1. Introduction

Under-five mortality refers to the death of infants and children under the age of five. It is estimated that the number of children under the age five dying globally has dropped remarkably from 12.6 million in 1990 to 6.6 million in 2012 [1]. Despite this reduction it is argued that the world is unlikely to achieve the Millennium Development Goal (MDG) 4 which targets a two-third reduction of the 1990 mortalities by 2015 [1].

In Ghana, statistics indicates that under-five mortality rate is on the decrease; 118.1, 99.1 and 74.4 per 1000 live birth for the years 1990, 2000, and 2010 respectively [2]. Moreover, a recent study in the Kassena Nankana district of the country shown that under-five mortality rate has declined [3]. However, under-five deaths are increasingly concentrated in sub-Saharan Africa and South Asia despite the marked decline in under-five mortality globally [4].

Efficient interventions can be made to further reduce under-five mortality globally if the potential determinants are well researched. To improve child survival in developing countries, Mosley and Chen [5] provided analytical framework based on the premise that all social and economic determinants of child mortality operate through a common set of biological mechanisms, or proximate determinants to exert an impact on mortality. Furthermore, in order to study the determinants of under-five mortality in Nigeria, research was carried out to identify the maternal, child, family and other risk factors associated with under-five mortality [6]. Infant mortality has been found to be higher in mothers with secondary education compared to uneducated mothers in the Ondo state of Nigeria [7]. Findings of a recent study based on the South African Demographic and Health Survey data revealed that the duration of breastfeeding, marital status and ownership of flush toilet are key predictors of under-five mortality [8]. In addition, high parity has been found to be associated with under-five mortality [9]. Sonneveldt et al. [10] explained that this association is partly due to low coverage of key health interventions among children born to mothers of high parity. One study done in the Builsa district of Ghana revealed that children of mothers with previous child deaths are about 8 times more likely to die (OR 7.45), while those who had not had vitamin A supplementation were about 10 times more likely to die (OR 9.57) [11]. It is also known that short birth intervals (less than or equal to 18 months), high parity (6 or more children), low maternal age (less than 20 years) and high maternal age (35 and more years) adversely impact infant and child mortality [12].

However, other risk factors including exclusive breastfeeding (OR 0.72), use of insecticide-treated bed-net (OR 0.12), the number of live children a mother had (OR 0.54) and immunization (OR 0.53) have been identified as protective factors of under-five mortality in the Builsa district of Ghana [11]. In the Chokwe district of Gaza province, Mozambique, a child survival program which covered 80% of bed net use, 94% of oral rehydration therapy for children with diarrhoea and prompt care-seeking from trained providers for children with danger signs was implemented and this resulted to 66% reduction in infant mortality and 62% reduction in under-five mortality [13]. Research has shown that health seeking behaviour, breastfeeding children for > 18 months, use of contraception, small family size, having one wife, low birth order, normal birth weight, child spacing, living in urban areas, and good sanitation reduces the odds of under-five mortality in Nigeria [6]. Similarly, higher national incomes are known to be associated with lower under-five mortality [14].

The study of the causal relationship between under-five mortality and potential risk factors has extensively been considered within the framework of statistical modeling. The logit regression model provides a mathematical framework that allows for functional relationship between a dichotomous response and one or more predictor variables. Within the context of the background of this paper, under-five mortality with the categories Yes or No represents the response variable and the risk factors denote the predictor variables. The aim of this study is to use the logit model to determine the key predictors of under-five mortality in the Tano South district of Ghana.

2. Materials and Methods

2.1. Study Setting

This study was carried out in the Tano South district of the Brong Ahafo region in Ghana to study the factors associated with under-five mortality in the area. The study was restricted to mothers. The district was divided into four zones and the target populations were identified using the purposive sampling. A total sample size of 200 mothers aged 15 years or older was used, of which 50 was selected randomly from each zone. Questionnaires were designed to obtain data from mothers. The study variables; including environmental factors such as parity of mother, use of treated bed-net, and clinical factors, specifically diseases in children, child vaccination and breastfeeding as well as information about under-five mortality status of mothers were captured in the questionnaires.

