Developing a weighting strategy to include mobile phone numbers into an ongoing population health survey using an overlapping dualframe design with limited benchmark information
 Margo L Barr^{1, 2}Email author,
 Raymond A Ferguson^{1},
 Phil J Hughes^{2} and
 David G Steel^{2}
DOI: 10.1186/1471228814102
© Barr et al.; licensee BioMed Central Ltd. 2014
Received: 13 January 2014
Accepted: 29 August 2014
Published: 4 September 2014
Abstract
Background
In 2012 mobile phone numbers were included into the ongoing New South Wales Population Health Survey (NSWPHS) using an overlapping dualframe design. Previously in the NSWPHS the sample was selected using random digit dialing (RDD) of landline phone numbers. The survey was undertaken using computer assisted telephone interviewing (CATI). The weighting strategy needed to be significantly expanded to manage the differing probabilities of selection by frame, including that of children of mobileonly phone users, and to adjust for the increased chance of selection of dualphone users. This paper describes the development of the final weighting strategy to properly combine the data from two overlapping sample frames accounting for the fact that population benchmarks for the different sampling frames were not available at the state or regional level.
Methods
Estimates of the number of phone numbers for the landline and mobile phone frames used to calculate the differing probabilities of selection by frame, for New South Wales (NSW) and by stratum, were obtained by apportioning Australian estimates as none were available for NSW. The weighting strategy was then developed by calculating person selection probabilities, selection weights, applying a constant composite factor to the dualphone users sample weights, and benchmarking to the latest NSW population by age group, sex and stratum.
Results
Data from the NSWPHS for the first quarter of 2012 was used to test the weighting strategy. This consisted of data on 3395 respondents with 2171 (64%) from the landline frame and 1224 (36%) from the mobile frame. However, in order to calculate the weights, data needed to be available for all core weighting variables and so 3378 respondents, 2933 adults and 445 children, had sufficient data to be included. Average person weights were 3.3 times higher for the mobileonly respondents, 1.3 times higher for the landlineonly respondents and 1.7 times higher for dualphone users in the mobile frame compared to the dualphone users in the landline frame. The overall weight effect for the first quarter of 2012 was 1.93 and the coefficient of variation of the weights was 0.96. The weight effects for 2012 were similar to, and in many cases less than, the effects found in the corresponding quarter of the 2011 NSWPHS when only a landline based sample was used.
Conclusions
The inclusion of mobile phone numbers, through an overlapping dualframe design, improved the coverage of the survey and an appropriate weighing procedure is feasible, although it added substantially to the complexity of the weighting strategy. Access to accurate Australian, State and Territory estimates of the number of landline and mobile phone numbers and type of phone use by at least age group and sex would greatly assist in the weighting of dualframe surveys in Australia.
Background
Since 2002 information about the health of the New South Wales (NSW) population has been obtained using the NSW Population Health Survey (NSWPHS) [1]. This survey is a continuous sample survey of approximately 15,000 persons each year. The survey is stratified by health administration area and equal numbers are selected from each of the strata, using random digit dialing (RDD) of landline phone numbers and computer assisted telephone interviewing (CATI) with one person from the selected household being randomly selected.
Because of the potential for noncoverage bias from the growing number of mobileonly phone users in the population, estimated to be 19% in Australia in 2011 [2], mobile phone numbers were included in 2012 using an overlapping dualframe design. Coverage bias is the product of the proportion of the population not covered and the difference in the mean of the variable of interest between the covered group and the noncovered group [3]. Evidence from the National Health Interview Survey (NHIS) in the US has shown the mobileonly phone users substantial different for the health indicators: five or more drinks in one day at least once in the past year (17.5% v 30.5%  74% higher), current smokers (14.5% v 24.3%  68% higher), and ever diagnosed with diabetes (10.8% v 6.2%  43% lower) [4].
The landline phone sample procedures were the same as in previous years. The mobile phone sample procedures were as follows; NSW residents were selected using RDD of mobile phone numbers using CATI and the mobile phone owner was selected. If the respondent had one or more children one child was also selected at random in order to ensure that children of people who did not have a landline were also included. Further details about the methodology, call outcomes and representation of the sample in the first quarter of 2012 are provided in Barr et al. [5], and the questions in the questionnaire are available from the survey website [1]. In the overlapping dualframe design there are three types of phone use; mobileonly, landlineonly and dualphone userspeople with a mobile phone and living in a household with a landline phone—who could now be selected though either the landline or mobile phone number sampling frames.
