC
arm (DiD aOR = .30 [95\% CI: .23 – .40], p$<.001$).

Residents in the IRS arm (Fig. \ref{mdaVSsoc},upper right) also showed
significantly lower odds of qPCR confirmed malaria in relation to SoC
residents. All surveys measured impact 5 – 7 months following intervention
rounds, with the exception of survey 3, which showed significant impact in
residents receiving MDA+IRS 3 months after receiving 2 rounds of the
intervention compared to residents receiving SoC (DiD aOR = .11 [95\% CI: .07 –
.15], p$<.001$) and residents receiving IRS (DiD aOR = .30 [95\% CI: .21 –
.41], p$<.001$). The lower panels of Fig. \ref{mdaVSsoc} show the same trends
in microscopy confirmed malaria for all ages.

These comparisons highlight the large protective impact of not only adding
chemoprevention to IRS, but also the protective impact IRS+ITNs have over ITNs
alone in this high transmission setting.
%\begin{figure}[!ht]
%\includegraphics[width=0.85\textwidth]{figSupplMDAvsSOCqPCR.png}
%\caption{The DiD adjusted odds ratio for qPCR confirmed malaria in residents of
%all ages receiving MDA+IRS versus those with standard of care (SoC). 95\%
%Confidence intervals are indicated.}
%\label{mdaVSsoc}
%\end{figure}

\begin{figure}[!htb]
\centering
  \begin{tabular}{@{}cc@{}}
    \includegraphics[width=0.45\textwidth]{figSupplMDAvsSOCqPCR.png} &
    \includegraphics[width=0.45\textwidth]{figSupplIRSvsSoCqPCR.png} \\
    \includegraphics[width=0.45\textwidth]{figSupplMDAvsSoCmicro.png} &
    \includegraphics[width=0.45\textwidth]{figSupplIRSvsSoCmicro.png}
  \end{tabular}
\caption{Top left: the DiD adjusted odds ratio for qPCR confirmed malaria in
residents of all ages receiving MDA+IRS versus those with standard of care
(SoC). Top right: the same DiD adjusted odds ratio for qPCR confirmed malaria
in residents of all ages receiving IRS, without MDA, versus those with standard
of care. The lower panels display the same as the panels above except for
malaria in residents confirmed by microscopy. Horizontal bars indicate 95\%
confidence intervals.}
\label{mdaVSsoc}
\end{figure}

\subsection*{Appendix III. Malaria prevalence tables}

See included excel spreadsheet.






\end{document}
