ABSTRACT

 

The aim of this project is to examine the trend at which patients attends the hospital over the period of study. The study therefore, shows the usefulness of statistics to medicine and hence advice had always been sought by medical and health administrators from the Department of Statistics on the analysis and interpretation of medical data. The work is presented in five chapters. The first chapter being the introduction, the second chapter is the review of related literature where views of various writers on the topic concerned were analyzed. Chapter three is the research methodology, it examine the various research methods and procedure used in the data collection, it also highlight the techniques for data collections, where the historical and survey research method were adopted, all the data collected were presented and analysed in chapter four. Finally, chapter five summaries the whole research work, conclusion were drawn from the study and suggestion / recommendation on how to improve health care delivery to the people.

 

 

TABLE OF CONTENTS

Title Page

Approval Page

Declaration

Dedication

Acknowledgement

Abstract

Table Contents

 

CHAPTER ONE

1.1    Introduction

1.2    Aims of Objective

1.3    Scope and Limitation

1.4    Historical Background of Source of Data

 

CHAPTER TWO

2.1    Literature Review

2.2    Statistical Tools

2.3    Definition of Basic Concept

 

CHAPTER THREE

3.1    Methodology

3.2    Method of Data Collection

3.3    Data Presentation

 

CHAPTER FOUR

4.0    Computation and Data Analysis

 

CHAPTER FIVE

5.1    Conclusion

5.2    Summary

5.3    Recommendation

Reference

 

 

CHAPTER ONE

1.1    INTRODUCTION

Hajia Gambo Sawaba General Hospital since its inception in 1975 has received considerable amount of people, for treatment medical advice, family planning and a host of other reason. Different categories of people have patronized the hospital for its efficiency.

 

It is therefore in the best interest of the researcher to use his or her knowledge of statistic application is the attendance of ill health (patients) attending the hospital. It does not and here the research as will look forward to classifying, arranging and recording the monthly, quarterly, annual, bi-annual attendance of patients in the hospital.

 

In an attempt to introduce efficient methods and routine towards comparing the total attendance of, in and out patient this in general comprises of male, female and children patient attending the hospital.

 

To crown it all, it shall be in form of data (secondary, primary data) depending on the set of people wishing to use it and purpose or criterion behind using the research, the data collected will be analysis organized, summarized and compiled. Since hospital patronage is consistent and continuous process, it will be an efficient data collection, centres and will promote statistical application and voluminous data i.e. moving average and time series analysis.

 

1.2    AIMS OF OBJECTIVE

1. To determine whether there is an increase or decrease in patients’ attendance.
2. To forecast the patient attendance by using linear trend method
3. To forecast for patient attendance using the fitted trend equation from 2008 to 2012

 

1.3    SCOPE AND LIMITATION

This research will limit it analysis on the comparison of the attendance of patient. (IN and OUT) based on secondary data collected from the hospital Hajiya Gambo Sawaba General Hospital Zaria from (1998 to 2007).

 

1.4    HISTORICAL BACKGROUND OF SOURCE OF DATA

The hospital was established and commissioned by His Excellency the Governor of Kano State Late Alaji Audu Bako in 1975. The hospital is directly under Kaduna State Ministry of Health.

 

VARIOUS DEPARTMENT OF THE HOSPITAL

The hospital consists of nine (9) departments. The various departments include:

Medical Department: The Medical Director is the overall boss of the hospital. He is only answerable to the Kaduna State Commissioner of Health. He is in charge of all medical cases.

 

Administration Department: Hospital secretary is the head of this department. He heads all the administrative staff of various departments of the hospital and all heads of department are under him and answerable them, as every head administered on his behalf.

 

Nursing Service Department: The nursing service department is in charge with central of nurses, their posting, their duty roster, their shifting training to other post basic courses.

 

Medical Record Department: This department deals with keeping record and collection of data.

 

Laboratory: Technologist works in the laboratory and for the operation of laboratories equipment.

 

Pharmacy Department: The pharmaceutical department is in charge with the supply of drugs, drugs custody, drug protection and storage etc.

 

Radiology Department: The radiology is in charge with x-ray e.g. chinstraps etc.