In the previous landline based samples for the NSWPHS, equal sample sizes were used in each stratum, even though the populations differed substantially and therefore the probability of selection varied by stratum. Moreover, as one person was randomly selected from each selected household, the probability of selection also varied by household size. Weights were calculated for use in survey estimation to account for the differences in probabilities of selection and then benchmarked to the latest NSW population by age group, sex and stratum as shown in Steel [6] and summarised in Appendix A. The use of equal probabilities to select landline phones in each stratum meant that the factor $\frac{{T}_{h}}{{t}_{h}}$, which is the ratio of phone numbers T_{ h } in stratum h to the number of phone numbers in the sample t_{ h }, cancelled in the previous calculation of the weights, and so the actual number of landline phone numbers in each of the strata did not need to be known. However, with the inclusion of the mobile phone frame this is not the case and the number of landlines and mobile phone numbers in the population for each stratum needed to be estimated. In 2011 the Australian Communication and Media Authority (ACMA) estimated that there were 29.28 million mobile phone numbers and 10.54 million landline phone numbers in Australia [2]. Estimates, however, are not routinely provided by State, let alone by health administration area.
As the previous NSWPHS samples came from a single frame the weighting did not need to account for the differing chances of selection by type of phone use. However, with the inclusion of the mobile phone numbers, using an overlapping dualframe design, dualphone users now have an increased chance of selection because they could be selected from either frame. There is currently a growing body of knowledge on issues and methods to deal with overlapping frames as summarised in the American Association for Public Opinion Research (AAPOR): Cell Phone Task Force Report [7], and in particular the use of composite weights to adjust for the increased chance of selection of dualphone users. However the most recent detailed description of dual frame weighting available in Australia from the Dualframe Omnibus Survey conducted in 2012 did not need to deal with disproportionate stratification of the landline frame, data needing to be collected about children as well as adults, and how to apply an overlap adjustment [8].
Hartley 1962 and 1974 [9, 10] first described the calculation of these composite weights in overlapping frames. We use the notation of A for landline frame, B for the mobile frame, Y for the population total of interest, y for the estimator, a for landline only component, b for mobile only component and ab for dual phone users component. In this case the composite estimator is defined as y_{ comp } = y_{ a } + y_{ b } + y_{ λ } where the estimate for the overlap population is ${y}_{\lambda}={y}_{\mathit{ab}}^{A}+\left(1\lambda \right){y}_{\mathit{ab}}^{B}$ with ${y}_{\mathit{ab}}^{A}$ and ${y}_{\mathit{ab}}^{B}$ being the estimators for persons with both mobile and landlines from frame A and B respectively and the composite factor being between 0 and 1 (0 < λ <1). Most overlapping dual frame surveys conducted to date have used a constant composite factor λ and the most common value is 0.5 [11–13]. So with overlapping dualframes design surveys being relatively new in Australia [5, 8, 14, 15] the use of λ = 0.5 as the compositing factor was considered appropriate.
Calculation of weights, in an overlapping dualframe design, ideally requires type of phone use benchmarks as well as population benchmarks [7]. In the USA type of phone use benchmarks, at the national level, are collected using the NHIS [16], where questions on residential phone use have been included since 1963 and mobile phone use since 2003.
Currently there is no equivalent source of information on type of phone use in Australia, although landline phone use from the Australian Health Survey (AHS) conducted by the Australian Bureau of Statistics (ABS), are expected to be available in 2014 [17]. However, landline and mobile phone use questions have been included in the Roy Morgan Single Source Survey (RMSSS) since 2005 [18] for ACMA communication reporting. It was estimated in the 2010–11 report that as at June 2011, 74% of adults in Australia lived in a household with a landline and a mobile phone, 5% lived in a household with a landline but no mobile phone, and 19% lived in a household with only a mobile phone; with the highest mobileonly phone rates being in young adults (37% in 18 to 24 year olds) [2].
Because weights are used to eliminate bias that would arise from ignoring the differences in selection probabilities and also to improve estimates by adjusting to known population benchmarks, when a design change occurs it is also important to assess how the design effect changes due to weighting, using weighting effects. The design effect is the factor by which the sampling variances are larger (or smaller) than those associated with a simple random sample and no weighting [3].
This paper describes and details the final weighting strategy adopted to properly combine the data from the two overlapping sample frames in the NSWPHS and the benchmark populations used, based on the limited information available in Australia. We then compare the weight effects for the overlapping dualframe sampling design to the previous landline frame sampling design.
Methods
Within a stratum the landline sample was selected using equal probability of selection of landline phone numbers and then random selection of one person from the selected household. In the mobile phone sample an equal probability sample of mobile phone numbers in Australia was selected and screened for adult residents in NSW. If the respondent has one or more children one child was selected at random.
Final weighting strategy
For the sampling design used person selection probabilities for the landline frame and mobile frame were derived as follows:

person ijh from the landline frame ${\pi}_{\mathit{ijh}}^{A}=\frac{{t}_{h}^{A}}{{T}_{h}^{A}}\frac{{T}_{\mathit{jh}}^{A}}{{N}_{\mathit{jh}}}$

adult i from the mobile frame ${\pi}_{i}^{B}=\frac{{t}^{B}}{{T}^{B}}\frac{{T}_{i}^{B}}{{N}_{i}}$

child c from parent p from the mobile frame ${\pi}_{\mathit{cj}}^{B}={\pi}_{p}^{B}\frac{{N}_{\mathit{cp}}}{{N}_{\mathit{cj}}}$
Where: i denotes an eligible person; c denotes a child of an eligible person; p denotes a parent; h denotes the stratum; j denotes a household; N denotes population size; T denotes number of phone numbers in the population; t denotes number of phone numbers in the sample; A denotes landline frame; B denotes mobile frame. For the design used N_{ i } = 1 and N_{ cp } is the number of parents that a child selected through a parent in the mobile phone frame has and N_{ cj } is the number of children in the household of the parent. The weights were then the inverse w = π^{− 1} in each situation.
The sample weights of the dual phoneusers were then adjusted using the composite factor λ set at 0.5. So for those dual phoneusers selected from:

the landline frame the composite weights were ${w}_{\mathit{ijh}}^{\lambda}=\lambda {w}_{\mathit{ijh}}^{A}$

the mobile frame the composite weights were ${w}_{i}^{\lambda}=\left(1\lambda \right){w}_{i}^{B}$
Benchmarking to the reference population was then performed, as per previous years, by adjusting the weights obtained from the combined landline and mobile phone sample, by age and sex to the ABS midyear population estimates for each stratum, N_{ dh }[19]. This was achieved by summing the weights for the age and sex cell d in stratum h, to produce a survey estimate of the population in that cell, ${\widehat{N}}_{\mathit{dh}}$ and then multiplying the weights by $\frac{{N}_{\mathit{dh}}}{{\widehat{N}}_{\mathit{dh}}}$.
Estimation of number of phone numbers in NSW by frame
The weights described above require the number of landline telephones in stratum h, ${T}_{h}^{A}$, and the number of mobile phone numbers in NSW, ${T}_{\mathit{NSW}}^{B}$. As there was no specific NSW residential landline phone data ${T}_{h}^{A}$ available we divided the number of residential landline phone numbers in Australia, using the ACMA estimate [2], by the proportion of the population in that stratum, using the ABS estimates [19], after having first adjusted it by the percentage of the population who had landline phones in that stratum, using the RMSSS estimates [18]. As there was no specific NSW mobile phone data ${T}_{\mathit{NSW}}^{B}$ available we divided the number of mobile phone numbers in Australia, using the ACMA estimate [2], by the proportion of the population in NSW, using the ABS estimates [19], having first adjusted it by the percentage of the population in NSW who had mobile phones, using the RMSSS estimates [18].
Where ${\widehat{P}}_{h}^{A}$ denotes the estimated proportion of people living in a household with a landline phone in stratum h and ${\widehat{P}}_{\mathit{NSW}}^{B}$ is the estimated proportion of people in NSW with a mobile phone.
Number of phone numbers by frame for NSW
Health administration area (stratum for landline frame)  Landline frame  Mobile frame  