Data gathered was organized in the SPSS software package and the logit regression model was implemented to study the predictors of under-five mortality. In this framework the factors such as parity of mother, use of treated bed-net, diseases, child vaccination and breastfeeding were used as predictor variables. Under-five mortality which was measured on a dichotomous scale (Yes or No) was used as the response variable.

2.2. The Logit Model

The Logit regression model is appropriate when the response variable is categorical with two possible outcomes known as dichotomous or binary outcomes. We define a dichotomous variable as

The dichotomous variable, was binary valued, taking on values 0 or 1, and modeled using the binomial distribution

with probabilities

and denoting success and failure respectively. The logit which is the ratio of the probability of success to the probability of failure of the binomial random variables were found as

(1)

The logit regression model was built by expressing the logit in Equation 1 as a function of several predictor variables. This model is given by

where:

is the intercept and are the regression coefficients associated with the predictor variables

The measure of effect was obtained by the odds ratio denoted (OR) which is defined as the ratio of the odds for to the odds for and is given by the equation

Moreover, a p-value less than 0.05 indicate that the coefficient, is significant at 5% level in predicting the response variable. The measure of variance in data explained by the model is based on the pseudo-R square. Specifically, the Cox and Snell pseudo-R square which is given by Equation 2 was used

(2)

For a normal generalized linear model this formula has a maximum of one, but for logit regression its maximum is 0.75 or lower. A correction to the Cox and Snell pseudo-R square known as the Nagelkerke pseudo-R square given in Equation 3 was also used. It adjusts Equation 2 to range between zero and one. The corrected formula is

(3)

3. Results

To facilitate the progress of this study, the age of mothers was grouped into three categories as found in table 1.

Table 1. Frequency Distribution of Mothers stratified by Age Age (years) Frequency Percentage 15-24 45 22.5 25-34 88 44.0 35+ 67 33.5 Total 200 100.0

Of the 200 mothers used in the study, 22.5%, 44.0% and 33.5% were aged 15-24, 25-34 and 35+ respectively.

Table 2 below shows the descriptive statistics of the environmental and clinical factors of mothers. The table gives the responses on the environmental and clinical factors in relation to under-five mortality.

Table 2. Descriptive Statistics of Environmental and Clinical Factors Explanatory Variables Categories (Coding) Response Variable:Under-five Mortality Yes (1) No (0) Parity Primigravidae (0) 9 (8.8%) 25 (25.5%) Multigravidae (1) 27 (26.5%) 58 (59.2%) Grandmultigravidae (2) 66 (64.7%) 15 (15.3%) Treated Bed-net use No (0) 78 (79.6%) 46 (45.1%) Yes (1) 20 (20.4%) 56 (54.9%) Disease Diarrhoea (0) 2 (2.0%) 7 (7.1%) Anaemia (1) 32 (31.3%) 13 (13.3%) Malnutrition (2) 6 (5.9%) 10 (10.2%) Malaria (3) 59 (57.8%) 61 (62.2%) Pneumonia (4) 3 (2.9%) 7 (7.1%) Use of child vaccine No (0) 67 (68.4%) 61 (59.8%) Yes (1) 31 (31.6%) 41 (40.2%) Breast feeding None (0) 37 (48.1%) 29 (23.6%) Exclusive (1) 17 (22.1%) 46 (37.4%) Not-exclusive (2) 23 (29.9%) 48 (39.0%)

From Table 2, under-five mortality was common among mothers of grandmultigravida parity (64.7%). Among those of multigravida parity 26.5% experienced under-five mortality and fewer among those of primigravida parity (8.8%). Mothers who practiced exclusive breast feeding experienced fewer cases of under-five mortality (22.1%) than those who practiced not exclusive breast feeding (29.9%). The mothers who did not practice any of these had more cases (48.1%), compared to those who practiced exclusive and not exclusive breastfeeding.

Moreover, under-five mortality was fewer among mothers who vaccinated their children (31.6%), than does who did not (68.4%). The respective cases of under-five mortality for children who sleep under treated bed-net and those who do not are 20.4% and 79.6%. Malaria alone accounted for 57.8% of under-five mortality, compared to diarrhoea (2.0%), anaemia (31.3%), malnutrition (5.9%) and pneumonia (2.9%).

Table 3 shows results of omnibus test for logit regression model fitted for the environmental and clinical factors of mothers associated with under-five mortality. The table provides a test for the hypothesis stated below:

Hypothesis for Logit Model Coefficients

H₀: Information about the environmental and clinical factors do not allow for better prediction of under-five mortality.