 

Ophthalmology Department: Ophthalmology department is in charge with all cases of eye, its treatment etc.

 

E.N.T Department: This department is in charge with all cases of ear.

 

CHAPTER TWO

2.1    LITERATURE REVIEW

Health is wealth. This is a popular slogan, which shows the link between health and economic wellbeing.

 

This was further exposed by Dr. HIRISHI NAKAJIMA director general WHO in World Health paper page 3, January to February 1999, when he stated that health goes hand in hand with economic and social development and that every man, woman and child should be in position to choose a healthy way of life. To do this, they must be adequately informed on health. The environment, water, food, good habit, and bad ones, he stated that health is our most precious possession, both individual and collectively, if they need for information on health statistics for research and planning on purpose as emphasized by Dr. Nakaima.

 

The above was also emphasized by Mr. Ukarine in the standard news papers of 3^rd March 1990 page 3 column 1 when he presented a paper titled the primary health in which he stated that if the goals of health for all by the year 2000 “through primary health care is to be achieved” which is free of charge.

 

Therefore, comprehensive medical information which must be planned, executed and monitored must be available in our health delivery systems. He mentions that in most public and primary health institution, record keeping is virtually non-existence. This has deprived the medical personal of adequate historical information about their patient problems for this reason he said “there is need for the involvement of more medical records offices to take charge of day to day administration of the records of primary, secondary and tertiary level of health care delivery system.

 

According to a final year student BUKOLA TAIWO 1998, wrote a report based on his research title “statistical analysis of patient in Ibrahim Sani Abacha Memorial Hospital 1994-1996. The project, which was aimed at comparing in the out patient attendance with that of another year.

 

The highest affected eye illness was observed in 1994 while the lowest in 1995. The same applied to general ophthalmologic in age specific rate. This fall of affected eye illness was due to hospital charges.

 

To study the growth areas of a population in a certain geographical areas of given period, we consider all the factors that affect growth of population. This factor could be either statistical, agree, but we tend to think that all the data produced by the government that relating to population is the most useful.

 

2.2    STATISTICAL TOOLS

Analysis of Time Series (Theoretical Concept)

In this chapter, the theoretical concept associated with time series shall be discussed and derived formula in interpreting the data collected.

2.3    DEFINITION OF BASIC CONCEPT

A time series could simply be defined as a series of value assumed by a variable at different point in time. It can also be seen as set of observation taken at specific time, usually at equal intervals. A good example of time series is a fire in factory delaying prevaluation, the cinema admission, the hourly temperature announced by weather bureau of a city and the total monthly sales in department store.

 

Mathematically, a time series is defined by a value y, y, y – – – – – of a variable Y (temperature, closing price of a share etc) at time t, t, t, – – – – – – thus Y is a function of t, symbolized by Y = F (t).

 

COMPONENT OF TIME SERIES

The component of time series is often called characteristics movement of time series and may be classified in four main types:

1. Long-term or secular movements
2. Cyclical movements
3. Seasonal movements
4. Irregular or random movements

 

1. Long Term or Secular Movements

This refers to the general path or direction in which the graph of a time series appears to be going over a long interval of time. In the below graph this secular movement or as it sometimes called secular variation or secular trend, is indicated by a trend curve, shown below, for some time series a trend time may be appropriate.

 

Fig. 1.1: A graph showing a trend time

 

 

 

 

 

 

Long-Term Trend

2. Cyclical Movement

This in other word refers to as a cyclical variation which refers to the log-term oscillation or swings about a trend line or curve. This cycles as they are sometime equal intervals of time. In business and economic activity, movements are considered cyclical only if they recur after time intervals of more than on year.

 

A good example of cyclical movement is the business cycle, representing intervals of prosperity, recession, depression and recovery.

 

Fig. 1.2: A graph showing cyclical movement

 

 

 

 

 

3. Seasonal Movement

This refers to the identical or almost identical, pattern which time series appears to follow during corresponding months of successive years. Such movements are due to recurring events, which take place annually, as for instance the sudden increase of department store sales before Christmas.