% stratum with landline  Estimated number of lines  % stratum with landline  Estimated number of lines  
Sydney  74.0%  254015  
South Western Sydney  79.0%  406768  
South Eastern Sydney  76.0%  381287  
Illawarra Shoalhaven  82.0%  194868  
Western Sydney  79.0%  385908  
Nepean Blue Mountains  84.0%  177441  
Northern Sydney  86.0%  431456  
Central Coast  82.0%  162390  
Hunter New England  84.0%  443603  
Northern NSW  85.0%  157109  
Mid North Coast  81.0%  106940  
Southern NSW  82.0%  97434  
Murrumbidgee (inc Albury LGA)  82.8%  153043  
Western NSW  80.0%  137306  
Far West  90.0%  23764  
TOTAL  80.8%  3,513,333  85.8%  9,385,073 
Results
Data from the NSWPHS for the first quarter of 2012 was used to test the weighting strategy. This consisted of data on 3395 respondents with 2171 (64%) from the landline frame, with 17.6% being landlineonly, and 1224 (36%) from the mobile frame, with 25.8% being mobileonly.
Core weighting variables
Data needed to be available for all core weighting variables including age, sex, stratum, number of landline phones, number of mobile phones they personally have, and eligible persons in the household. If the respondent refused to provide their age or sex the interview was terminated. For the landline frame imputation was used for number of persons in household (1 if missing and 10 if greater than 10), number of landlines phones in household (1 if 0 or missing and 5 if greater than 5), number of personal mobile phones (substitute with 0 if missing and to 5 if greater than 5). For the mobile frame imputation was used for number of children in household (1 if missing and 6 if greater than 6), number of landlines in household (substitute with 0 if missing and to 5 if greater than 5) and number of personal mobile phones (substitute with 1 if 0 or missing and to 5 if greater than 5). If values could not be imputed for missing and/or erroneous core weighting variables then the record was removed from the dataset.
Data needed to be imputed, using these rules for 29 respondents for number of landline phones in the household (10 from landline frame and 19 from the mobile frame) and 26 respondents for number of personal mobile phones (15 from the landline frame and 11 from the mobile frame). The majority of respondents (97%) recruited through the landline frame were, using postcode/suburb and/or local government area provided by the respondent during the interview, in the same stratum as initially allocated, with the majority of the mismatches being within the metropolitan health administration areas (55/72; 76%) where phone numbers are more transportable. All of the respondents recruited through the mobile frame, except for 17, could be allocated to a stratum using postcode/suburb and/or local government area provided by the respondent during the interview. This resulted in 3378 respondents, 2933 adults and 445 children, for which weights could be calculated.
Calculation of the weights
Summary of the person selection probability, composite and benchmark weight statistics for each of the frames
Group  Phone type  Description  Formula  Sum  Ave  Median  Min  Max 