H_A: Information about the environmental and clinical factors allow for better prediction of under-five mortality.

Table 3. Omnibus Tests of the Logit Model for Under-five Mortality Chi-square d.f P-value Step 77.968 43 0.001 Block 77.968 43 0.001 Model 77.968 43 0.001

From Table 3, the Chi-square value and its corresponding p-value are 77.968 and 0.001 respectively for the entire Omnibus test criterion. These results suggest that the entire tests are statistically significant at 5% level, therefore leading to the rejection of the null hypothesis. This brings out the implication that the information about the environmental and clinical factors allow for better prediction of under-five mortality within context of the logit model.

In Table 4, the estimated coefficients, standard errors, odds ratio and p-values of the logit regression model for the environmental and clinical factors related to under-five mortality are presented.

Table 4. Logit Regression Model for Factors associated with under-five Mortality Variables Estimate Std. Error Odds Ratio P-Value Intercept 2.714 1.183 15.089 0.307 Parity Primigravidae 0.000 0.000 1.000 Multigravidae 0.511 1.017 1.667 0.435 Grandmultigravidae 0.808 0.798 2.243 0.037 Treated bed net use No 0.000 0.000 1.000 Yes -2.587 0.500 0.075 0.000 Diseases Diarrhoea 0.000 0.000 1.000 Anaemia 2.491 1.281 12.073 0.042 Malnutrition 2.168 1.340 8.741 0.093 Malaria 2.500 1.381 12.182 0.039 Pneumonia 1.912 1.384 6.767 0.378 Use of child vaccine No 0.000 0.000 1.000 Yes -0.580 0.241 0.560 0.001 Breast feeding None 0.000 0.000 1.000 Exclusive -4.022 1.917 0.018 0.036 Not-exclusive -3.699 1.769 0.025 0.037

The intercept of 3.714 with odds ratio of 41.018 is not significant (p-value=0.307) at 5% level. For the parity factor only high parity, specifically grandmultigravida with estimated coefficient of 0.808 and corresponding p-value of 0.037 is significantly associated with under-five mortality. The OR of grandmultigravida parity is 2.243. This suggests that mothers of grandmultigravida parity are 2.243 times more likely to experience under-five mortality compared to those of primigravida parity.

Furthermore, treated bed-net use is significantly associated with under-five mortality (coefficient=-2.587; p-value=0.000) with estimated OR of 0.075. The value of the OR gives an indication that under-five mortality is less likely to occur in mothers who uses treated bed-nets in their homes for their children, compared to those who do not use it. Whilst malnutrition (p-value=0.093) and pneumonia (p-value=0.378) with respective OR of 8.741 and 6.767 are not significant, anaemia (p-value=0.042) and malaria (p-value=0.039) are significantly associated with under-five mortality. Compare to diarrhoea, under-five mortality caused by malaria and anaemia are 12.182 and 12.073 times more likely. The use of child vaccine showed significant (p-value=0.000) negative association with under-five mortality with estimated odds ratio of 0.560. This depicts that under-five mortality is less likely to occur in mothers who vaccinate their children, compared to those who do not.

Similarly, both exclusive (p-value=0.036) and not-exclusive (p-value=0.037) breastfeeding showed significant negative association with under-five mortality with respective odds ratio of 0.018 and 0.025. From the odds ratios it is evident that under-five mortality are less likely among mothers who practice exclusive and not-exclusive breastfeeding compared to those who do not breastfeed their children.

These findings clearly depicts that the key predictors of under-five mortality in the Tano South district are grand multigravida parity, treated bed-net use, anaemia, malaria, use of child vaccine, exclusive and not-exclusive breast feeding. Using these predictors, the fitted logit regression model for under-five mortality is

Where

UFM- Under-five mortality

GMP- grandmultigravida parity

TBN- treated bed net

ANA- anaemia

MAL- malaria

UCV- use of child vaccine

EBF- exclusive breastfeeding

NEBF- not exclusive breastfeeding

Table 5 shows the result of multiple coefficient of determination of the logit regression model. Specifically, this is given by the Cox and Snell Pseudo R square, and Nagelkerke R Pseudo Square.