 

Despite the fact that seasonal movement in general refers to annual periodicity in business or economic theory, the idea involved can also be extended to include periodicity over any interval of time such as daily, weekly, hourly etc depending on the type of data at hand.

 

Fig. 1.3: A graph showing cyclical and seasonal movement

 

 

 

 

 

 

4. Irregular or Random Movement

This refers to the sporadic motion of time series due to chance events such as flood, strikes, elections, etc. Although ti is ordinary assumed that such events produce variations lasting only a short time, it is conceivable that they may so intense as to result in new cyclical or other movement.

 

Estimation of the Component

Statistical estimation is concerned with using the data obtained from a random sample to obtain information about unknown population parameter.

 

There are two different types of estimation of population parameter, this include point estimate and interval estimate. A point estimate is an estimate of a population parameter given by a single value called a point estimate of the parameter may be considered to be called an interval estimate of the parameter. Interval estimate is preferable to point estimate because it indicate the precision or accuracy of an estimate.

 

1. Estimate of Trend

Estimation of trend can be achieve in several possible ways, this include:

1. The method of moving average
2. The method of least squares
3. Free hand method
4. Method of semi average

 

1. Method of Moving Average: By moving average of appropriate orders, cyclical, seasonal and irregular patterns, may be eliminated and thus leave only the trend movement. The procedure for applying the method of moving average is as follows:
2. List the series vertically
3. Compute the moving total and insert these at the mid-point of the relevant periods
4. Compute the moving averages
5. If there is an even number of seasons average the adjacent moving average to give contered average on each season
6. Computer (actual figure divided by central average) x 100. This gives the individual seasonal variations
7. Find the mean of individual seasonal variation for each season
8. Adjust these means so that the sum of all seasonal variation is 100 x number of season. The figure arrived after this adjustment is the final variation. If a set of T observation is arranged chronological as:

x₁, x₂, x₃ – – – – – – – x_t, x_{t + 1}, – – – – – – x_T

y₁ = y_n (x₁ + x₂) – – – + x_n)

y₂ = y_n (x₂ + x₃) – – – + x_n + x_{n + 1})

y₃ = y_n (x₃ + x₄ + x_n + x_{n + 1} + x_{n = 2})

And so on, these average are called n-point moving observations are involved.

They are very useful in studying trend in time series are disadvantages of this method is that data at the beginning and end of a series are lost.

 

Another disadvantage is that moving averages may generate cycles or other movements which were not present in the original data.

 

The third disadvantage is that moving averages are strongly affected by extreme values to overcome this somewhat a weighted moving average with appropriate weight is some time used. In such case the central item (or items) is given the largest weight and extreme volume are given small weights.

 

2. Method of Least Squares

In computing time series, least square method can be found, the equation of an appropriate trend line or trend curves from this equation we can compute the trend value of T easily.

 

The appropriate formula is given as y = x + B_xi + e_i where x and B are constant, x is the slope of the equation, B represent the intercept, x_i is the independent variable and finally e_i is classified as the error term. It will be more précised to estimate the errors committed in approximating a non-linear data to linear data since the aim is to fit a linear model in every data under study.

 

It will also be of interest to calculate x and B so as to fit the mode y = x + B_xi.

This estimation can be only conveniently done based on the following assumptions:

1. The variance of the error term is constent i.e. var (ei) = 0
2. The expectation of the error term is zero i.e. E (ei) = 0, i and j. Now using the equation y_i = x + B_xi + e_i we can estimate the value of x and B and this can only be done by minimizing the error terms in respect to x and B.

Y_i = x + B_xi + e_i

Making the errors term the subject of the formula implies that:

e_i = y_i – (x + B_xi)

Square both sides

e_i² = (y_i – (x + B_xi)²

Note: Let e_i² = S

Therefore S = (y_i – (x + B_xi)²

Differentiating with respect to x

ds/dx = -2 (y_i – (x + B_xi))

to minimize and we set ds/dx = 0

-2 (y_i – (x + B_xi)) = 0

Divide both side by -2

Y_i x – B_xi = 0

Take the sum of both sides

∑Y_i  – nx – B∑ x_i = 0 – – – – – – – – – – – – (1)

