Data for: Intermittent preventive treatment of malaria during pregnancy- a generalized linear model with negative binomial distribution

Data for the study is a longitudinal count data obtained from the Sunyani Municipal Hospital in the Brong Ahafo Region, Ghana. The hospital serves approximately 150,000 residents. Count data generally are numbers of events per interval. Mathematically, counts are non-negative integers, since an event cannot happen an incomplete or a negative number of times and essentially, there is no upper boundary to a count, because there can theoretically be close to an infinite number of events taking place. The longitudinal data set comprises vital maternal variables of interest such as antenatal clinic registration of pregnant women, IPTp uptake, age of pregnant women, family planning, number of visits at the clinic, number of pregnancies and births by pregnant women, distance from their homes to the hospital, male partner attendance at clinic were recorded over the period of nine years (from December, 2008 to January, 2017). These events were recorded on a monthly basis. The Negative Binomial method which is an extension of the Generalized Linear Models was used in analyzing the longitudinal data set. This method was chosen because the counts or values recorded for the IPT dosage (IPTp 1 through to IPTp 5) were over-dispersed (i.e. variance is greater than the mean). The distribution of Negative Binomial Model for the over-dispersed count data is expressed as; Pr⁡(Y=y│λ,α)=(Γ(y+α^(-1)))/(y!Γ(α^(-1))) (α^(-1)/(α^(-1)+λ))^(α^(-1) ) (λ/(α^(-1)+λ))^y (1) Where: 𝜆 is the mean or the expected value of the distribution, 𝛼 is the over-dispersion parameter. The Negative Binomial Model (log transformed) for the study is therefore; log⁡〖IPT_i=β_0+β_1 ANC_REG 〗+ β_2 M_ANC+β_3 ANC_V1+β_4 ANC_V2+β_5 ANC_V4+β_6 B_(〖15〗_19 )+β_7 B_(〖20〗_24 )+β_8 B_(〖25〗_29 )+β_9 B_(〖30〗_34 )+β_10 B_35+β_11 M_PARA+β_12 P_ARA (2) For i=1,2,…,5. Where, IPT_i = Intermittent Preventive Treatment 1 through to 5 ANCREG = antenatal clinic registration of pregnant women MANC = male involvement at antenatal clinic B_15_19 = pregnant women of ages 15 to 19 who received IPTp B_20_24 = pregnant women of ages 20 to 24 who received IPTp B_25_29 = pregnant women of ages 25 to 29 who received IPTp B_30_34 = pregnant women of ages 30 to 34 who received IPTp B_35 = pregnant women of age ≥35 years who received IPTp ANC_V1 = one visit to the antenatal clinics by pregnant women ANC_V2 = two visits to the antenatal clinics by pregnant women ANC_V4 = four visits to the antenatal clinics by pregnant women M_PARA = four and greater number of births P_PARA = first birth of a woman.

本研究所用数据为取自加纳布朗阿哈福地区苏尼亚尼市政医院的纵向计数数据。该医院服务人口约15万。计数数据一般指单位时段内的事件发生次数。从数学层面而言，计数为非负整数——事件发生次数不可能为不完全次数或负数，且计数本质上无上限，理论上事件发生次数可趋近于无穷多。
本次纵向数据集涵盖了关键的孕产妇相关变量，包括孕妇产前门诊（Antenatal Clinic, ANC）登记情况、间歇性预防性妊娠治疗（Intermittent Preventive Treatment in Pregnancy, IPTp）依从情况、孕妇年龄、计划生育情况、门诊就诊次数、孕妇妊娠与分娩次数、住宅至医院的距离，以及男性伴侣陪同就诊情况，数据采集周期为9年（2008年12月至2017年1月），且以月度为单位记录。
本研究采用广义线性模型（Generalized Linear Models, GLM）的延伸方法——负二项回归法对该纵向数据集进行分析。之所以选择该方法，是因为IPTp剂量（IPTp 1至IPTp 5）的计数数据存在过度离散现象（即方差大于均值）。针对过度离散计数数据的负二项分布模型表达式如下：
$$Pr(Y=y|lambda,alpha)=frac{Gamma(y+alpha^{-1})}{y!Gamma(alpha^{-1})}left(frac{alpha^{-1}}{alpha^{-1}+lambda}
ight)^{alpha^{-1}}left(frac{lambda}{alpha^{-1}+lambda}
ight)^y ag{1}$$
其中，$lambda$为分布的均值或期望值，$alpha$为过度离散参数。
本研究所用的对数转换负二项模型如下：
$$logleft(IPT_i
ight)=eta_0+eta_1 ANC\_REG + eta_2 M\_ANC+eta_3 ANC\_V1+eta_4 ANC\_V2+eta_5 ANC\_V4+eta_6 B_{15\_19}+eta_7 B_{20\_24}+eta_8 B_{25\_29}+eta_9 B_{30\_34}+eta_{10} B_{35}+eta_{11} M\_PARA+eta_{12} P\_ARA ag{2}$$
其中$i=1,2,dots,5$，各变量含义如下：
$IPT_i$：第1至第5次间歇性预防性妊娠治疗
$ANC\_REG$：孕妇产前门诊登记情况
$M\_ANC$：男性参与产前门诊检查情况
$B_{15\_19}$：接受IPTp治疗的15~19岁孕妇群体
$B_{20\_24}$：接受IPTp治疗的20~24岁孕妇群体
$B_{25\_29}$：接受IPTp治疗的25~29岁孕妇群体
$B_{30\_34}$：接受IPTp治疗的30~34岁孕妇群体
$B_{35}$：接受IPTp治疗的35岁及以上孕妇群体
$ANC\_V1$：孕妇前往产前门诊就诊1次
$ANC\_V2$：孕妇前往产前门诊就诊2次
$ANC\_V4$：孕妇前往产前门诊就诊4次
$M\_PARA$：分娩次数≥4次的产妇
$P\_ARA$：产妇的首次分娩（注：原文此处模型变量为$P\_ARA$，与文末标注的$P\_PARA$存在笔误不一致，保留原文变量名）