Table 5. Pseudo R Square of the Logit Regression Model for Under-five Mortality Statistic Value Proportion of Total Variance Cox and Snell R Square 0.423 0.75 Nagelkerke R Square 0.531 1.00

From Table 5 the Cox and Snell pseudo R square is 0.423 out of 0.75 for total variance explained. Moreover, Nagelkerke pseudo R square is 0.531 out of 1.00 for total explained variability in data. These imply that the proportion of the total variance in the study data explained by the fitted model is larger than the proportion which is unexplained. In conclusion, these findings depict that the fitted model is consistent with the data used in this research.

From the logit model, the estimated odds of under-five mortality among mothers of grandmultigravida parity (GMP=2), controlling the effect of other factors in the model is

Therefore, from the odds the estimated probability is

In addition, controlling the effect of other factors, the estimated odds of under-five mortality among mothers who uses treated bed nets (TBN=1) is

with estimated probability of

Similarly, the estimated odds of under-five mortality among mothers with children infected with anaemia (ANA=1), controlling the effect of other factors in the model is

The probability is given by

3.1. Discussions

The frequency of under-five mortality recorded globally has dropped from 12.6 million in 1990 to 6.6 million in 2012 [1]. Yet, this reduction in under-five mortality is still not sufficient to reach the Millennium Development Goal (MDG) target of a two-thirds reduction of 1990 mortality levels by the year 2015 [1]. This has resulted to a growing interest in understanding the underlying determinants or predictors of under-five mortality in recent studies [6, 8, 9, 11, 14].

This study investigated the determinants of under-five mortality in the Tano South district of Ghana. It was found that low parity, specifically primigravida and multigravida are not significantly associated with under-five mortality. However, this study and that by Bicego [12] and Kozuki et al. [9] consistently showed that high parity is significantly associated with increased odds of under-five mortality. This association has been partly ascribed to low coverage of key health interventions among children born to mothers of high parity [10].

Secondly, the results suggest that anaemia, malnutrition, malaria and pneumonia adversely affect under-five mortality. However, only the effect of anaemia and malaria are statistically significant. The estimated effect of malaria (OR=12.182) and anaemia (OR=12.073) on under-five mortality are comparable, but malaria appears to be the most important risk factor that increases the likelihood of under-five mortality. To the best of our knowledge, there are no studies that researched the association of under-five mortality and diseases, therefore making it impossible to compare these finding with literature.

Moreover, we found that the likelihood of under-five mortality among mothers with children who sleep in treated bed-nets (OR=0.075) was lower than those who did not sleep in treated bed-nets (OR=1.00). Under-five mortality is less likely among mothers who vaccinated their children, compared to those who did not. Similarly, a lower likelihood of under-five mortality was observed in mothers who practiced exclusive and not-exclusive breastfeeding, compared to those who did not practice any of these. These findings are similar to those of one research conducted in Nigeria [6]. However, they are consistent with the study done in the Builsa district of Ghana [11] and may give partial explanation to the decreasing pattern of under-five mortality observed in the country [2, 3].

4. Conclusions

The underlying predictors of under-five mortality are well researched in a probabilistic context if we make an assumption that not all mothers have ever experienced this phenomenon. The present study accommodated with this assumption by choosing a logit model with probability of responses under the binomial distribution for studying the predictors of under-five mortality in the Tano South district of Ghana. This study revealed that grandmultigravida parity, malaria and anaemia are associated with increased likelihood of under-five mortality. Moreover, treated bed-net use, use of child vaccine, exclusive and not-exclusive breast feeding are associated with lower odds of under-five mortality. The evidence of increased likelihood for under-five mortality associated with the grandmultigravida parity, malaria and anaemia highlights the need to tailor interventions to address these factors in the district. Moreover, we recommend that the residents of the district will be more aware of the possible benefits of using treated bed-net, child vaccine, and practicing either exclusive or not-exclusive breast feeding. Research is still needed concerning the key predictors of under-five mortality. Future studies should especially focus on interactions between the risk factors and also capture the frequency of under-five mortality a mother has ever experienced in the framework of statistical modeling. In recognizing the full complexity of under-five mortality we might improve our ability to predict needs and achieve better interventions to further control the burdens of under-five mortality in modern societies.