Again, S = (y_i – (x + B_xi))²

Differentiating with respect to B

ds/d_B = -2 _xi (y_i – (x + B_xi))

set ds/d_B = 0

-2_xi (y_i – (x + B_xi)) = 0

-2 (y_i x_i – xx_i + B_xi²) = 0

Divide both side by (-2) and take sum

∑x_iy  – x∑x_i – B∑x_i² = 0 – – – – – – – – – – – – (2)

Multiply equation (1) by ∑x­i

∑x_i ∑y_i  – nx∑x_i – B (∑x_i)² = 0 – – – – – – – – (3)

Multiply equation (2) by n, we have

n∑x_i y_i  – nx∑y_i – nB ∑x_i² = 0 – – – – – – – – (4)

Equation (4) – equation (3)

n∑x_i y_i  – nx∑x_i – nB∑x_i² – ∑x_i ∑y_i  – nx∑x_i – B (∑x_i)²

n∑x_i y_i  – ∑x_i ∑y_i = B(n∑x_i² – (∑x_i)²)

n∑x_i y_i  – ∑x_i ∑y_i

B = – – – – – – – – – – – – – –

n∑x_i²  – (∑x_i²)

and x = y – Bx

Where y = ∑yi / n and x = ∑xi/n

The parameters “x” is the average value of y and x = 0 while “B” is the amount by which the dependent variable changes as a result of a unit change in the independent variable.

3. Method of Semi Moving Averages

It involves the separation of data into two parts (preferably equal) and averaging the data in each part, thus obtaining two points on the graph of the time series. A trend line can be determined directly a graph.

 

Although, this method is easy to apply, it may lead to poor result when used indiscriminately. Also, it is applicable only where the trend is linear or approximately linear, although it can be extended to the case where the data can be broken up into several parts in each of which the trend is linear.

 

Estimation of Seasonal Variations

In determining the seasonal factors in time series, we must estimate how the data in the time series vary from month throughout a typical year. Various methods listed below are available in computing a seasonal index as it is sometime called.

1. The average percentage method
2. The percentage trend or ratio to trend method
3. Percentage moving average or ratio moving average method
4. The link relative method

 

1. Estimation of cyclical variation

Under this method, the data involved is first depersonalized, they can also be adjusted for trend by simply dividing the data by corresponding trend value. According to the equation of multiplication model i.e. y = T x c x s x I = TCSI, the process of adjusting for seasoning variation and trend, corresponds to division of y by ST. which gives CI, i.e. cyclical and irregular variation. An approximate moving average of a few months duration serves to smooth out irregular variation and leave only the cyclical variations.

 

 

1. Estimation of Irregular or Random Variation

Estimation of irregular variation can be achieved by adjusting data for trend, seasonal and cyclical variation. This amounts to division of original data y by T, S and C which by multiplication equation yield 1.

 

In practice, it is found that irregular movement tend to be of small magnitude and that they often follow the pattern of a normal distribution i.e. small deviation occur with large frequency, large deviation occur with small frequency.

 

Deseasonalization of Data

If the original data are divided by the corresponding seasonal index numbers, the resulting data are said to be depersonalized or adjusted for seasonal variation, such data still include trend cyclical and irregular movements.

 

Forecasting

The ideas presented about the estimation of the components can be used to aid in the unimportant problem of forecasting time series. However, it must be realized that mathematical treatment of data does not in itself solve all problems coupled with the common sense, experience, ingenuity and good judgment of an investigation, such mathematical analysis can nevertheless be of value both for language and short range forecasting.

 

Types of Models in Time Series

Basically, there are two different models in approaching problem. Time series, these include, additive and multiplicative model. This two types of analysis mentioned above when applying original data y, it is often referred to as decomposition of time series.

 

The multiplicative models is when the data y = T x C x S x I = TCSI.

Variation S = is the seasonal variation, I = is the irregular variation.

This equation can be expressed in different ways, depending on the variation under study or interest.

The additive model is when the data are in arithmetic progression i.e. they are very close. And it is similar in nature, in that the multiplication sign is replaced with addition signs e.g. Y = t + C + S= I