Landline Frame (n = 2171)  
Adult and children (n = 2171)  All types (n = 2171)  Interviews divided by universe of phone numbers  $\frac{{t}_{h}^{A}}{{T}_{h}^{A}}$  2.68  0.0012  0.0007  0.00017  0.0041 
Lines in household divided by eligible persons in household  $\frac{{T}_{\mathit{jh}}^{A}}{{N}_{\mathit{jh}}}$  1216.69  0.5699  0.50000  0.11111  3.0000  
Person selection probability $\left({\pi}_{\mathit{ijh}}^{A}\right)$  $\frac{{t}_{{}_{h}}^{A}}{{T}_{h}^{A}}\frac{{T}_{\mathit{jh}}^{A}}{{N}_{\mathit{jh}}}$  1.59  0.0007  0.0003  0.00003  0.0082  
Selection weight $\left({w}_{\mathit{ijh}}^{A}\right)$  $\frac{1}{{\pi}_{\mathit{ijh}}^{A}}$  8939582  4113.94  2864.6  121.31  35214.76  
Landline only (n = 383)  Selection weight $\left({w}_{\mathit{ijh}}^{A}\right)$  $\frac{1}{{\pi}_{\mathit{ijh}}^{A}}$  1074321  2805.02  1725.43  121.31  29345.64  
Both (n = 1788)  Selection weight $\left({w}_{\mathit{ijh}}^{A}\right)$  $\frac{1}{{\pi}_{\mathit{ijh}}^{A}}$  78765261  4394.00  2911.00  169.30  35214.76  
Composite weight $\left({w}_{\mathit{ijh}}^{\lambda}\right)$ (where λ = 0.5)  $\lambda {w}_{\mathit{ijh}}^{A}$  3932630  2197.00  1455.50  84.65  17607.38  
Mobile Frame (n = 1207)  
Adults (n = 1069)  All types (n = 1069)  Interviews divided by universe of phone numbers  $\frac{{t}^{B}}{{T}_{B}}$  0.14  0.0001  0.0001  0.00013  0.0001 
Mobile phones for person divided by eligible persons (where N_{ i } = 1)  $\frac{{T}_{i}^{B}}{{N}_{i}}$  1168.00  1.0947  1.00000  1.00000  5.0000  
Person selection probability $\left({\pi}_{i}^{B}\right)$  $\frac{{t}^{B}}{{T}^{B}}\frac{{T}_{i}^{B}}{{N}_{i}}$  0.15  0.0001  0.00013  0.00013  0.0007  
Selection weight $\left({w}_{i}^{B}\right)$  $\frac{1}{{\pi}_{i}^{B}}$  7819874  7328.84  7655.04  1531.01  7655.04  
Mobile only (n = 284)  Selection weight $\left({w}_{i}^{B}\right)$  $\frac{1}{{\pi}_{i}^{B}}$  2071325  7319.17  7655.04  1913.76  7655.04  
Both (n = 785)  Selection weight $\left({w}_{{i}^{B}}\right)$  $\frac{1}{{\pi}_{i}^{B}}$  5748549  7332.33  7655.04  1531.01  7655.04  
Composite weight $\left({w}_{i}^{\lambda}\right)$  $\left(1\lambda \right){w}_{i}^{B}$  2874274  3666.17  3827.52  765.50  3827.52  
Children (n = 138)  All types (n = 138)  Parents probability of selection  ${\pi}_{p}^{B}$  0.02  0.0001  0.0001  0.00013  0.0003 
Number of parents divided by eligible children in household  $\frac{{N}_{\mathit{cp}}}{{N}_{\mathit{cj}}}$  177.57  1.2867  1.00000  0.33333  2.0000  
Person selection probability $\left({\pi}_{\mathit{cp}}^{B}\right)$  ${\pi}_{p}^{B}\frac{{N}_{\mathit{cp}}}{{N}_{\mathit{cj}}}$  0.03  0.0002  0.0001  0.00004  0.0005  
Selection weight $\left({w}_{\mathit{cp}}^{B}\right)$  $\frac{1}{{\pi}_{\mathit{cp}}^{B}}$  964534  6989.38  7655.04  1913.76  22965.11  
Mobile only (n = 26)  Selection weight $\left({w}_{\mathit{cp}}^{B}\right)$  $\frac{1}{{\pi}_{\mathit{cp}}^{B}}$  158842  6109.31  3827.52  1913.76  15310.07  
Both (n = 112)  Selection weight $\left({w}_{\mathit{cp}}^{B}\right)$  $\frac{1}{{\pi}_{\mathit{cp}}^{B}}$  805692  7193.68  7655.04  1913.76  22965.11  
Composite weight $\left({w}_{\mathit{cp}}^{\lambda}\right)$  $\left(1\lambda \right){w}_{\mathit{cp}}^{B}$  402846  3596.84  3827.52  956.88  11482.55  
Both frames (n = 3378)  
Adults and children (n = 3378)  All types (n = 3378)  Selection weight (composite for both users) see note (a)  ${w}_{i}^{U}$  10514239  3112.56  2934.56  84.65  29345.64 
Selection weight (composite for both users) scaled back to the number of respondents  ${w}_{i}^{U*}$  3378  1.00000  0.8698  0.04779  10.999  
Post stratification weight (benchmarked to the population by age × sex × health admin) $\left({W}_{i}^{U}\right)$  $\frac{{N}_{\mathit{dh}}}{{\widehat{N}}_{\mathit{dh}}}{w}_{i}^{{U}^{*}}$  7272086  2152.78  1634.97  13.54  21807 
The weight effects were calculated using $\mathit{weff}=n\frac{{\displaystyle \sum {\mathit{w}}_{\mathit{i}}^{2}}}{({\displaystyle \sum {w}_{i}){}^{2}}}$ where: n denotes sample size and w denotes weights [20–22]. The weight effect is the design effect due to weighting and is equal to $1+{C}_{W}^{2}$, where C_{ W } is the coefficient of variation of the weights (i.e. the standard deviation of the weights divide by the mean of the weights) and is a standardised measure of the variation of the weights.
Weight effects by weighting parameters for quarter 1 of the 2012 and 2011 NSWPHS
Category  2012  2011  

n  SUM(WGT)2  (SUMWGT)  (SUMWGT)2  weff  C _{ w }  weff(n = 3377)  
Age Group  013 years  368  7297166859  1244521  1548832668784  1.73  0.86  1.58 
1424 years  317  5728404905  1066508  1137439271404  1.60  0.77  1.71  
2534 years  397  4372748462  1057202  1117675032746  1.55  0.74  1.73  
3544 years  346  4278905532  974108  948886376182  1.56  0.75  1.76  
4554 years  489  3262991785  995006  990036601734  1.61  0.78  1.91  
5564 years  624  2097445465  852381  726553045256  1.80  0.90  1.93  
65 plus  837  3136171943  1082361  1171505485852  2.24  1.11  1.63  
Sex  Males  1429  16560322718  3600556  12964003293103  1.83  0.91  2.13 
Females  1949  13613512232  3671530  13480134523526  1.97  0.98  2.54  
Health admin area  Syd  303  1698048663  585360  342646633987  1.50  0.71  1.80 
SWS  314  4303110764  892880  797234926549  1.69  0.83  1.62  
SES  213  5079590457  843566  711603697584  1.52  0.72  1.81  
IS  173  1303216701  391278  153098535888  1.47  0.69  1.82  
WS  286  3618759102  846389  716374051549  1.44  0.67  1.65  
NBM  200  1062941408  347524  120772881923  1.76  0.87  1.86  
NS  303  3343021760  846173  716008052067  1.41  0.64  1.80  
CC  210  1022421509  320135  102486405420  2.09  1.05  2.16  
HNE  314  4347558425  885170  783525875790  1.74  0.86  1.74  
NNSW  140  1082404196  300456  90273555553  1.68  0.82  1.68  
MNC  336  451722818  216328  46797881462  3.24  1.50  1.93  
SNSW  240  462055826  205377  42179613548  2.63  1.28  2.31  
M  129  885322373  241598  58369453477  1.84  0.91  1.89  
WNSW  120  1025192088  268286  71977640717  1.71  0.84  2.29  
FW  97  18833284  30750  945569265  1.93  0.97  1.80  
Overall  3378  30173834950  7272086  52883238281997  1.93  0.96  2.37 
Discussion
The development of the weighting strategy, weighted for the person selection probabilities by frame, composite weights applied to dualphone users, and benchmarked to the NSW population, was more complex than it had been for the previous landline frame. It was however encouraging that the weight effects were similar to those found in the previous year, when only a landline based sample was used.
The need to estimate the number of phone numbers for NSW and by stratum from the Australia figures, used to calculate the differing probabilities of selection, highlighted the desirability to be able to access accurate information at least at the State and Territory level. This is reiterated in the AAOPR report [7] which has the following comment: “A particularly troublesome issue here is that there is a dearth of highly accurate population parameters to use in weighting cell phone samples of regional, state and local areas”.
Although the first estimates of landline phone use from the AHS conducted by the ABS are expected to be available in 2014 [13], there are currently no plans to collect mobile phone use in this national survey and so the landline phone use data will be of limited use as the majority of phone users in Australia are dualphone users [2, 5, 8, 14, 15].
Access to more accurate type of phone use benchmarks would have also allowed weighting by type of phone use. We considered using the type of phone use totals collected by RMSSS [18] to generate benchmark populations by age group, sex, stratum and type of phone use. However, after conducting a sensitivity analysis we concluded that potential errors in the type of phone use estimates provided by age group, sex and stratum, which were well below the design level of the survey, were likely to impact on the NSWPHS health indicator estimates.
The compositing factor λ used for the composite weights was set at 0.5. However the use of 0.5 as the composite factor assumes that all sampled units respond. Skinner (1991) and Skinner and Rao (1996) have explored ways to reduce nonresponse bias by raking the estimates to type of phone use totals from an independent source [23, 24]. However, when Brick (2006) applied these to the Current Population Survey (CPS) he found that none of the suggested estimation schemes substantially reduced the nonresponse bias of the estimate [25]. It is possible to determine a value of this factor that minimises the sampling variance of the estimator, but this value will be variable specific. The AAOPR Cell Phone Task Force Report [7], acknowledges that variance estimation for dual frame sample designs is somewhat more complex than for single frame designs. This issue is considered by Lohr and Rao (2000) and summarised in Lohr (2009) [26, 27].
Moreover, it is likely that for various reasons, the estimates obtained for the overlapping component of the population, obtained from the two sampling frames do not have the same expectation, and using λ = 0.5 ensures that the two frames are given equal prominence in the estimation. Although further research needs to be undertaken to explore other estimation schemes using Australian data.
Conclusions
The inclusion of the mobile phone numbers through an overlapping dualframe design, improved the coverage of the survey and an appropriate weighing procedure is feasible, although it added substantially to the complexity of the weighting strategy. Access to accurate Australian, State and Territory estimates of the number of landline and mobile phone numbers and type of phone use by at least age group and sex would greatly assist in the weighting of dualframe surveys in Australia.
Appendix A
Previous landline weighting strategy
Calculation of the raw person weight that accounts for the different selection probabilities.
Adjust the weights to agree with externally derived population benchmarks, N_{ dh }.
This allowed the factor $\frac{{T}_{h}}{{t}_{h}}$ to cancel in the calculation of W_{ ijh }, so that if ${z}_{\mathit{jh}}=\frac{{N}_{\mathit{jh}}}{{T}_{\mathit{jh}}}$, then ${W}_{\mathit{ijh}}=\frac{{N}_{\mathit{ah}}}{{\displaystyle \sum _{\mathit{ijh}\in {s}_{\mathit{dh}}}{z}_{\mathit{jh}}}}{z}_{\mathit{jh}}$.
The weights are then summed to produce estimates of totals for any category and will agree with the external agesex benchmarks. That is $\sum _{\mathit{ijh}\in {s}_{\mathit{dh}}}{W}_{\mathit{ijh}}}={N}_{\mathit{dh}},\phantom{\rule{0.5em}{0ex}}{\displaystyle \sum _{\mathit{ijh}\in {s}_{h}}{W}_{\mathit{ijh}}}={N}_{h$ and $\sum _{\mathit{ijh}\in s}{W}_{\mathit{ijh}}}=N$
where
i denotes an eligible person
h denotes a strata j denotes eligible the household
d denotes an agesex cell
N denotes population size
n denotes sample size
T denotes number of phone lines in the population
t denotes number of phone lines in the sample
s denotes the sample
Authors’ information
MLB is a PhD student with the National Institute for Applied Statistics Research, University of Wollongong, Wollongong Australia.
Abbreviations
 AAPOR:

American Association for Public Opinion Researchers
 ABS:

Australian Bureau of Statistics
 ACMA:

Australian Communication and Media Authority
 AHS:

Australian Health Survey
 CATI:

Computer Assisted Telephone Interviewing
 NHIS:

National Health Interview Survey
 NSW:

New South Wales
 NSWPHS:

NSW Population Health Survey
 RDD:

Random Digit Dialing
 RMSSS:

Roy Morgan Single Source Survey.
Declarations
Acknowledgments
We acknowledge the interviewing staff and supervisors at the Centre for Epidemiology and Evidence, NSW Ministry of Health for collecting the data and providing their comments. We also acknowledge the respondents for participating in the survey.
Authors’ Affiliations
References
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